BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Theo Raedschelders (VUB (Brussels))
DTSTART:20200420T120000Z
DTEND:20200420T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/1
DESCRIPTION:Title: Proper connective differential graded algebras and th
eir geometric realizations\nby Theo Raedschelders (VUB (Brussels)) as
part of Paris algebra seminar\n\nLecture held in Zoom.\n\nAbstract\nA dg a
lgebra A admits a geometric realization if the category of perfect dg A-mo
dules can be embedded into the bounded derived category of a smooth projec
tive variety. In this talk\, I will first give an overview of Orlov's resu
lts on geometric realizations of dg algebras\, and then explain how all dg
algebras with finite dimensional cohomology\, which are moreover concentr
ated in non-positive degrees\, admit such realizations. The proof is based
on a generalization of the Auslander algebra of a finite dimensional alge
bra to the setting of finite-dimensional A-infinity algebras. If time allo
ws\, I will discuss several corollaries related to finite-dimensional mode
ls\, noncommutative motives\, and non-Fourier-Mukai functors. This is base
d on joint work with Alice Rizzardo\, Greg Stevenson\, and Michel Van den
Bergh.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Orsay)
DTSTART:20200427T120000Z
DTEND:20200427T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/2
DESCRIPTION:Title: Associahedra and the Grothendieck group of an extrian
gulated structure on the cluster category\nby Pierre-Guy Plamondon (Or
say) as part of Paris algebra seminar\n\nLecture held in Zoom.\n\nAbstract
\nThe associahedron is a polytope that encodes Catalan families. One of it
s many avatars is as a polytopal realization of the g-vector fan of a clus
ter algebra of type A. Given a cluster algebra with fixed initial seed\,
the space of all polytopal realizations of its g-vector fan has been of in
terest to physicists\, appearing for instance in the work of Arkani-Hamed\
, Bai\, He and Yan.\n\nIn this talk\, we will see how a description of the
set of all polytopal realizations of the g-vector fan of any cluster alge
bra of finite type with any initial seed can be described by looking for a
minimal set of relations between its g-vectors. To find such a set\, we
will see how a sub-extriangulated structure of the triangulated structure
of the cluster category allows for a categorification of g-vectors\, and f
ind all relations in its Grothendieck group.\n\nThis is a report on a join
t work with Arnau Padrol\, Yann Palu and Vincent Pilaud.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Cuntz (Hannover)
DTSTART:20200504T120000Z
DTEND:20200504T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/3
DESCRIPTION:Title: Frieze patterns with coefficients\nby Michael Cun
tz (Hannover) as part of Paris algebra seminar\n\nLecture held in Zoom.\n\
nAbstract\nFriezes with coefficients are maps assigning numbers to the edg
es and diagonals of a regular polygon such that all Ptolemy relations for
crossing diagonals are satisfied. These are relevant for example for the s
tudy of cluster algebras\, in a special case they may also be viewed as ro
ot systems of certain quantum groups. \nIn this talk I will report on rece
nt results on subpolygons of friezes. Depending on the domain of the entri
es of the friezes\, these subpolygons satisfy interesting arithmetic obstr
uctions.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (覃㠶) (Shanghai Jiao Tong)
DTSTART:20200518T120000Z
DTEND:20200518T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/4
DESCRIPTION:Title: Dual canonical bases and quantum cluster algebras
\nby Fan Qin (覃㠶) (Shanghai Jiao Tong) as part of Paris algebra semina
r\n\nLecture held in Zoom.\n\nAbstract\nFomin and Zelevinsky invented clus
ter algebras\, which are algebras with distinguished generators called clu
ster variables. For any symmetrizable Kac-Moody algebra and Weyl group ele
ment\, the corresponding quantum unipotent subgroup possesses the dual can
onical basis\, and it can be viewed as a (quantum) cluster algebra. As a m
ain motivation by Fomin and Zelevinsky\, it has been long conjectured that
the quantum cluster monomials (certain monomials of cluster variables) be
long to the dual canonical basis up to scalar multiples. We sketch a proof
of this conjecture in full generality.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hironori Oya (Shibaura Inst. of Technology)
DTSTART:20200525T120000Z
DTEND:20200525T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/5
DESCRIPTION:Title: Newton-Okounkov polytopes of Schubert varieties arisi
ng from cluster structures and representation-theoretic polytopes\nby
Hironori Oya (Shibaura Inst. of Technology) as part of Paris algebra semi
nar\n\n\nAbstract\nThe theory of Newton-Okounkov bodies is a generalizatio
n of \nthat of Newton polytopes for toric varieties. One of the ingredient
s for \nthe definition of a Newton-Okounkov body is a valuation on the fun
ction \nfield of a given projective variety. In this talk\, we consider Ne
wton-\nOkounkov bodies of Schubert varieties defined from specific valuati
ons \nwhich generalize extended g-vectors in cluster theory. We show that
they \nprovide polytopes unimodularly equivalent to string polytopes and \
nNakashima-Zelevinsky polytopes\, both of which are well-known polytopes \
nin representation theory. Indeed\, this framework allows us to connect \n
string polytopes with Nakashima-Zelevinsky polytopes by tropicalized \nclu
ster mutations. \nThis talk is based on a joint work with Naoki Fujita.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrien Brochier (University of Paris)
DTSTART:20200511T120000Z
DTEND:20200511T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/6
DESCRIPTION:Title: On invertible braided tensor categories\nby Adrie
n Brochier (University of Paris) as part of Paris algebra seminar\n\n\nAbs
tract\nDualizability and invertibility are two natural properties one can
ask for objects in (possibly\nhigher) symmetric monoidal categories. On th
e one hand\, it recovers as special cases various\nimportant notions in ge
ometry and representation theory. On the other hand\, it connects those\nn
otions to topology via the cobordism hypothesis. I will explain various ex
amples of this philosophy\, with an emphasis on applications to finite bra
ided tensor categories. This is based on joint work with D. Jordan\, P. Sa
fronov and N. Snyder.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustavo Jasso (Bonn)
DTSTART:20200601T120000Z
DTEND:20200601T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/7
DESCRIPTION:Title: The symplectic geometry of higher Auslander algebras<
/a>\nby Gustavo Jasso (Bonn) as part of Paris algebra seminar\n\n\nAbstrac
t\nIt is well known that the partially wrapped Fukaya category of a marked
\ndisk is equivalent to the perfect derived category of a Dynkin quiver of
\ntype A. In this talk I will present a higher-dimensional generalisation\
nof this equivalence which reveals a connection between three a\npriori un
related subjects:\n\n* Floer theory of symmetric products of marked surfac
es
\n* Higher Auslander-Reiten theory in the sense of Iyama
\n* Wald
hausen K-theory of differential graded categories\n\nIf time permits\, as
a first application of the above relationship\, I\nwill outline a symplect
o-geometric proof of a recent result of Beckert\nconcerning the derived eq
uivalence between higher Auslander algebras of\ndifferent dimensions. This
is a report on joint work with Tobias\nDyckerhoff and Yankı Lekili.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Rognerud (University of Paris)
DTSTART:20200608T120000Z
DTEND:20200608T123000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/8
DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, I\
nby Baptiste Rognerud (University of Paris) as part of Paris algebra semin
ar\n\n\nAbstract\nQuasi-hereditary algebras were introduced by Cline\, Par
shall and Scott as a tool to study highest weight theories which arise in
the representation theories of semi-simple complex Lie algebras and reduct
ive groups. Surprisingly\, there are now many examples of such algebras\,
such as Schur algebras\, algebras of global dimension at most two\, incide
nce algebras and many more.\n\nA quasi-hereditary algebra is an Artin alge
bra together with a partial order on its set of isomorphism classes of sim
ple modules which satisfies certain conditions. In the early examples the
partial order predated (and motivated) the theory\, so the choice was clea
r. However\, there are instances of quasi-hereditary algebras where there
is no natural choice for the partial ordering and even if there is such a
natural choice\, one may wonder about all the possible orderings.\nIn this
talk we will explain that all these choices for an algebra $A$ can be org
anized in a finite partial order which is in relation with the tilting the
ory of $A$. In a second part of the talk we will focus on the case where $
A$ is the path algebra of a Dynkin quiver.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (Bielefeld)
DTSTART:20200608T123000Z
DTEND:20200608T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/9
DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, II
\nby Yuta Kimura (Bielefeld) as part of Paris algebra seminar\n\n\nAbstrac
t\nQuasi-hereditary algebras were introduced by Cline\, Parshall and Scott
as a tool to study highest weight theories which arise in the representat
ion theories of semi-simple complex Lie algebras and reductive groups. Sur
prisingly\, there are now many examples of such algebras\, such as Schur a
lgebras\, algebras of global dimension at most two\, incidence algebras an
d many more.\n\nA quasi-hereditary algebra is an Artin algebra together wi
th a partial order on its set of isomorphism classes of simple modules whi
ch satisfies certain conditions. In the early examples the partial order p
redated (and motivated) the theory\, so the choice was clear. However\, th
ere are instances of quasi-hereditary algebras where there is no natural c
hoice for the partial ordering and even if there is such a natural choice\
, one may wonder about all the possible orderings.\nIn this talk we will e
xplain that all these choices for an algebra $A$ can be organized in a fin
ite partial order which is in relation with the tilting theory of $A$. In
a second part of the talk we will focus on the case where $A$ is the path
algebra of a Dynkin quiver.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss (UNAM)
DTSTART:20200615T120000Z
DTEND:20200615T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/10
DESCRIPTION:Title: Generic bases for surface cluster algebras\nby C
hristof Geiss (UNAM) as part of Paris algebra seminar\n\n\nAbstract\nThis
is a report on joint work with D. Labardini-Fragoso and J. Schröer. We sh
ow that for most marked surfaces with non-empty boundary\, possibly with p
unctures\, the generic Caldero-Chapoton functions form a basis of the corr
esponding cluster algebras for any choice of geometric coefficients. For s
urfaces without punctures the $\\tau$-reduced components of the correspond
ing gentle Jacobian algebra are naturally parametrized by X-laminations of
the surface\, and it is easy to see that for principal coefficients\, the
generic basis coincides with the bangle basis introduced by Musiker-Schif
fler-Williams.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myungho Kim (Kyung Hee University\, Seoul)
DTSTART:20200622T120000Z
DTEND:20200622T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/11
DESCRIPTION:Title: Braid group action on the module category of quantum
affine algebras\nby Myungho Kim (Kyung Hee University\, Seoul) as par
t of Paris algebra seminar\n\n\nAbstract\nLet $g_0$ be a simple Lie algebr
a of type $ADE$ and let $U′_q(g)$ be the corresponding untwisted quantum
affine algebra. We found an action of the braid group $B(g_0)$ on the qua
ntum Grothendieck ring $K_t(g)$ of Hernandez-Leclerc's category $C^0_g$. I
n the case of $g_0=A_{N−1}$\, we construct a monoidal autofunctor $S_i$
for each integer $i$ on a category $T_N$ arising from the quiver Hecke al
gebra of type $A_\\infty$. \nSince there is an isomorphism between the Gro
thendieck ring $K(T_N)$ of $T_N$ and the quantum Grothendieck ring $K_t(A^
(1)_{N−1})$\, the functors $S_i$\, $(i=1\, ...\, N-1)$\, recover the act
ion of the braid group $B(A_{N−1})$. \nThis is a joint work with Masaki
Kashiwara\, Euiyong Park and Se-jin Oh.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Iyama (Nagoya)
DTSTART:20200713T120000Z
DTEND:20200713T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/13
DESCRIPTION:Title: Tilting theory of contracted preprojective algebras
and cDV singularities\nby Osamu Iyama (Nagoya) as part of Paris algebr
a seminar\n\n\nAbstract\nA preprojective algebra of non-Dynkin type has a
family of tilting modules associated with the elements in the correspondin
g Coxeter group W. This family is useful to study the representation theor
y of the preprojective algebra and also to categorify cluster algebras.\nI
n this talk\, I will discuss tilting theory of a contracted preprojective
algebra\, which is a subalgebra eAe of a preprojective algebra A given by
an idempotent e of A. It has a family of tilting modules associated with t
he chambers in the contracted Tits cone. They correspond bijectively with
certain double cosets in W modulo parabolic subgroups. \nI will apply thes
e results to classify a certain family of reflexive modules over a cDV sin
gularities R\, called maximal modifying (=MM) modules. We construct an inj
ective map from MM R-modules to tilting modules over a contracted preproje
ctive algebra of extended Dynkin type. This is bijective if R has at worst
an isolated singularity. We can recover previous results (Burban-I-Keller
-Reiten\, I-Wemyss) as a very special case.\nThis is joint work with Micha
el Wemyss.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linyuan Liu (刘琳媛) (Sydney)
DTSTART:20200629T120000Z
DTEND:20200629T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/14
DESCRIPTION:Title: Modular Brylinski-Kostant filtration of tilting modu
les\nby Linyuan Liu (刘琳媛) (Sydney) as part of Paris algebra semi
nar\n\n\nAbstract\nLet $G$ be a reductive algebraic group over a field $k$
. When $k=\\mathbb{C}$\, R. K. Brylinski constructed a filtration of weigh
t spaces of a $G$-module\, using the action of a principal nilpotent eleme
nt of the Lie algebra\, and proved that this filtration corresponds to Lus
ztig's $q$-analogue of the weight multiplicity. Later\, Ginzburg discovere
d that this filtration has an interesting geometric interpretation via the
geometric Satake correspondence. Recently\, we managed to generalise this
result to the case where $k$ is a field of good positive characteristics.
I will give a brief introduction to both historical results and our new r
esult in the talk.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fang (房欣) (Cologne)
DTSTART:20200706T120000Z
DTEND:20200706T123000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/15
DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\
, I\nby Xin Fang (房欣) (Cologne) as part of Paris algebra seminar\n
\n\nAbstract\nIn this talk\, we will explain relations between exact struc
tures on an additively finite additive category and degenerations of the a
ssociated Hall algebras. The first part of the talk will be devoted to the
main motivation provided by concrete examples of degenerations of negativ
e parts of quantum groups arising as Hall algebras of quiver representatio
ns. We will then turn to Lie theory in order to establish a link from thes
e examples to tropical flag varieties and certain quiver Grassmannians. In
the second part of the talk we will present results in the general case a
nd sketch their proofs based on Auslander-Reiten theory. If time permits\,
we will briefly discuss further conjectural examples and generalizations.
\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Stuttgart)
DTSTART:20200706T123000Z
DTEND:20200706T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/16
DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\
, II\nby Mikhail Gorsky (Stuttgart) as part of Paris algebra seminar\n
\n\nAbstract\nIn this talk\, we will explain relations between exact struc
tures on an additively finite additive category and degenerations of the a
ssociated Hall algebras. The first part of the talk will be devoted to the
main motivation provided by concrete examples of degenerations of negativ
e parts of quantum groups arising as Hall algebras of quiver representatio
ns. We will then turn to Lie theory in order to establish a link from thes
e examples to tropical flag varieties and certain quiver Grassmannians. In
the second part of the talk we will present results in the general case a
nd sketch their proofs based on Auslander-Reiten theory. If time permits\,
we will briefly discuss further conjectural examples and generalizations.
\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Prague)
DTSTART:20200914T120000Z
DTEND:20200914T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/17
DESCRIPTION:Title: The Cohen–Macaulay property in derived algebraic g
eometry\nby Liran Shaul (Prague) as part of Paris algebra seminar\n\n\
nAbstract\nIn this talk\, we explain how to extend the theory of Cohen-Mac
aulay\nrings to the setting of commutative non-positive DG-rings. By study
ing\nlocal cohomology in the DG-setting\, one obtains certain amplitude\ni
nequalities about certain DG-modules of finite injective dimension.\nWhen
these inequalities are equalities\, we arrive at the notion of a\nCohen-Ma
caulay DG-ring.\n\nWe then show that these arise naturally in many situati
ons\, and\nexplain their basic theory. We explain that any derived quotien
t of a \nCohen-Macaulay ring is Cohen-Macaulay\,\nand show that Cohen-Maca
ulayness is the generic local situation in\nderived algebraic geometry: un
der mild hypothesis\, every eventually\ncoconnective locally noetherian de
rived scheme is Cohen-Macaulay on a\ndense open set.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (Stuttgart)
DTSTART:20200928T120000Z
DTEND:20200928T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/18
DESCRIPTION:Title: $B_\\infty$-algebras and Keller’s conjecture for s
ingular Hochschild cohomology\nby Zhengfang Wang (Stuttgart) as part o
f Paris algebra seminar\n\n\nAbstract\nWe first give a basic introduction
to $B_\\infty$-algebras. Then from a $B_\\infty$-algebra A\, we contruct
two new $B_\\infty$-algebras by using two different swapping maps: the opp
osite $B_\\infty$-algebra and the transpose $B_\\infty$-algebra. Quite sur
prisingly\, we show that under a certain condition on A (satisfied\, for i
nstance\, by brace $B_\\infty$-algebras or Gerstenhaber-Voronov algebras)
these two $B_\\infty$-algebras are naturally isomorphic\, which is motivat
ed from Kontsevich-Soibelman's minimal operad. \n\nWe also explain the rol
e of the above result in the proof of Keller's conjecture for singular Hoc
hschild cohomology in the case of radical square zero algebras. This is jo
int work with Xiaowu Chen and Huanhuan Li.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Julia Redondo (Bahia Blanca)
DTSTART:20200921T120000Z
DTEND:20200921T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/19
DESCRIPTION:Title: $L_\\infty$-structure on Barzdell's complex for mono
mial algebras\nby Maria Julia Redondo (Bahia Blanca) as part of Paris
algebra seminar\n\n\nAbstract\nWhen dealing with a monomial algebra $A$\,
Bardzell’s complex $B(A)$ has shown to be more efficient for computing H
ochschild cohomology groups of $A$ than the Hochschild complex $C(A)$.\nSi
nce $C(A)[1]$ is a dg Lie algebra\, it is natural to ask if the comparison
morphisms between these complexes allows us to transfer the dg Lie struct
ure to $B(A)[1]$. This is true for radical square zero algebras\, but it
is not true in general for monomial algebras.\nIn this talk\, I will descr
ibe an explicit $L_\\infty$-structure on $B(A)$ that induces a weak equiva
lence of $L_\\infty$-algebras between $B(A)$ and $C(A)$. This allows us t
o describe the Maurer-Cartan equation in terms of elements of degree 2 in
$B(A)$ and make concrete computations when $A$ is a truncated monomial alg
ebra.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (UBC Vancouver)
DTSTART:20201005T120000Z
DTEND:20201005T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/20
DESCRIPTION:Title: Wall-crossing and differential equations\nby Dyl
an Allegretti (UBC Vancouver) as part of Paris algebra seminar\n\n\nAbstra
ct\nThe Kontsevich-Soibelman wall-crossing formula describes the wall-cros
sing behavior of BPS invariants in Donaldson-Thomas theory. It can be form
ulated as an identity between (possibly infinite) products of automorphism
s of a formal power series ring. In this talk\, I will explain how these s
ame products also appear in the exact WKB analysis of Schrödinger's equat
ion. In this context\, they describe the Stokes phenomenon for objects kno
wn as Voros symbols.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Fujita (Paris\, IMJ-PRG)
DTSTART:20201012T120000Z
DTEND:20201012T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/22
DESCRIPTION:Title: Twisted Auslander-Reiten quivers\, quantum Cartan ma
trix and representation theory of quantum affine algebras\nby Ryo Fuji
ta (Paris\, IMJ-PRG) as part of Paris algebra seminar\n\n\nAbstract\nFor a
complex simple Lie algebra $g$\, its quantum Cartan matrix plays an impor
tant role in the representation theory of the quantum affine algebra of $g
$. When $g$ is of type ADE\, Hernandez-Leclerc (2015) related its quantum
Cartan matrix with the representation theory of Dynkin quivers and hence w
ith the combinatorics of adapted words in the Weyl group of the correspond
ing ADE type. In this talk\, we introduce the notion of Q-data\, which can
be regarded as a combinatorial generalization of a Dynkin quiver with hei
ght function\, and its twisted Auslander-Reiten quiver. Using them\, we re
late the quantum Cartan matrix of type BCFG with the combinatorics of twis
ted adapted words in the Weyl group of the corresponding unfolded ADE type
introduced by Oh-Suh (2019). Also\, we see their relation to the represen
tation theory of quantum affine algebras. For example\, we present a (part
ially conjectural) unified expression of the denominators of R-matrices be
tween the Kirillov-Reshetikhin modules in terms of the quantum Cartan matr
ices. This is a joint work with Se-jin Oh.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norihiro Hanihara (Nagoya)
DTSTART:20201019T120000Z
DTEND:20201019T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/23
DESCRIPTION:Title: Cluster categories of formal dg algebras\nby Nor
ihiro Hanihara (Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nCl
uster categories are Calabi-Yau triangulated categories endowed with clust
er tilting objects. They have played an important role in the (additive) c
ategorification of cluster algebras. We study the version developed by Ami
ot-Guo-Keller\, which is defined in terms of CY dg algebras. Given a negat
ively graded (non-dg) CY algebra\, we view it as a dg algebra with trivial
differential. We give a description of the cluster category of such a for
mal dg algebra as the triangulated hull of an orbit category of a derived
category\, and also as the singularity category of a finite dimensional al
gebra. Furthermore\, if time permits\, we will talk about a certain conver
se of this construction\, giving a \nMorita-type theorem for CY triangulat
ed categories arising from hereditary algebras\, partially generalizing th
at of Keller-Reiten.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/23
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Launois (Kent)
DTSTART:20201109T130000Z
DTEND:20201109T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/24
DESCRIPTION:Title: Catenarity and Tauvel’s height formula for quantum
nilpotent algebras\nby Stéphane Launois (Kent) as part of Paris alge
bra seminar\n\n\nAbstract\nThis talk is based on joint work with Ken Goode
arl and Tom Lenagan. \nI will explain why quantum nilpotent algebras are
catenary\, that is\, why all saturated chains of inclusions of prime ideal
s in a quantum nilpotent algebra have the same length. As a corollary\, we
obtain that Tauvel’s height formula holds for quantum nilpotent algebra
s. Time permitting\, \nI will present a different strategy to prove the la
tter result.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/24
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wai-kit Yeung (Tokyo\, IPMU)
DTSTART:20201026T130000Z
DTEND:20201026T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/25
DESCRIPTION:Title: Pre-Calabi-Yau algebras\nby Wai-kit Yeung (Tokyo
\, IPMU) as part of Paris algebra seminar\n\n\nAbstract\nPre-Calabi-Yau ca
tegories are algebraic structures first studied by Kontsevich and Vlassopo
ulos. They can be viewed as a noncommutative analogue of Poisson structure
s\, just like Calabi-Yau structures can be viewed as a noncommutative anal
ogue of symplectic structures. In this talk\, we discuss several aspects o
f this notion.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/25
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleonore Faber (Leeds)
DTSTART:20201116T130000Z
DTEND:20201116T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/26
DESCRIPTION:Title: McKay quivers of complex reflection groups and the M
cKay correspondence\nby Eleonore Faber (Leeds) as part of Paris algebr
a seminar\n\n\nAbstract\nFinite complex reflection groups were classified
by Shepherd\nand Todd: up to finitely many exceptions they are the groups
G(r\,p\,n).\nIn this talk we give a combinatorial description of the McKay
quivers of\nthese groups. Further we will comment on a McKay corresponden
ce for\ncomplex reflection groups. This is joint work with R.-O. Buchweitz
\, C.\nIngalls\, and M. Lewis.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/26
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Scherotzke (Luxembourg)
DTSTART:20201123T130000Z
DTEND:20201123T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/27
DESCRIPTION:Title: Cotangent complexes of moduli spaces and Ginzburg dg
algebras\nby Sarah Scherotzke (Luxembourg) as part of Paris algebra s
eminar\n\n\nAbstract\nWe start by giving an introduction to the notion of
moduli stack of a dg category. Then we will explain what shifted symplecti
c structures are and how they are connected to Calabi-Yau structures on dg
categories. More concretely\, we will show that the cotangent complex of
the moduli stack of a dg category A is isomorphic to the moduli stack of t
he *Calabi-Yau completion* of A. This answers a conjecture of Keller-Yeung
. This is joint work with Damien Calaque and Tristan Bozec available on the arXiv.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/27
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elie Casbi (MPI Bonn)
DTSTART:20201102T130000Z
DTEND:20201102T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/28
DESCRIPTION:Title: Equivariant multiplicities of simply-laced type flag
minors\nby Elie Casbi (MPI Bonn) as part of Paris algebra seminar\n\n
\nAbstract\nThe study of remarkable bases of (quantum) coordinate rings ha
s been an area of\nintensive research since the early 90's. For instance\,
the multiplicative properties of \nthese bases (in particular the dual ca
nonical basis) was one of the main motivations for\nthe introduction of cl
uster algebras by Fomin and Zelevinsky around 2000. \nIn recent work\, Bau
mann-Kamnitzer-Knutson introduced an algebra morphism \n$\\overline{D}$ f
rom the coordinate algebra $\\mathbb{C}[N]$ of a maximal unipotent subgrou
p $N$\nto the function field of a maximal torus. It is related to the geom
etry of \nMirkovic-Vilonen cycles via the notion of equivariant multiplici
ty. This morphism \nturns out to be useful for comparing good bases of the
coordinate algebra \n$\\mathbb{C}[N]$. We will focus on comparing the va
lues taken by $\\overline{D}$ on several distinguished elements of the Mir
kovic-Vilonen basis and the dual canonical basis. For the latter one\,\nwe
will use Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster
\nstructure of the cluster structure of $\\mathbb{C}[N]$ via quiver Hecke
algebras as well as\nrecent results by Kashiwara-Kim. This will lead us to
an explicit description of\nthe images under $\\overline{D}$ of the flag
minors of $\\mathbb{C}[N]$ as well as remarkable\nidentities between them.
\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/28
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Bochum)
DTSTART:20201130T130000Z
DTEND:20201130T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/29
DESCRIPTION:Title: Wild quantum dilogarithm identities\nby Markus R
eineke (Bochum) as part of Paris algebra seminar\n\n\nAbstract\nWe formula
te and discuss "wild" analogues of the Fadeev-Kashaev identity for quantum
dilogarithms. We review a general quiver setup\nfor such identities\, res
ulting from wall-crossing formulas\, motivic Donaldson-Thomas invariants\,
and the geometry of quiver moduli spaces. The quantum dilogarithm identit
ies are then derived from special properties of representations of general
ized Kronecker quivers.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/29
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manon Defosseux (Université de Paris)
DTSTART:20210111T130000Z
DTEND:20210111T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/30
DESCRIPTION:Title: Brownian motion in the unit interval and the Littelm
ann path model\nby Manon Defosseux (Université de Paris) as part of P
aris algebra seminar\n\n\nAbstract\nWe will present for a Brownian motion
in the unit interval a Pitman type\ntheorem obtained recently in joint wor
k with Philippe Bougerol. We will focus\non algebraic aspects and will exp
lain how it is related to the Littelmann path\nmodel for an affine Kac–M
oody algebra of extended type $A_1$.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/30
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Estanislao Herscovich (Grenoble)
DTSTART:20210118T130000Z
DTEND:20210118T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/31
DESCRIPTION:Title: Double quasi-Poisson algebras are pre-Calabi-Yau
\nby Estanislao Herscovich (Grenoble) as part of Paris algebra seminar\n\n
\nAbstract\nDouble Poisson and double quasi-Poisson algebras were introduc
ed by M. Van den Bergh in his study of noncommutative quasi-Poisson geomet
ry. Namely\, they satisfy the so-called Kontsevich-Rosenberg principle\, s
ince the representation scheme of a double (quasi-)Poisson algebra has a n
atural (quasi-)Poisson structure. On the other hand\, N. Iyudu and M. Kont
sevich found a link between double Poisson algebras and pre-Calabi-Yau alg
ebras\, a notion introduced by Kontsevich and Y. Vlassopoulos. The aim of
this talk will be to explain how such a connection can be extended to doub
le quasi-Poisson algebras\, which thus give rise to pre-Calabi-Yau algebra
s. This pre-Calabi-Yau structure is however more involved in the case of d
ouble quasi-Poisson algebras since\, in particular\, we get an infinite nu
mber of nonvanishing higher multiplications for the associated pre-Calabi-
Yau algebra\, which involve the Bernoulli numbers. \n\nThis is joint work
with D. Fernández from the Universität Bielefeld.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/31
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Letellier (Université de Paris)
DTSTART:20201214T130000Z
DTEND:20201214T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/32
DESCRIPTION:Title: E-series of character varieties associated with non
orientable surfaces\nby Emmanuel Letellier (Université de Paris) as p
art of Paris algebra seminar\n\n\nAbstract\nIn this talk we will be intere
sted in two kinds of character varieties associated to a compact non-orien
table surface S. The first one is just the quotient stack of all represent
ations of the fundamental group of S in GL(n\,C). For the second one\, we
consider k punctures of S as well as k semisimple conjugacy classes of GL(
n\,C). We then consider the stack of anti-invariant local systems on the
orientation covering of S with local monodromies around the punctures in t
he prescribed conjugacy classes. We compute the number of points of these
spaces over finite fields and we give a cohomological interpretation of ou
r counting formulas. For the second kind of character varieties\, we give
a conjectural formula for the mixed Poincaré series in terms of Macdonald
symmetric functions.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/32
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruslan Maksimau (Montpellier)
DTSTART:20201207T130000Z
DTEND:20201207T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/33
DESCRIPTION:Title: KLR algebras for curves and semi-cuspidal representa
tions\nby Ruslan Maksimau (Montpellier) as part of Paris algebra semin
ar\n\n\nAbstract\nThe talk is based on the preprint arXiv:2010.01419. This
is joint work with Alexandre Minets.\n\nThe KLR algebras (also called qui
ver Hecke algebras) are known to have the following geometric construction
: they are isomorphic to the (equivariant) Borel-Moore homology of the Ste
inberg variety. A point of this variety is given by a representation of a
quiver and two full flags of subrepresentations.\n\nWe define and study an
alogues of KLR algebras for curves (curve Hecke algebras). We define these
algebras geometrically\, similarly to usual KLR algebras. But we replace
representations of a quiver by torsion sheaves on a smooth curve C. In par
ticular\, for C=P1\, we get a geometric realization of the affine zigzag a
lgebra of type A1. The case C=P1 is particularly interesting because it al
lows us to describe the imaginary semi-cuspidal category for the KLR algeb
ra for affine sl2.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/33
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Lebed (Caen)
DTSTART:20210125T130000Z
DTEND:20210125T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/34
DESCRIPTION:Title: Homotopical tools for computing rack homology\nb
y Victoria Lebed (Caen) as part of Paris algebra seminar\n\n\nAbstract\nRa
cks are certain algebraic structures yielding powerful tools for knot theo
ry\, Hopf algebra classification and other areas. Rack homology plays a cr
ucial role in these applications. The homology of a rack is very easy to d
efine (via an explicit chain complex)\, but extremely difficult to compute
. Until recently\, the full homology was known only for three families of
racks. Together with Markus Szymik\, we added a forth family to this list\
, the family of permutation racks. More importantly\, our work unexpectedl
y brought homotopical methods into the area\, and showed that in spite of
their abstract flavour they can yield concrete computations. The necessary
background on racks and their homology\, as well as an overview of the to
ols previously used for its computation\, will be given.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/34
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Yekutieli (Ben Gurion University)
DTSTART:20210301T130000Z
DTEND:20210301T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/35
DESCRIPTION:Title: Rigidity\, Residues and Duality: Overview and Recent
Progress\nby Amnon Yekutieli (Ben Gurion University) as part of Paris
algebra seminar\n\n\nAbstract\nIn this lecture\, we explain the theory of
rigid residue complexes in commutative algebra and algebraic geometry. Un
like all previous approaches to Grothendieck Duality\, the rigid approach
concentrates on rigid residue complexes over rings\, and their intricate y
et robust properties. Most of the lecture will about the results for rings
. The geometrization\, i.e. the passage to rigid residue complexes on sche
mes and Deligne-Mumford (DM) stacks\, by gluing\, is fairly easy. In the g
eometric part of the theory\, the main results are the Rigid Residue Theor
em and the Rigid Duality Theorem for proper maps between schemes\, and for
tame proper maps between DM stacks. These results will only be outlined b
riefly. \n\nMore details are available in the eprint with the same title a
t\nhttps://arxiv.org/abs/2102.00255\n\nThe lecture notes can be downloaded
from \nhttp://www.math.bgu.ac.il/~amyekut/lectures/RRD-2021/notes.pdf\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/35
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Tamaroff (Dublin)
DTSTART:20210201T130000Z
DTEND:20210201T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/36
DESCRIPTION:Title: Poincaré--Birkhoff--Witt theorems: homotopical and
effective computational methods for universal envelopes\nby Pedro Tama
roff (Dublin) as part of Paris algebra seminar\n\n\nAbstract\nIn joint wor
k with V. Dotsenko\, we developed a categorical framework for Poincaré-Bi
rkhoff-Witt type theorems about universal enveloping algebras of various a
lgebraic structures\, and used methods of term rewriting for operads to ob
tain new PBW theorems\, in particular answering an open question of J.-L.
Loday. Later\, in joint work with A. Khoroshkin\, we developed a formalism
to study Poincaré–Birkhoff–Witt type theorems for universal envelope
s of algebras over differential graded operads\, motivated by the problem
of computing the universal enveloping algebra functor on dg Lie algebras i
n the homotopy category. Our formalism allows us\, among other things\, to
obtain a homotopy invariant version of the classical Poincaré–Birkhoff
–Witt theorem for universal envelopes of Lie algebras\, and extend Quill
en's quasi-isomorphism C(g) ---> BU(g) to homotopy Lie algebras. I will su
rvey and explain the role homological algebra\, homotopical algebra\, and
effective computational methods play in the main results obtained with bot
h V. Dotsenko (1804.06485) and A. Khoroshikin (2003.06055) and\, if time a
llows\, explain a new direction in which these methods can be used to stud
y certain operads as universal envelopes of pre-Lie algebras.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/36
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Kus (Bochum)
DTSTART:20210315T130000Z
DTEND:20210315T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/37
DESCRIPTION:Title: Prime representations in the Hernandez-Leclerc categ
ory\nby Deniz Kus (Bochum) as part of Paris algebra seminar\n\n\nAbstr
act\nGenerators and relations of graded limits of certain finite dimension
al irreducible representations of quantum affine algebras have been determ
ined in recent years. For example\, the representations in the Hernandez-L
eclerc category corresponding to cluster variables appear to be certain tr
uncations of representations for current algebras and tensor products are
related to the notion of fusion products. In this talk we will discuss som
e known results on this topic and study the classical and graded character
s of prime representations in the HL category.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/37
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern)
DTSTART:20210215T130000Z
DTEND:20210215T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/38
DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen
Yakimov (Northeastern) as part of Paris algebra seminar\n\n\nAbstract\nWe
will describe a theory of root of unity quantum cluster algebras\, which
are not necessarily specializations of quantum cluster algebras. All such
algebras are shown to be polynomial identity (PI) algebras. Inside each of
them\, we construct a canonical central subalgebra which is proved to be
isomorphic to the underlying cluster algebra. (In turn\, this is used to s
how that two exchange graphs are canonically isomorphic). This setting gen
eralizes the De Concini-Kac-Procesi central subalgebras in big quantum gro
ups and presents a general framework for studying the representation theor
y of quantum algebras at roots of unity by means of cluster algebras as th
e relevant data becomes (PI algebra\, canonical central subalgebra)=(root
of unity quantum cluster algebra\, underlying cluster algebra). We also ob
tain a formula for the corresponding discriminant in this general setting
that can be applied in many concrete situations of interest\, such as the
discriminants of all root of unity quantum unipotent cells for symmetrizab
le Kac-Moody algebras\, defined integrally over Z[root of unity]. This is
a joint work with Bach Nguyen (Xavier Univ) and Kurt Trampel (Notre Dame U
niv).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/38
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sondre Kvamme (Uppsala)
DTSTART:20210208T130000Z
DTEND:20210208T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/39
DESCRIPTION:Title: Admissibly finitely presented functors for exact cat
egories\nby Sondre Kvamme (Uppsala) as part of Paris algebra seminar\n
\n\nAbstract\nIn this talk we introduce the category of admissibly finitel
y presented functors mod_{adm}(E) for an exact category E. In particular\
, we characterize exact categories of the form mod_{adm}(E)\, and show tha
t they have properties similar to module categories of Auslander algebras.
For a fixed idempotent complete category C\, we also use this constructio
n to show that exact structures on C correspond to certain resolving subca
tegories in mod(C). This is joint work with Ruben Henrard and Adam-Christi
aan van Roosmalen.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/39
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Fujita (University of Paris)
DTSTART:20210308T130000Z
DTEND:20210308T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/40
DESCRIPTION:Title: Isomorphisms among quantum Grothendieck rings and pr
opagation of positivity\nby Ryo Fujita (University of Paris) as part o
f Paris algebra seminar\n\n\nAbstract\nFor a complex simple Lie algebra $\
\mathfrak{g}$\, finite-dimensional representations of its quantum loop alg
ebra form an interesting monoidal abelian category\, which has been studie
d from various perspectives. Related to the fundamental problem of determi
ning the characters of irreducible representations\, we consider its quant
um Grothendieck ring\, a 1-parameter deformation of the usual Grothendieck
ring. When $\\mathfrak{g}$ is of simply-laced type\, Nakajima and Varagno
lo-Vasserot proved that it enjoys some positivity properties based on the
geometry of quiver varieties. In this talk\, we show that the same positiv
ities hold also for non-simply-laced type by establishing an isomorphism b
etween the quantum Grothendieck ring of non-simply-laced type and that of
''unfolded'' simply-laced type. In addition\, we find that an analog of Ka
zhdan-Lusztig conjecture holds for several new cases in non-simply-laced t
ype. This is a joint work with David Hernandez\, Se-jin Oh\, and Hironori
Oya.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/40
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander P. Veselov (Loughborough (UK) and Moscow (Russia))
DTSTART:20210322T130000Z
DTEND:20210322T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/42
DESCRIPTION:Title: Automorphic Lie algebras and modular forms\nby A
lexander P. Veselov (Loughborough (UK) and Moscow (Russia)) as part of Par
is algebra seminar\n\n\nAbstract\nThe automorphic Lie algebras can be view
ed as generalisations of twisted loop Lie algebras\, when a group $G$ acts
holomorphically and discretely on a Riemann surface and by automorphisms
on the chosen Lie algebra. \n \nIn the talk we will discuss the automorphi
c Lie algebras of modular type\, when $G$ is a finite index subgroup of th
e modular group $\\Gamma=SL(2\, \\mathbb Z)$ acting on the upper half pla
ne. In the case when the action of $G$ can be extended to $SL(2\,\\mathbb
C)$ we prove analogues of Kac’s isomorphism theorem for the twisted loop
Lie algebras.\nFor the modular group and some of its principal congruence
subgroups we provide an explicit description of such isomorphisms using t
he classical theory of modular forms.\n \nThe talk is based on the ongoing
joint work with Vincent Knibbeler and Sara Lombardo.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/42
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Ovsienko (Reims)
DTSTART:20210222T130000Z
DTEND:20210222T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/43
DESCRIPTION:Title: Combinatorial and analytic properties of q-deformed
real numbers\nby Valentin Ovsienko (Reims) as part of Paris algebra s
eminar\n\n\nAbstract\nI will explain a recent notion of \nq-deformed real
numbers\, and discuss its various combinatorial and analytic properties. A
"\nq-deformed real" is a Laurent series in one variable\, \nq\, with inte
ger coefficients. The subject is connected to different theories\, such as
knot invariants\, continued fractions\, and cluster algebras. I will form
ulate a challenging conjecture about the convergence of the series arising
as \nq-deformed real numbers. (Here we understand \nq as a complex variab
le.) The conjecture is proved in particular cases and concrete examples. I
n the most simple examples of q-Fibonacci and q-Pell numbers\, the explici
t formulas for the radius of convergence are very similar to certain formu
las of Ramanujan. \nThe talk is based on a joint work with Ludivine Lecler
e\, Sophie Morier-Genoud and Alexander Veselov.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/43
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksandr Tsymbaliuk (Purdue)
DTSTART:20210503T120000Z
DTEND:20210503T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/44
DESCRIPTION:Title: Quantum loop groups and shuffle algebras via Lyndon
words\nby Oleksandr Tsymbaliuk (Purdue) as part of Paris algebra semin
ar\n\n\nAbstract\nClassical q-shuffle algebras provide combinatorial model
s for the positive half U_q(n) of a finite quantum group. We define a loop
version of this construction\, yielding a combinatorial model for the pos
itive half U_q(Ln) of a quantum loop group. In particular\, we construct a
PBW basis of U_q(Ln) indexed by standard Lyndon words\, generalizing the
work of Lalonde-Ram\, Leclerc and Rosso in the U_q(n) case. We also connec
t this to Enriquez' degeneration A of the elliptic algebras of Feigin-Odes
skii\, proving a conjecture that describes the image of the embedding U_q(
Ln) ---> A in terms of pole and wheel conditions. Joint work with Andrei N
egut.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/44
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregg Musiker (Minnesota)
DTSTART:20210426T120000Z
DTEND:20210426T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/45
DESCRIPTION:Title: Combinatorial Expansion Formulas for Decorated Super
-Teichmüller Spaces\nby Gregg Musiker (Minnesota) as part of Paris al
gebra seminar\n\n\nAbstract\nMotivated by the definition of super Teichmul
ler spaces\, and Penner-Zeitlin's recent extension of this definition to d
ecorated super Teichmuller space\, as examples of super Riemann surfaces\,
we use the super Ptolemy relations to obtain formulas for super lambda-le
ngths associated to arcs in a bordered surface. In the special case of a d
isk\, we are able to give combinatorial expansion formulas for the super l
ambda-lengths associated to diagonals of a polygon in the spirit of Ralf S
chiffler's T-path formulas for type A cluster algebras. We further connect
our formulas to the super-friezes of Morier-Genoud\, Ovsienko\, and Tabac
hnikov\, and obtain partial progress towards defining super cluster algebr
as of type A. In particular\, following Penner-Zeitlin\, we are able to ge
t formulas (up to signs) for the mu-invariants associated to triangles in
a triangulated polygon\, and explain how these provide a step towards unde
rstanding odd variables of a super cluster algebra. This is joint work wi
th Nicholas Ovenhouse and Sylvester Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/45
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College Dublin)
DTSTART:20210329T120000Z
DTEND:20210329T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/47
DESCRIPTION:Title: Operadic approach to wall-crossing and attractor inv
ariants\nby Sergey Mozgovoy (Trinity College Dublin) as part of Paris
algebra seminar\n\n\nAbstract\nWall-crossing describes how various invaria
nts in algebraic geometry and theoretical physics transform under the vari
ation of parameters. In this talk I will discuss a framework\, reminiscent
of collections and plethysms in the theory of operads\, that concenptuali
zes those transformation rules. I will describe how some new and existing
wall-crossing formulas can be proved using this approach. In particular\,
I will discuss applications to attractor invariants (also called initial d
ata in the theory of scattering diagrams).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/47
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Darpoe (Nagoya)
DTSTART:20210412T120000Z
DTEND:20210412T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/48
DESCRIPTION:Title: Periodic trivial extension algebras and fractionally
Calabi–Yau algebras\nby Erik Darpoe (Nagoya) as part of Paris algeb
ra seminar\n\n\nAbstract\nAn important open problem in the homological alg
ebra of self-injective algebras is to characterise periodic algebras. An a
lgebra B is said to be periodic if if has a periodic projective resolution
as a B-B-bimodule.\n\nIn this talk\, I will present a solution to this pr
oblem for trivial extension algebras: the trivial extension algebra T(A) o
f a finite-dimensional algebra A is periodic if and only if A has finite g
lobal dimension and is fractionally Calabi-Yau.\n\nThis is based on joint
work with Chan\, Iyama and Marczinzik.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/48
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Baumann (Strasbourg)
DTSTART:20210510T120000Z
DTEND:20210510T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/49
DESCRIPTION:Title: Explicit calculations in the geometric Satake equiva
lence\nby Pierre Baumann (Strasbourg) as part of Paris algebra seminar
\n\n\nAbstract\nLet $G$ be a complex connected reductive group. As shown b
y Mirković and Vilonen\, the geometric Satake equivalence yields a basis
in each irreducible rational representation of $G$\, defined out of algebr
aic cycles in the affine Grassmannian of the Langlands dual of $G$. Goncha
rov and Shen extended this construction to each tensor product of irreduci
ble representations. We will investigate the properties of all these bases
and explain a method to compute them. Based on a joint work with Peter Li
ttelmann and Stéphane Gaussent.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/49
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Calaque (Montpellier)
DTSTART:20210531T120000Z
DTEND:20210531T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/50
DESCRIPTION:Title: Calabi-Yau structures for multiplicative preprojecti
ve algebras\nby Damien Calaque (Montpellier) as part of Paris algebra
seminar\n\n\nAbstract\nI will start by motivating and recalling Calabi-Yau
structures and relative versions thereof. \nI will then provide several e
xamples of Calabi-Yau structures occurring in the context of (dg-versions
of) multiplicative preprojective algebras. The A_2 case\, that we will des
cribe in detail\, will be used as a building block for general quivers. At
the end of the talk\, I will describe a strategy for a comparison with ot
her constructions\, for instance Van den Bergh's quasi-bi-hamiltonian stru
ctures. \nThis is a report on joint work with Tristan Bozec and Sarah Sche
rotzke.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/50
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Leicester)
DTSTART:20210419T120000Z
DTEND:20210419T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/51
DESCRIPTION:Title: The higher Stasheff–Tamari orders in representatio
n theory\nby Nicholas Williams (Leicester) as part of Paris algebra se
minar\n\n\nAbstract\nOppermann and Thomas show that tilting modules over I
yama's higher Auslander algebras of type A are in bijection with triangula
tions of even-dimensional cyclic polytopes. Triangulations of cyclic polyt
opes are partially ordered in two natural ways known as the higher Stashef
f–Tamari orders\, which were introduced in the 1990s by Kapranov\, Voevo
dsky\, Edelman\, and Reiner as higher-dimensional generalisations of the T
amari lattice. These two partial orders were conjectured to be equal in 19
96 by Edelman and Reiner\, but this is still an open problem. We show how
the higher Stasheff–Tamari orders correspond in even dimensions to natur
al orders on tilting modules which were studied by Riedtmann\, Schofield\,
Happel\, and Unger. This then allows us to complete the picture of Opperm
ann and Thomas by showing that triangulations of odd-dimensional cyclic po
lytopes correspond to equivalence classes of d-maximal green sequences\, w
hich we introduce as higher-dimensional analogues of Keller’s maximal gr
een sequences. We show that the higher Stasheff–Tamari orders correspond
to natural orders on equivalence classes of d-maximal green sequences\, w
hich relate to the no-gap conjecture of Brüstle\, Dupont\, and Perotin. I
f time permits\, we will also briefly discuss more recent work concerning
the relation between the first higher Stasheff–Tamari orders and the hig
her Bruhat orders\, which are higher-dimensional analogues of the weak Bru
hat order on the symmetric group.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/51
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Gautam (Ohio State)
DTSTART:20210517T120000Z
DTEND:20210517T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/52
DESCRIPTION:Title: Poles of finite-dimensional representations of Yangi
ans\nby Sachin Gautam (Ohio State) as part of Paris algebra seminar\n\
n\nAbstract\nThe Yangian associated to a simple Lie algebra g is a Hopf al
gebra which quantizes the Lie algebra of polynomials g[t]. Its finite-dime
nsional representation theory has remarkable connections with equivariant
cohomology\, combinatorics\, integrable systems and mathematical physics.
Concretely\, a finite-dimensional representation of the Yangian is prescri
bed by a finite collection of operators whose coefficients are rational fu
nctions\, satisfying a list of commutation relations.\n\nIn this talk I wi
ll give an explicit combinatorial description of the sets of poles of the
rational currents of the Yangian\, acting on an irreducible finite-dimensi
onal representation. This result uses the generalization of Baxter's Q-ope
rators obtained by Frenkel-Hernandez. Based on a joint work with Curtis We
ndlandt (arxiv:2009.06427).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/52
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (Lille)
DTSTART:20210614T120000Z
DTEND:20210614T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/53
DESCRIPTION:Title: Rationality at admissible levels of the simple W-alg
ebras associated with subregular nilpotent elements in sp_4\nby Justin
e Fasquel (Lille) as part of Paris algebra seminar\n\n\nAbstract\nW-algebr
as are certain vertex algebras obtained from the quantized Drinfeld-Sokolo
v reduction of universal affine vertex algebras associated with a complex
parameter k and a simple complex Lie algebra g. Their simple quotients are
believed to be rational for specific values of k\, called admissible\, wh
ich depend on the choice of a nilpotent orbit in g. Here\, by rationality\
, one means the complete reducibility of their positively graded modules.\
n\nThis conjecture was partially proved by Arakawa-van Ekeren and Creutzig
-Linshaw. In this talk\, I will discuss some consequences of the rationali
ty for a very concrete example\, namely the W-algebra associated with a su
bregular nilpotent element of the symplectic Lie algebra sp_4. In particul
ar\, we will be interested in certain actions on the W-algebra and the set
of its simple modules.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/53
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Kaplan (Birmingham)
DTSTART:20210524T120000Z
DTEND:20210524T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/54
DESCRIPTION:Title: Multiplicative preprojective algebras for Dynkin qui
vers\nby Dan Kaplan (Birmingham) as part of Paris algebra seminar\n\n\
nAbstract\nCrawley-Boevey and Shaw defined the multiplicative preprojectiv
e algebra to understand Kac’s middle convolution and to solve the Delign
e-Simpson problem. In Shaw’s thesis he noticed a curious phenomenon: for
the D_4 quiver the multiplicative preprojective algebra (with parameter q
=1) is isomorphic to the (additive) preprojective algebra if and only if t
he underlying field has characteristic not two. Later\, Crawley-Boevey pro
ved the multiplicative and additive preprojective algebras are isomorphic
for all Dynkin quivers over the complex numbers. Recent work of Etgü-Leki
li and Lekili-Ueda\, in the dg-setting\, sharpens the result to hold over
fields of good characteristic\, meaning characteristic not 2 in type D\, n
ot 2 or 3 in type E and not 2\, 3\, or 5 for E_8. Neither work produces an
isomorphism. \n\nIn this talk\, I will explain how to construct these iso
morphisms and prove their non-existence in the bad (i.e.\, not good) chara
cteristics. For each bad characteristic\, a single class in zeroth Hochsch
ild homology obstructs the existence of an isomorphism. Time permitting\,
I’ll explain how to interpret these results in the dg-setting where the
2-Calabi-Yau property allows us to recast these obstructions as non-trivia
l deformations\, using Van den Bergh duality.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/54
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (Orsay)
DTSTART:20210607T120000Z
DTEND:20210607T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/55
DESCRIPTION:Title: The flow tree formula for Donaldson-Thomas invariant
s of quivers with potentials\nby Pierrick Bousseau (Orsay) as part of
Paris algebra seminar\n\n\nAbstract\nVery generally\, Donaldson-Thomas inv
ariants are counts of stable objects in Calabi-Yau triangulated categories
of dimension 3. A natural source of examples is provided by the represent
ation theory of quivers with potentials. I will present a proof of a formu
la\, conjectured by Alexandrov-Pioline from string-theory arguments\, whic
h computes Donaldson-Thomas invariants of a quiver with potential in terms
of a much smaller set of "attractor invariants". The proof uses the frame
work of scattering diagrams to reorganize sequences of iterated applicatio
ns of the Kontsevich-Soibelman wall-crossing formula. This is joint work w
ith Hülya Argüz.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/55
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Tōhoku)
DTSTART:20210621T120000Z
DTEND:20210621T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/56
DESCRIPTION:Title: Categorical dynamical systems arising from sign-stab
le mutation loops\nby Shunsuke Kano (Tōhoku) as part of Paris algebra
seminar\n\n\nAbstract\nA pair formed by a triangulated category and an au
toequivalence is called a \ncategorical dynamical system. Its complexity i
s measured by the so-called categorical entropy. \nIn this talk\, I will p
resent a computation of the categorical entropies of categorical dynamical
systems obtained by lifting a sign-stable mutation loop of a quiver to an
autoequivalence of the derived category of the corresponding Ginzburg dg
algebra.\nThe notion of sign-stability is introduced as a generalization o
f the pseudo-Anosov property of mapping classes of surfaces. If time permi
ts\, we will discuss the pseudo-Anosovness of the autoequivalences constru
cted.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/56
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Amiens)
DTSTART:20210628T120000Z
DTEND:20210628T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/57
DESCRIPTION:Title: Braid varieties\, positroids\, and Legendrian links<
/a>\nby Mikhail Gorsky (Amiens) as part of Paris algebra seminar\n\n\nAbst
ract\nI will discuss a class of affine algebraic varieties associated with
positive braids\, their cluster structures and their relation to open Bot
t-Samelson varieties. First\, I will explain our motivation which comes bo
th from symplectic topology and from the study of HOMFLY-PT polynomials. T
hen we will discuss how the study of DG algebras associated with certain L
egendrian links may help us to better understand the algebraic geometry of
Richardson varieties in type A. I will illustrate our results and conject
ures concerning this interplay between topology and algebraic geometry wit
h the example of open positroid varieties in Grassmannians. If time permit
s\, I will briefly explain conjectural relations between certain stratific
ations of braid varieties and cluster structures on their coordinate rings
. This is joint work with Roger Casals\, Eugene Gorsky\, and José Simenta
l.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/57
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ehud Meir (Aberdeen)
DTSTART:20210705T120000Z
DTEND:20210705T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/58
DESCRIPTION:Title: Interpolations of monoidal categories by invariant t
heory\nby Ehud Meir (Aberdeen) as part of Paris algebra seminar\n\n\nA
bstract\nIn this talk\, I will present a recent construction that enables
one to\ninterpolate symmetric monoidal categories by interpolating algebra
ic\nstructures and their automorphism groups.\nI will explain how one can
recover the constructions of Deligne for\ncategories such as Rep(S_t)\, Re
p(O_t) and Rep(Sp_t)\, the constructions\nof Knop for wreath products with
S_t and GL_t(O_r)\, where O_r is a\nfinite quotient of a discrete valuati
on ring\, and also the TQFT\ncategories recently constructed from a ration
al function by Khovanov\, Ostrik\, and Kononov.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/58
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Cerulli Irelli (Rome La Sapienza)
DTSTART:20211004T120000Z
DTEND:20211004T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/59
DESCRIPTION:Title: On degeneration and extensions of symplectic and ort
hogonal quiver representations\nby Giovanni Cerulli Irelli (Rome La Sa
pienza) as part of Paris algebra seminar\n\n\nAbstract\nMotivated by linea
r degenerations of flag varieties\, and the study of 2-nilpotent B-orbits
for classical groups\, I will review the representation theory of symmetri
c quivers\, initiated by Derksen and Weyman in 2002. I will then focus on
the problem of describing the orbit closures in this context and how to re
late it to the orbit closures for the underlying quivers. In collaboration
with M. Boos we have recently given an answer to this problem for symmetr
ic quivers of finite type. I believe that this result is a very special ca
se of a much deeper and general result that I will mention in the form of
conjectures and open problems. The talk is based on the preprint version o
f my paper with Boos available on the arXiv as 2106.08666.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/59
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Gurevich (Technion\, Haifa)
DTSTART:20211011T120000Z
DTEND:20211011T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/60
DESCRIPTION:Title: RSK-transform for L-parameters\nby Maxim Gurevic
h (Technion\, Haifa) as part of Paris algebra seminar\n\nAbstract: TBA\n\n
What is common between the Specht construction for modules over\npermutati
on groups\, normal sequences of quiver Hecke algebra modules à\nla Kashiw
ara-Kim\, and the local Langlands classification for GL_n ?\nI would like
to show how these themes fit well together under a\nframework of a represe
ntation-theoretic Robinson-Schensted-Knuth\ntransform\, devised recently i
n my work with Erez Lapid on\nrepresentations of p-adic groups.\n\nOn one
hand\, RSK-standard modules are curious models for all smooth\nirreducible
GL_n-representations. Yet\, going through Bernstein-Rouquier\ncategorical
equivalences this notion is quantized into its natural\nexistence in the
realm of type A quiver Hecke algebras. A convenient\nbridge is thus portra
yed between the cyclotomic approach of classifying\nsimple modules through
a generalized Specht construction\, and the\nPBW-basis approach from Lusz
tig's work on quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/60
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (Leeds)
DTSTART:20211018T120000Z
DTEND:20211018T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/63
DESCRIPTION:Title: A cluster character for y-variables\nby Matthew
Pressland (Leeds) as part of Paris algebra seminar\n\n\nAbstract\nGiven a
(Frobenius or triangulated) cluster category\, I will explain how to categ
orify various cluster algebraic identities via lattice maps associated to
pairs of cluster-tilting objects. For example\, one such map is the index\
, well-known to categorify g-vectors. Using this formalism\, I will recall
the cluster character for x-variables developed by Caldero–Chapoton\, P
alu\, Fu–Keller and others\, and give a similar categorical expression f
or y-variables. This is joint work with Jan E. Grabowski.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/63
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haicheng Zhang (Nanjing Normal University)
DTSTART:20211108T130000Z
DTEND:20211108T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/66
DESCRIPTION:Title: Hall algebras of extriangulated categories and quant
um cluster algebras\nby Haicheng Zhang (Nanjing Normal University) as
part of Paris algebra seminar\n\n\nAbstract\nFirstly\, we define the Hall
algebra of an extriangulated category\, a notion introduced by Nakaoka an
d Palu. Then for a finite acyclic valued quiver Q\, we consider the Hall a
lgebras of certain subcategories of the bounded derived category of the re
presentation category of Q over a finite field\, which are extriangulated
categories. We recover the quantum Caldero-Chapoton formula via the Hall a
lgebra approach and give the higher-dimensional (cluster) multiplication f
ormulas in the quantum cluster algebra of Q with arbitrary coefficients\,
which can be viewed as the quantum version of the Caldero-Keller multiplic
ation formula in the cluster algebra. This talk is based on the joint prep
rints arXiv:2005.10617\, 2107.05883 and 2108.03558.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/66
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Fujita (University of Paris)
DTSTART:20211122T130000Z
DTEND:20211122T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/67
DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojecti
ve algebras\, II\nby Ryo Fujita (University of Paris) as part of Paris
algebra seminar\n\n\nAbstract\nIn their study of deformed W-algebras asso
ciated with complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) in
troduced certain two parameter deformations of the Cartan matrices. They p
lay an important role in the representation theory of quantum affine algeb
ras. In the former half of this talk\, we explain a representation-theoret
ic interpretation of these deformed Cartan matrices and their inverses in
terms of the generalized preprojective algebras recently introduced by Gei
ss-Leclerc-Schröer (2017). In the latter half of the talk\, we discuss it
s application to the representation theory of quantum affine algebras in c
onnection with the theory of cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/67
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kota Murakami (Kyoto)
DTSTART:20211122T130000Z
DTEND:20211122T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/68
DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojecti
ve algebras\, I\nby Kota Murakami (Kyoto) as part of Paris algebra sem
inar\n\n\nAbstract\nIn their study of deformed W-algebras associated with
complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) introduced cer
tain two parameter deformations of the Cartan matrices. They play an impor
tant role in the representation theory of quantum affine algebras. In the
former half of this talk\, we explain a representation-theoretic interpret
ation of these deformed Cartan matrices and their inverses in terms of the
generalized preprojective algebras recently introduced by Geiss-Leclerc-S
chröer (2017). In the latter half of the talk\, we discuss its applicatio
n to the representation theory of quantum affine algebras in connection wi
th the theory of cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/68
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (Edinburgh)
DTSTART:20211025T120000Z
DTEND:20211025T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/69
DESCRIPTION:Title: (Canonical) bases of the elliptic Hall algebra\n
by Lucien Hennecart (Edinburgh) as part of Paris algebra seminar\n\n\nAbst
ract\nThe global nilpotent cone is a closed substack of the stack of Higgs
sheaves on a smooth projective curve whose geometry has been studied in d
epth and is also an essential object in the geometric Langlands program. I
t is a highly singular stack and in particular it has several irreducible
components which were rather recently explicitly described by Bozec. In th
is talk\, we will concentrate on elliptic curves. We will recall Bozec's p
arametrization of the set of irreducible components of the global nilpoten
t cone and present another parametrization of the same set using (a refine
ment of) the Harder-Narasimhan stratification of the stack of coherent she
aves on the elliptic curve. Then\, we raise the question of the comparison
of these two bases\, showing the emergence piecewise linear structures. W
e will also see how the second description can be useful to understand a p
art of the cohomological Hall algebra of an elliptic curve.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/69
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (Edinburgh)
DTSTART:20220131T130000Z
DTEND:20220131T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/70
DESCRIPTION:Title: Local Normal Forms of Noncommutative Functions\n
by Michael Wemyss (Edinburgh) as part of Paris algebra seminar\n\n\nAbstra
ct\nThis talk will explain how to generalise Arnold's results classifying
commutative singularities into the noncommutative setting\, and will class
ify finite dimensional Jacobi algebras arising on the d-loop quiver. The
surprising thing is that a classification should exist at all\, and it is
even more surprising that ADE enters. I will spend most of my time explai
ning what the algebras are\, why they classify\, and how to intrinsically
extract ADE information from them. At the end\, I'll briefly explain why I
'm really interested in this problem\, the connection with different quive
rs\, and the applications of the above classification to curve counting an
d birational geometry. This is all joint work with Gavin Brown.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/70
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (Cambridge)
DTSTART:20211115T130000Z
DTEND:20211115T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/71
DESCRIPTION:Title: Generalized cluster dualities\nby Lang Mou (Camb
ridge) as part of Paris algebra seminar\n\n\nAbstract\nFock and Goncharov
introduced dualities between cluster varieties. I will explain how this du
ality under the framework of Gross-Hacking-Keel-Kontsevich can be naturall
y extended to generalized cluster varieties in the sense of Chekhov-Shapir
o. In particular\, I will construct generalized cluster scattering diagram
s which are used to construct bases of functions on the dual varieties. As
a generalized A-cluster variety yields a generalized cluster algebra\, ce
rtain positivity property of the cluster monomials will be derived as a re
sult of the positivity of the corresponding scattering diagram. This talk
is mainly based on arXiv: 2110.02416.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/71
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Fraser (Minnesota)
DTSTART:20211129T130000Z
DTEND:20211129T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/72
DESCRIPTION:Title: Automorphisms of open positroid varieties from braid
s\nby Chris Fraser (Minnesota) as part of Paris algebra seminar\n\n\nA
bstract\nPositroid varieties are distinguished subvarieties of Grassmannia
ns which have cluster structure(s). I will give some reminders on the comb
inatorics underlying these cluster structures\, partially based on a joint
work with Melissa Sherman-Bennett. In a previous work\, I described an ac
tion of a certain braid group on the top-dimensional positroid subvariety
by "quasi" cluster automorphisms. I will explain how a similar statement c
an be extended to arbitrary open positroid varieties. This is joint with B
ernhard Keller.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/72
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abel Lacabanne (Clermont-Ferrand)
DTSTART:20211213T130000Z
DTEND:20211213T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/73
DESCRIPTION:Title: Higher rank Askey-Wilson algebras as skein algebras<
/a>\nby Abel Lacabanne (Clermont-Ferrand) as part of Paris algebra seminar
\n\n\nAbstract\nThe skein algebra of a surface is built from the framed un
oriented links in the thickened surface\, modulo the Kauffman bracket rela
tions. If the surface is the $4$-punctured sphere\, it turns out that the
skein algebra is a central extension of the universal Askey-Wilson algebra
. De Bie\, De Clercq and Van de Vijver proposed a definition of higher ran
k Askey-Wilson algebras\, as a subalgebra of an $n$-fold tensor product of
$U_q(\\mathfrak{sl}_2)$. The aim of this talk is to explain an isomorphis
m between these higher rank Askey-Wilson algebras\, and the skein algebras
of punctured spheres. The diagrammatic flavour of the skein algebra provi
des then an efficient way to compute some relations between some elements
of the Askey-Wilson algebra\, notably the $q$-commutation relations discov
ered by De Clercq. This is joint work with J. Cooke.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/73
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Ovenhouse (Minnesota)
DTSTART:20211206T130000Z
DTEND:20211206T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/74
DESCRIPTION:Title: q-Rational Numbers and Finite Schubert Varieties
\nby Nicholas Ovenhouse (Minnesota) as part of Paris algebra seminar\n\n\n
Abstract\nRecently\, Morier-Genoud and Ovsienko generalized the notion of
q-integers to include rational numbers. The q-analogue of a rational numbe
r is some rational function with integer coefficients. There are some know
n combinatorial interpretations of the numerators as rank generating funct
ions of certain posets. I will review this interpretation\, and re-phrase
it in terms of lattice paths on "snake graphs". Using this snake graph int
erpretation\, I will explain how the numerators count the number of points
in some variety over a finite field. This variety is a union of Schubert
cells in some Grassmannian.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/74
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (Oaxaca)
DTSTART:20220117T130000Z
DTEND:20220117T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/75
DESCRIPTION:Title: Deformation theory for finite cluster complexes\
nby Alfredo Nájera Chávez (Oaxaca) as part of Paris algebra seminar\n\n\
nAbstract\nCluster complexes are a certain class of simplicial complexes t
hat naturally arise in the theory of cluster algebras. They codify a wealt
h of fundamental information about cluster algebras. The purpose of this t
alk is to elaborate on a geometric relationship between cluster algebras a
nd cluster complexes. In vague words\, this relationship is the following:
cluster algebras of finite cluster type with universal coefficients may b
e obtained via a torus action on a Hilbert scheme. In particular\, we will
discuss the deformation theory of the Stanley-Reisner ring associated to
a finite cluster complex and present some applications related to the Grö
bner theory of the ideal of relations among cluster and frozen variables o
f a cluster algebra of finite cluster type. Time permitting I will elabora
te on how to generalize this approach to the context of tau-tilting finite
algebras.\n\nThis is based on a joint project with Nathan Ilten and Hipol
ito Treffinger whose first outcome is the preprint arXiv:2111.02566.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/75
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Hamburg)
DTSTART:20220124T130000Z
DTEND:20220124T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/76
DESCRIPTION:Title: Gluing constructions of Ginzburg algebras and cluste
r categories\nby Merlin Christ (Hamburg) as part of Paris algebra semi
nar\n\n\nAbstract\nGinzburg algebras are a class of 3-CY dg algebras\, whi
ch have attracted attention for their use in the categorification of clust
er algebras. Given a marked surface with a triangulation\, there is an ass
ociated Ginzburg algebra G. I will begin by describing how its derived cat
egory D^perf(G) can be glued from the derived categories of the relative G
inzburg algebras of the ideal triangles of the triangulation. We will see
that the passage to Amiot's cluster category\, defined as the quotient D^p
erf(G)/D^fin(G)\, does not commute with this gluing. As we will discuss\,
this can fixed by instead starting with the relative Ginzburg algebra of t
he triangulation and again applying Amiot's quotient formula. Remarkably\,
this resulting relative version of cluster category turns out to be equiv
alent to the 1-periodic topological Fukaya category of the surface.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/76
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Brav (HSE Moscow)
DTSTART:20220110T130000Z
DTEND:20220110T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/77
DESCRIPTION:Title: Non-commutative string topology\nby Chris Brav (
HSE Moscow) as part of Paris algebra seminar\n\n\nAbstract\nWe explain how
relative Calabi-Yau structures on dg functors\, more generally relative o
rientations\, give a non-commutative generalisation of oriented manifolds
with boundary. We then construct genus zero string topology operations on
the relative Hochschild homology HH_*(C\,D) of a dg functor D —> C equip
ped with a relative orientation. More precisely\, we prove a relative vers
ion of the cyclic Deligne conjecture\, stating that this shifted relative
Hochschild homology carries a natural structure of framed E_2-algebra. Exa
mples include 1) the functor of induction of local systems for the inclusi
on of the boundary into an oriented manifold with boundary\, in which case
the relative Hochschild homology is identified with the relative loop hom
ology 2) the functor of pushforward of coherent sheaves for the inclusion
of the anti-canonical divisor into a variety\, in which case relative Hoch
schild homology can be related to differential forms\, and 3) various exam
ples coming from representation theory.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/77
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Cologne)
DTSTART:20220207T130000Z
DTEND:20220207T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/78
DESCRIPTION:Title: Equivalence of maximal green sequences\nby Nicho
las Williams (Cologne) as part of Paris algebra seminar\n\n\nAbstract\nIt
is natural to study the set of maximal green sequences of an algebra under
an equivalence relation. The resulting set of equivalence classes has the
structure of a poset\; it is a lattice in type A\, where the equivalence
classes are in bijection with triangulations of three-dimensional cyclic p
olytopes. There are at least four appealing ways of defining an equivalenc
e relation on maximal green sequences: commutation\, exchange pairs\, tau-
rigid summands\, and bricks. The main result of my talk will be that the f
irst three methods define the same equivalence relation\, while the fourth
does not. This gives a surprising lack of duality between bricks\, which
correspond to simples\, and tau-rigid summands\, which correspond to proje
ctives. This is a report on joint work in progress with Mikhail Gorsky.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/78
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (Connecticut)
DTSTART:20220214T130000Z
DTEND:20220214T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/79
DESCRIPTION:Title: Connection between knot theory and Jacobian algebras
\nby Véronique Bazier-Matte (Connecticut) as part of Paris algebra se
minar\n\n\nAbstract\nThis is joint work with Ralf Schiffler.\nIn knot theo
ry\, it is known that we can compute the Alexander polynomial of a knot fr
om the lattice of Kauffman states of a knot diagram. Recently\, my collabo
rator and I associated a quiver with a knot diagram. From this quiver\, on
e can obtain a Jacobian algebra. It appears that the lattice of submodules
of indecomposable modules over this algebra is in bijection with the latt
ice of Kauffman states. This bijection allows us to compute the Alexander
polynomial of a knot with a specialization of the F-polynomial of any inde
composable module over this algebra.\nAfter a brief introduction to knot t
heory\, I will explain how to compute an Alexander polynomial from a F-pol
ynomial.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/79
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonçalo Tabuada (Warwick)
DTSTART:20220221T130000Z
DTEND:20220221T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/80
DESCRIPTION:Title: Jacques Tits motivic measure\nby Gonçalo Tabuad
a (Warwick) as part of Paris algebra seminar\n\n\nAbstract\nThe Grothendie
ck ring of varieties\, introduced in a letter from Alexander Grothendieck
to Jean-Pierre Serre (August 16th 1964)\, plays an important role in algeb
raic geometry. However\, despite the efforts of several mathematicians\, t
he structure of this ring still remains poorly understood. In order to cap
ture some of the flavor of Grothendieck’s ring of varieties\, a few moti
vic measures have been built throughout the years. In this talk I will pre
sent a new motivic measure\, called the Jacques Tits motivic measure\, and
describe some of its numerous applications.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/80
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Versailles)
DTSTART:20220228T130000Z
DTEND:20220228T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/81
DESCRIPTION:Title: Cluster algebras\, categorification\, and some confi
guration spaces\nby Pierre-Guy Plamondon (Versailles) as part of Paris
algebra seminar\n\n\nAbstract\nThe real part of the configuration space M
_{0\,n} of n points on a projective line has a connected component which i
s closely related to the associahedron. As an affine variety\, it is defi
ned by explicit equations which are in close connection with exchange rela
tions for cluster variables in type A. This has been generalized to all D
ynkin types.\n\nIn this talk\, we will construct an affine variety associa
ted to any representation-finite finite-dimensional algebra over an algebr
aically closed field. The equations defining the variety will be obtained
from the F-polynomials of indecomposable modules over the algebra. This
generalizes previous results\, which can be recovered by applying our cons
truction to Jacobian algebras in Dynkin types.\n\nThis talk is based on an
ongoing project with Nima Arkani-Hamed\, Hadleigh Frost\, Giulio Salvator
i and Hugh Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/81
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léa Bittmann (Edinburgh)
DTSTART:20220425T120000Z
DTEND:20220425T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/82
DESCRIPTION:Title: A Schur-Weyl duality between Double Affine Hecke Alg
ebras and quantum groups\nby Léa Bittmann (Edinburgh) as part of Pari
s algebra seminar\n\nLecture held in hybrid.\n\nAbstract\nSchur-Weyl duali
ty is often used to relate type A Lie groups (or quantum groups) to symmet
ric groups (or Hecke algebras). In this talk\, I will use ribbon calculus
and skein modules to describe an instance of this Schur-Weyl duality betwe
en representations of the type A quantum group at roots of unity and repre
sentations of the Double Affine Hecke Algebra. This is based on joint work
with A. Chandler\, A. Mellit and C. Novarini.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/82
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bitoun (Calgary)
DTSTART:20220516T120000Z
DTEND:20220516T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/83
DESCRIPTION:Title: On centralizers in Azumaya domains\nby Thomas Bi
toun (Calgary) as part of Paris algebra seminar\n\nLecture held in hybrid.
\n\nAbstract\nWe prove a positive characteristic analogue of the classical
result that the centralizer of a nonconstant differential operator in one
variable is commutative. This leads to a new\, short proof of that classi
cal characteristic zero result\, by reduction modulo p. This is joint work
with Justin Desrochers available at https://arxiv.org/abs/2201.04606.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/83
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHES)
DTSTART:20220307T130000Z
DTEND:20220307T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/84
DESCRIPTION:Title: The ribbon quiver complex and the noncommutative Leg
endre transform\nby Alex Takeda (IHES) as part of Paris algebra semina
r\n\n\nAbstract\nThe structure of a fully extended oriented 2d TQFT is giv
en by a Frobenius algebra. If one wants to lift this structure to a cohomo
logical field theory\, the correct notion is that of a Calabi-Yau algebra
or category\; the CohFT operations can be described by a certain graph com
plex. There are two different notions of Calabi-Yau structure on categorie
s\, both requiring some type of finiteness or dualizability. In this talk
I will discuss a variation that works in non-dualizable cases as well\; in
this case the graphs get replaced by quivers. The resulting complex calcu
lates the homology of certain moduli spaces of open-closed surfaces\, and
can be used to give a fully explicit description of these operations. In t
he second half of the talk\, I will describe some of these constructions\,
including how to produce operations from smooth and/or relative Calabi-Ya
u structures\, and explain how\, in the smooth case\, this can be thought
of as a noncommutative version of the Legendre transform. This is joint wo
rk with M. Kontsevich and Y. Vlassopoulos.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/84
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norihiro Hanihara (Nagoya)
DTSTART:20220321T130000Z
DTEND:20220321T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/85
DESCRIPTION:Title: Tilting theory via enhancements\nby Norihiro Han
ihara (Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nTilting the
ory aims at giving equivalences among various triangulated categories\, su
ch as derived categories\, cluster categories\, and singularity categories
. Constructing such an equivalence provides a mutual understanding of thes
e categories. In this talk\, we study tilting theory for singularity categ
ories and cluster categories from the viewpoint of dg enhancements. We wil
l first review their construction in terms of their enhancements\, and the
n based on this we explain a general method of giving equivalences between
singularity categories and cluster categories. Our main steps are existen
ce of (weak) right Calabi-Yau structure on the dg singularity category of
commutative Gorenstein rings\, and a characterization of dg orbit categori
es among bigraded dg categories. This is a joint work with Osamu Iyama.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/85
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Pan (Zhejiang U.)
DTSTART:20220314T130000Z
DTEND:20220314T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/86
DESCRIPTION:Title: Positivity and polytope basis in cluster algebras vi
a Newton polytopes\nby Jie Pan (Zhejiang U.) as part of Paris algebra
seminar\n\n\nAbstract\nWe work in the generality of a totally sign-skew-sy
mmetric (e.g. skew-symmetrizable) \ncluster algebra of rank $n$. We study
the Newton polytopes of $F$-polynomials and\, more generally\, a\nfamily o
f polytopes $N_h$ indexed by vectors $h$ in $Z^n$. We use it to give a new
proof of Laurent \npositivity and to construct what we call the polytope
basis of the upper cluster algebra. The polytope \nbasis consists of certa
in universally indecomposable Laurent polynomials. It is strongly positive
\nand generalizes the greedy basis constructed by Lee-Li-Zelevinsky in ran
k 2.\nThis is a report on joint work with Fang Li\, cf. arXiv:2201.01440.\
n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/86
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (Australian National U.)
DTSTART:20220328T120000Z
DTEND:20220328T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/87
DESCRIPTION:Title: Categorical q-deformed rational numbers via Bridgela
nd stability conditions\nby Asilata Bapat (Australian National U.) as
part of Paris algebra seminar\n\n\nAbstract\nWe will discuss new categoric
al interpretations of two distinct q-deformations of the rational numbers.
The first one\, introduced by Morier-Genoud and Ovsienko in a different c
ontext\, enjoys fascinating combinatorial\, topological\, and algebraic pr
operties. The second one is a natural partner to the first\, and is new. W
e obtain these deformations via boundary points of a compactification of t
he space of Bridgeland stability conditions on the 2-Calabi-Yau category o
f the A2 quiver. The talk is based on joint work with Louis Becker\, Anand
Deopurkar\, and Anthony Licata.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/87
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hipolito Treffinger (City University of Paris)
DTSTART:20220404T120000Z
DTEND:20220404T123000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/88
DESCRIPTION:Title: Torsion classes and tau-tilting in higher homologica
l algebra\, I\nby Hipolito Treffinger (City University of Paris) as pa
rt of Paris algebra seminar\n\nLecture held in hybrid.\n\nAbstract\nHigher
homological algebra was introduced by Iyama in the late \n2000's. His poi
nt of view was that some classical results by Auslander \nand Auslander--R
eiten were somehow 2-dimensional and should have \nn-dimensional equivalen
ts. This new theory quickly attracted a lot of \nattention\, with many aut
hors generalising classical notions to the \nsetting of higher homological
algebra. Examples of such generalisations \nare the introduction of n-abe
lian categories by Jasso\, n-angulated \ncategories by Geiss--Keller--Oppe
rmann\, and n-torsion classes by Jørgensen.\n\nRecently\, it was shown by
Kvamme and\, independently\, by Ebrahimi and \nNasr-Isfahani\, that every
small n-abelian category is the \nn-cluster-tilting subcategory of an abe
lian category. In this talk\, we \nwill focus on the relation between n-to
rsion classes in an n-abelian \ncategory $\\mathcal{M}$ and (classical) to
rsion classes of the abelian \ncategory $\\mathcal{A}$ in which $\\mathcal
{M}$ is embedded. By \nconsidering functorially finite torsion classes\, t
his will allow us to \nrelate n-torsion classes with maximal tau_n-rigid o
bjects in $\\mathcal{M}$.\n\nSome of the results presented in this talk ar
e part of a joint work by \nJ. Asadollahi\, P. Jørgensen\, S. Schroll\, H
. Treffinger. The rest \ncorresponds to an ongoing project by J. August\,
J. Haugland\, \nK. Jacobsen\, S. Kvamme\,Y. Palu and H. Treffinger.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/88
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Palu (Amiens)
DTSTART:20220404T123000Z
DTEND:20220404T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/89
DESCRIPTION:Title: Torsion classes and tau-tilting in higher homologica
l algebra\, II\nby Yann Palu (Amiens) as part of Paris algebra seminar
\n\nLecture held in hybrid.\n\nAbstract\nHigher homological algebra was in
troduced by Iyama in the late \n2000's. His point of view was that some cl
assical results by Auslander \nand Auslander--Reiten were somehow 2-dimens
ional and should have \nn-dimensional equivalents. This new theory quickly
attracted a lot of \nattention\, with many authors generalising classical
notions to the \nsetting of higher homological algebra. Examples of such
generalisations \nare the introduction of n-abelian categories by Jasso\,
n-angulated \ncategories by Geiss--Keller--Oppermann\, and n-torsion class
es by Jørgensen.\n\nRecently\, it was shown by Kvamme and\, independently
\, by Ebrahimi and \nNasr-Isfahani\, that every small n-abelian category i
s the \nn-cluster-tilting subcategory of an abelian category. In this talk
\, we \nwill focus on the relation between n-torsion classes in an n-abeli
an \ncategory $\\mathcal{M}$ and (classical) torsion classes of the abelia
n \ncategory $\\mathcal{A}$ in which $\\mathcal{M}$ is embedded. By \ncons
idering functorially finite torsion classes\, this will allow us to \nrela
te n-torsion classes with maximal tau_n-rigid objects in $\\mathcal{M}$.\n
\nSome of the results presented in this talk are part of a joint work by \
nJ. Asadollahi\, P. Jørgensen\, S. Schroll\, H. Treffinger. The rest \nco
rresponds to an ongoing project by J. August\, J. Haugland\, \nK. Jacobsen
\, S. Kvamme\,Y. Palu and H. Treffinger.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/89
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (Hebrew University)
DTSTART:20220411T120000Z
DTEND:20220411T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/90
DESCRIPTION:Title: On exchange matrices from string diagrams\nby Pe
igen Cao (Hebrew University) as part of Paris algebra seminar\n\nLecture h
eld in Zoom.\n\nAbstract\nIn this talk\, we will first recall the construc
tions of triangular extension and of source-sink extensio for skew-symmetr
izable matrices and some invariants under these constructions. Secondly\,
we will recall the string diagrams introduced by Shen-Weng\, which are ver
y useful to describe many interesting skew-symmetrizable matrices closely
related with Lie theory. Thirdly\, we will sketch the proof of our main re
sult: the skew-symmetrizable matrices from string diagrams are in the smal
lest class of skew-symmetrizable matrices containing the (1 times 1) zero
matrix and closed under mutations and source-sink extensions. This result
applies to the exchange matrices of cluster algebras from double Bruhat ce
lls\, unipotent cells\, double Bott-Samelson cells among others. Finally\,
some immediate applications regarding reddening sequences and non-degener
ate potentials for many quivers from Lie theory are given.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/90
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Sorbonne Paris Nord)
DTSTART:20220523T120000Z
DTEND:20220523T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/91
DESCRIPTION:Title: Pre-Calabi-Yau algebras and homotopy double Poisson
gebras\nby Bruno Vallette (Sorbonne Paris Nord) as part of Paris algeb
ra seminar\n\n\nAbstract\nWe prove that the notion of a curved pre-Calabi
–Yau algebra is equivalent to the notion of a curved homotopy double Poi
sson gebra\, thereby settling the equivalence between the two ways to defi
ne derived noncommutative Poisson structures. We actually prove that the r
espective differential graded Lie algebras controlling both deformation th
eories are isomorphic. This allows us to apply the recent developments of
the properadic calculus in order to establish the homotopical properties o
f curved pre-Calabi–Yau algebras: infini-morphisms\, homotopy transfer t
heorem\, formality\, Koszul hierarchy\, and twisting procedure. (Joint wor
k with Johan Leray available at arxiv.org/abs/2203.05062).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/91
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasuki Kinjo (IPMU)
DTSTART:20220502T120000Z
DTEND:20220502T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/92
DESCRIPTION:Title: Deformed Calabi--Yau completion and its application
to DT theory\nby Tasuki Kinjo (IPMU) as part of Paris algebra seminar\
n\n\nAbstract\nIn this talk\, we investigate an application of the theory
of deformed Calabi--Yau completion to enumerative geometry. The notion of
Calabi--Yau completion was first introduced by Keller as a non-commutative
analogue of the canonical bundle. In the same paper\, he also introduced
a deformed version of the Calabi--Yau completion.\nWe will explain that th
e deformed Calabi--Yau completion is a non-commutative analogue of an affi
ne bundle modeled on the canonical bundle. Combining this observation with
a recent work of Bozec--Calaque--Scherotzke\, we prove that the moduli sp
ace of coherent sheaves on a certain non-compact Calabi--Yau threefold is
described as the critical locus inside a smooth moduli space. This descrip
tion has several applications in Donaldson--Thomas theory including Toda's
\\chi-independence conjecture of Gopakumar--Vafa invariants for arbitrary
local curves. By dimensional reduction\, it implies (and extends) Hausel-
-Thaddeus's cohomological \\chi-independence conjecture for Higgs bundles.
\n\nThis talk is based on a joint work with Naruki Masuda and another join
t work with Naoki Koseki.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/92
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Naef
DTSTART:20220509T120000Z
DTEND:20220509T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/93
DESCRIPTION:Title: The (non-)homotopy invariance of the string coproduc
t\nby Florian Naef as part of Paris algebra seminar\n\n\nAbstract\nA C
alabi-Yau structure on a smooth algebra allows one to identify Hochschild
homology with Hochschild cohomology. With this identification Hochschild h
omology acquires an additional Gerstenhaber algebra structure. One way to
formulate the amount of structure one has on Hochschild homology is to enc
ode it into a 2d TFT. This explains some of the string topology operations
on the free loop space of a manifold\, but not the string coproduct. If t
he algebra has additional structure (trivialization of its Hattori-Stallin
g Euler characteristic) one obtains an extra secondary operation on Hochsc
hild homology\, which recovers the string coproduct. Finally\, in the free
loop space setting\, this additional structure can either be recovered fr
om intersection theory of the manifold or from its underlying simple homot
opy type\, thus relating the two. Using this last relation one can express
the difference between the string coproduct of two homotopic but not nece
ssarily homeomorphic manifolds in terms of Whitehead torsion.\nThis is joi
nt work with Pavel Safronov\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/93
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Rickard (Bristol)
DTSTART:20220606T120000Z
DTEND:20220606T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/94
DESCRIPTION:Title: Generating the derived category\nby Jeremy Ricka
rd (Bristol) as part of Paris algebra seminar\n\n\nAbstract\nThe unbounded
derived category of (right) modules over a ring is a triangulated categor
y with infinite products and coproducts. As a triangulated category with c
oproducts it is easy to see that it is generated by the projective modules
\, and similarly it is generated as a triangulated category with products
by the injective modules.\n\nI will discuss the question of whether it is
generated as a triangulated category with coproducts by the injective modu
les\, or as a triangulated category with products by the projective (or fl
at) modules. I will describe the relationship with the finitistic dimensio
n conjecture\, as well as some more recent results.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/94
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuya Mizuno (Osaka Metropolitan University)
DTSTART:20220613T120000Z
DTEND:20220613T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/95
DESCRIPTION:Title: g-simplicial complex and silting theory\nby Yuya
Mizuno (Osaka Metropolitan University) as part of Paris algebra seminar\n
\n\nAbstract\nFor a finite dimensional algebra $A$\, the 2-term silting co
mplexes of $A$ give a simplicial complex $\\Delta(A)$\, which is called th
e g-simplicial complex.\nWe study several properties of $\\Delta(A)$ and\,
in particular\, we give tilting theoretic interpretations of the $h$-vect
ors and the Dehn-Sommerville equations of $\\Delta(A)$.\nConsequently\, w
e can explain a close correspondence between torsion classes and wide subc
ategories\, which can be regarded as a refinement of the Koenig-Yang corre
spondence.\nThis is joint work with Aoki-Higashitani-Iyama-Kase\, cf. http
s://arxiv.org/pdf/2203.15213.pdf\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/95
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Niklas Eberhardt (Bonn)
DTSTART:20220530T120000Z
DTEND:20220530T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/96
DESCRIPTION:Title: Motivic Springer Theory\nby Jens Niklas Eberhard
t (Bonn) as part of Paris algebra seminar\n\n\nAbstract\nAlgebras and thei
r representations can often be constructed geometrically in terms of convo
lution of cycles. \nFor example\, the Springer correspondence describes ho
w irreducible representations of a Weyl group can be realised in terms of
a convolution action on the vector spaces of irreducible components of Spr
inger fibers. Similar situations yield the affine Hecke algebra\, quiver H
ecke algebra (KLR algebra)\, quiver Schur algebra or Soergel bimodules.\nI
n this spirit\, we show that these algebras and their representations can
be realised in terms of certain equivariant motivic sheaves called Springe
r motives.\nOn our way\, we will discuss weight structures and their appli
cations to motives.\nThis is joint work with Catharina Stroppel.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/96
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shapiro (Edinburgh)
DTSTART:20220620T120000Z
DTEND:20220620T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/97
DESCRIPTION:Title: Positive representation theory\nby Alexander Sha
piro (Edinburgh) as part of Paris algebra seminar\n\n\nAbstract\nThe notio
ns of a modular tensor category\, 2d topological modular functor\, and 3d
topological quantum field theory are essentially equivalent. Fock and Gonc
harov conjectured that the quantised higher Teichmüller theory gives rise
to an analogue of a modular functor. Their construction in turn yields a
family of "positive" representations of quantum groups. I will argue that
these representations provide a compelling first step towards constructing
an analogue of a modular tensor category. This talk will be based on join
t works with Gus Schrader.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/97
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART:20220627T120000Z
DTEND:20220627T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/98
DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi-
)cluster structures\nby Daping Weng (UC Davis) as part of Paris algebr
a seminar\n\n\nAbstract\nGiven a plabic graph on R^2\, we can choose a con
ormal lift of its zig-zag strands to the unit cotangent bundle of R^2\, ob
taining a Legendrian link. If the plabic graph satisfies a “grid” cond
ition\, its Legendrian link admits a natural embedding into the standard c
ontact R^3. We study the Kashiwara-Schapira moduli space of microlocal ran
k 1 sheaves associated with the Legendrian link\, and construct a natural
(quasi-)cluster structure on this moduli space using Legendrian weaves. In
particular\, we prove that any braid variety associated with (beta Delta)
for a 3-strand braid beta admits cluster structures with an explicit cons
truction of initial seeds. We also construct Donaldson-Thomas transformati
ons for these moduli spaces and prove that the upper cluster algebra equal
s its cluster algebra. In this talk\, I will introduce the theoretical bac
kground and describe the basic combinatorics for constructing Legendrian w
eaves and the (quasi-)cluster structures from a grid plabic graph. This is
based on joint work with Roger Casals\, cf. https://arxiv.org/abs/2204.13
244.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/98
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll (Cologne)
DTSTART:20220704T120000Z
DTEND:20220704T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/99
DESCRIPTION:Title: Recollements of derived categories of graded gentle
algebras\nby Sibylle Schroll (Cologne) as part of Paris algebra semina
r\n\n\nAbstract\nGraded gentle algebras are classical objects in represent
ation theory. They are quadratic monomial algebras making them particularl
y amenable to study and they appear in many different areas of mathematics
such as in cluster theory\, in N=2 gauge theories and in homological mirr
or symmetry of surfaces. \nIn this talk\, we give a construction of a part
ial cofibrant dg algebra resolution of a graded quadratic monomial algebra
inducing an explicit recollement of their derived categories. We show tha
t for graded gentle algebras\, both the left and the right side of such a
recollement corresponds to cutting the underlying surface which can be ass
ociated to a graded gentle algebra. In the case of homologically smooth an
d proper graded gentle algebras this recollement can be restricted to the
derived categories with finite total cohomology\, thus inducing a recollem
ent of the corresponding partially wrapped Fukaya categories. We give some
consequences of this construction such as the existence of full exception
al sequences\, silting objects and simple minded collections. This is join
t work with Wen Chang and Haibo Jin https://arxiv.org/abs/2206.11196.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/99
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Labardini-Fragoso (UNAM)
DTSTART:20221107T130000Z
DTEND:20221107T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/100
DESCRIPTION:Title: Revisiting Derksen-Weyman-Zelevinsky's mutations\nby Daniel Labardini-Fragoso (UNAM) as part of Paris algebra seminar\n\n
Lecture held in room 01 of the Institut Henri Poincaré\, Paris\, France.\
n\nAbstract\nThe mutation theory of quivers with potential and their repre
sentations\, developed around 15 years ago by Derksen-Weyman-Zelevinsky\,
has had a profound impact both inside and outside the theory of cluster al
gebras. In this talk I will present results obtained in joint works with G
eiss and Schröer\, and with de Laporte\, about some interesting behaviors
of DWZ's mutations of representations. Namely\, despite needing several n
on-canonical choices of linear-algebraic data in order to be performed\, t
hey can always be arranged so as to become regular maps on dense open subs
ets of representation spaces rep(Q\,S\,d). As a consequence\, one obtains
the invariance of Geiss-Leclerc-Schröer's 'generic basis' under mutations
even in the Jacobi-infinite case\, thus generalizing a result of Plamondo
n. Furthermore\, given two distinct vertices k\, \\ell of a quiver with po
tential (Q\,S)\, the k-th mutation of representations takes the \\ell-th i
ndecomposable projective over (Q\,S) to the \\ell-th indecomposable projec
tive over \\mu_k(Q\,S). When a certain 'optimization' condition is satisfi
ed by \\ell\, this allows to compute certain 'Landau-Ginzburg potentials'
as F-polynomials of projective representations.\n\nIn-person talk at the r
oom 01 of the Institut Henri Poincaré\, Paris\, France\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Muller (Oklahoma)
DTSTART:20221010T120000Z
DTEND:20221010T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/101
DESCRIPTION:Title: Juggler's friezes\nby Greg Muller (Oklahoma) as
part of Paris algebra seminar\n\n\nAbstract\nFrieze patterns are infinite
strips of numbers satisfying certain determinantal identities. Originally
motivated by Gauss’ “miraculous pentagram” identities\, these patte
rns have since been connected to triangulations\, integrable systems\, rep
resentation theory\, and cluster algebras. In this talk\, we will review a
few characterizations and constructions of frieze patterns\, as well as a
generalization which allows friezes with a “ragged edge” described by
a juggling function. These “juggler’s friezes” correspond to specia
l points in positroid varieties\, in direct analogy with how classical fri
ezes correspond to special points in Grassmannians.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State)
DTSTART:20221017T120000Z
DTEND:20221017T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/102
DESCRIPTION:Title: Cluster Nature of Quantum Groups\nby Linhui She
n (Michigan State) as part of Paris algebra seminar\n\n\nAbstract\nWe pres
ent a rigid cluster model to realize the quantum group $U_q(g)$ for $g$ of
type ADE. That is\, we prove that there is a natural Hopf algebra isomorp
hism from the quantum group to a quotient algebra of the Weyl group invari
ants of a Fock-Goncharov quantum cluster algebra. By applying the quantum
duality of cluster algebras\, we show that the quantum group admits a clus
ter canonical basis $\\Theta$ whose structural coefficients are in $\\math
bb{N}[q^{\\frac{1}{2}}\, q^{-\\frac{1}{2}}]$. The basis $\\Theta$ satisfie
s an invariance property under Lusztig's braid group action\, the Dynkin a
utomorphisms\, and the star anti-involution.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slava Pimenov (Nottingham)
DTSTART:20221003T120000Z
DTEND:20221003T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/103
DESCRIPTION:Title: Planar Prop of Differential Operators of Associativ
e Algebras\nby Slava Pimenov (Nottingham) as part of Paris algebra sem
inar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleven speakers
DTSTART:20220905T120000Z
DTEND:20220905T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/104
DESCRIPTION:Title: Algebra days in Paris\nby Eleven speakers as pa
rt of Paris algebra seminar\n\n\nAbstract\nYou may be interested in the el
even talks delivered on September 5 and 6 at the Algebra days in Paris.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kapranov (Yale and IPMU)
DTSTART:20220912T120000Z
DTEND:20220912T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/105
DESCRIPTION:Title: Perverse sheaves and schobers on symmetric products
\nby Mikhail Kapranov (Yale and IPMU) as part of Paris algebra seminar
\n\n\nAbstract\nThe talk\, based on joint work in progress with V. Schecht
man\, will first recall our description of perverse sheaves on $Sym^n(\\ma
thbb{C})$\, the symmetric product of the complex line with its natural str
atification by multiplicities. This description proceeds in terms of conti
ngency matrices\, which are certain integer matrices appearing (besides th
eir origin in statistics) in three different contexts:\n\n- A natural cell
decomposition of $Sym^n(\\mathbb{C})$.\n\n- Compatibility of multiplicati
on and comultiplication in $\\mathbb{Z}_+$-graded Hopf algebras.\n\n- Para
bolic Bruhat decomposition for $GL_n$.\n\nPerverse sheaves on $Sym^n(\\mat
hbb{C})$ are described in terms of certain data of mixed functoriality on
contingency matrices which we call Janus sheaves. I will then explain our
approach to categorifying the concept of Janus sheaves\, in which sums are
replaced by filtrations with respect to the Bruhat order. Such data can b
e called Janus schobers. Examples can be obtained from $\\mathbb{Z}_+$-gra
ded Hopf categories\, a concept going back to Crane-Frenkel\, of which we
consider two examples related to representations of groups $GL_n$ over fin
ite fields (Joyal-Street) and $p$-adic fields (Bernstein-Zelevinsky). [Thi
s talk is kindly shared by Noncommutativ
e shapes.]\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Neeman (Australian National University)
DTSTART:20220926T120000Z
DTEND:20220926T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/106
DESCRIPTION:Title: Two results\, both developments of a 2015 article b
y Krause\nby Amnon Neeman (Australian National University) as part of
Paris algebra seminar\n\n\nAbstract\nIn 2020\, the pandemic hit\, and all
around the globe we went into lockdowns of various description. During the
first lockdown I carefully read Krause's 2015 article "Deriving Auslander
's formula".\n\nIn this talk\, I will outline how the ideas of Krause's pa
per underpin two articles written in 2020 in collaboration with Canonaco a
nd Stellari. One is about the uniqueness of enhancements of large classes
of triangulated categories\, while the second offers a counterexample to c
ertain vanishing conjectures in negative K-theory. [This talk is kindly sh
ared by Representation theory and triangulated categories.]\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Prague)
DTSTART:20220919T120000Z
DTEND:20220919T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/107
DESCRIPTION:Title: The finitistic dimension conjecture via DG-rings\nby Liran Shaul (Prague) as part of Paris algebra seminar\n\n\nAbstract\
nThe finitistic dimension of a ring A is defined to be the supremum of pro
jective dimensions among all A-modules of finite projective dimension. It
is an open problem whether this quantity is finite for finite dimensional
algebras over a field and for artin algebras.\n\nIn this talk\, I will exp
lain a new approach for studying the finiteness of the finitistic dimensio
n by embedding the ring A inside a nicely behaved differential graded alge
bra\, and using relation between this DG-algebra and A to deduce results a
bout the finitistic dimension.\nAs an application of these methods\, I wil
l explain how to generalize a recent sufficient condition of Rickard\, for
FPD(A)<∞ in terms of generation of D(A) from finite dimensional algebra
s over a field to all left perfect rings which admit a dualizing complex.\
n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Sauter (Bielefeld)
DTSTART:20221024T120000Z
DTEND:20221024T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/108
DESCRIPTION:Title: Tilting theory in exact categories\nby Julia Sa
uter (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nWe define
tilting subcategories in arbitrary exact categories to archieve the follo
wing. Firstly: Unify existing definitions of tilting subcategories to arbi
trary exact categories. Discuss standard results for tilting subcategories
: Auslander correspondence\, Bazzoni description of the perpendicular cate
gory. Secondly: We treat the question of induced derived equivalences sepa
rately - given a tilting subcategory T\, we ask if a functor on the perpen
dicular category induces a derived equivalence to a (certain) functor cate
gory over T. If this is the case\, we call the tilting subcategory ideq ti
lting. We prove a generalization of Miyashita's theorem (which is itself a
generalization of a well-known theorem of Brenner-Butler) and characteriz
e exact categories with enough projectives allowing ideq tilting subcatego
ries. In particular\, this is always fulfilled if the exact category is ab
elian with enough projectives.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sota Asai (Osaka)
DTSTART:20221031T130000Z
DTEND:20221031T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/109
DESCRIPTION:Title: TF equivalence classes and canonical decompositions
for E-tame algebras\nby Sota Asai (Osaka) as part of Paris algebra se
minar\n\n\nAbstract\nThis is joint work with Osamu Iyama. Let $A$ be a fin
ite dimensional algebra over an algebraically closed field. Then the numer
ical torsion pairs of Baumann-Kamnitzer-Tingley give an equivalence relati
on on the real Grothendieck group of finitely generated projective $A$-mod
ules\, which is called TF equivalence. By results of Yurikusa and Bruestle
-Smith-Treffinger\, we have that the g-vector cone of each 2-term presilti
ng complex is a TF equivalence class. To get more TF equivalence classes\,
we can use canonical decompositions of elements in the (integral) Grothen
dieck group of finitely generated projectives introduced by Derksen-Fei. W
e have showed that the cone defined by the canonical decomposition of each
element is contained in some single TF equivalence class. Moreover\, we h
ave also obtained that\, if $A$ is an E-tame algebra\, then this cone is p
recisely a TF equivalence class. In this talk\, I will explain these resul
ts and some important steps to prove them.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/10
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Marin (Amiens and CNRS)
DTSTART:20221114T130000Z
DTEND:20221114T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/110
DESCRIPTION:Title: Geometric realization via random variables\nby
Ivan Marin (Amiens and CNRS) as part of Paris algebra seminar\n\nLecture h
eld in room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbstra
ct\nTopological spaces up to (weak) equivalences are\nfaithfully represent
ed by simplicial combinatorial\nstructures. Through an identification of t
he\n$n$-dimensional simplex with the space of probability\nmeasures on a f
inite set of size $n+1$\, we investigate\nwhat happens when it is replaced
by the\nspace of random variables that naturally lies 'above' it.\nBy thi
s procedure\, we obtain in particular a simple description\nof the classif
ying set of a (discrete) group\, and also\na new concept of geometric real
ization. This new one\nalso induces an equivalence of categories up to hom
otopy\nwith simplicial sets and topological spaces. The 'probability-law'\
nmap then defines a natural transformation between the\ntwo corresponding
Quillen equivalences.\n\nIn-person talk at the room 01 of the Institut Hen
ri Poincaré\, Paris\, France\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euiyong Park (Seoul)
DTSTART:20221205T130000Z
DTEND:20221205T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/111
DESCRIPTION:Title: Extended crystal structures of Hernandez-Leclerc ca
tegories\nby Euiyong Park (Seoul) as part of Paris algebra seminar\n\n
\nAbstract\nIn this talk\, we will discuss the categorical crystal structu
re on the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. We de
fine extended crystals for quantum groups and show that there is a braid g
roup action on extended crystals. We then explain how the set of the isom
orphism classes of simple modules in $\\mathscr{C}_\\mathfrak{g}^0$ has an
extended crystal structure\, and discuss the braid group action from the
viewpoint of the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$
. This talk is based on joint work with M. Kashiwara (arXiv: 2111.07255 an
d 2207.11644).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustavo Jasso and Fernando Muro (Lund and Sevilla)
DTSTART:20221121T130000Z
DTEND:20221121T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/112
DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, I
\nby Gustavo Jasso and Fernando Muro (Lund and Sevilla) as part of Par
is algebra seminar\n\n\nAbstract\nIn these two talks\, we will start by in
troducing a result which establishes the existence and uniqueness of (DG)
enhancements for triangulated categories which admit an additive generator
whose endomorphism algebra is finite-dimensional (over a perfect field).
We will then present a generalisation of this result that allows us to tre
at a larger class of triangulated categories\, which instead admit a gener
ator with a strong regularity property (a so-called dZ-cluster tilting obj
ect). We will also explain how our result\, combined with crucial theorems
of August and Hua-Keller\, leads to a positive solution of the Donovan-We
myss Conjecture for contraction algebras as observed by Keller. We will al
so comment on some details about the proof.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Muro and Gustavo Jasso (Sevilla and Lund)
DTSTART:20221128T130000Z
DTEND:20221128T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/113
DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, I
I\nby Fernando Muro and Gustavo Jasso (Sevilla and Lund) as part of Pa
ris algebra seminar\n\n\nAbstract\nIn these two talks\, we will start by i
ntroducing a result which establishes the existence and uniqueness of (DG)
enhancements for triangulated categories which admit an additive generato
r whose endomorphism algebra is finite-dimensional (over a perfect field).
We will then present a generalisation of this result that allows us to tr
eat a larger class of triangulated categories\, which instead admit a gene
rator with a strong regularity property (a so-called dZ-cluster tilting ob
ject). We will also explain how our result\, combined with crucial theorem
s of August and Hua-Keller\, leads to a positive solution of the Donovan-W
emyss Conjecture for contraction algebras as observed by Keller. We will a
lso comment on some details about the proof.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Rouquier (UCLA)
DTSTART:20221212T130000Z
DTEND:20221212T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/114
DESCRIPTION:Title: Coherent realizations of 2-representations\nby
Raphaël Rouquier (UCLA) as part of Paris algebra seminar\n\n\nAbstract\n2
-representations of Kac-Moody algebras arise algebraically and as categori
es of constructible sheaves. We will discuss two settings involving cohere
nt sheaves: derived cotangent bundles to spaces of quiver representations
and spaces of quasi-maps in flag varieties.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alireza Nasr-Isfahani (IPM Isfahan)
DTSTART:20230116T130000Z
DTEND:20230116T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/115
DESCRIPTION:Title: Lower bound cluster algebras generated by projectiv
e cluster variables\nby Alireza Nasr-Isfahani (IPM Isfahan) as part of
Paris algebra seminar\n\n\nAbstract\nWe introduce the notion of a lower (
upper) bound cluster algebra generated by projective cluster variables. Pr
ojective cluster variables are often categorified\nby projective modules o
f the corresponding quiver with relations.\nWe show that under an acyclici
ty assumption\, the cluster algebra and the lower bound cluster\nalgebra g
enerated by projective cluster variables coincide.\nIn this case\, we use
our results to construct a basis for the cluster algebra.\nWe also show th
at the coincidence between cluster algebra and the lower bound cluster\nal
gebra generated by projective cluster variables holds beyond acyclic seeds
. Part of this talk is based on joint work with Karin Baur. - This talk wi
ll be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (University at Albany)
DTSTART:20230123T130000Z
DTEND:20230123T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/116
DESCRIPTION:Title: A generalization of the Murnaghan-Nakayama rule for
$K$-$k$-Schur and $k$-Schur functions\nby Duc-Khanh Nguyen (Universit
y at Albany) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce
a generalization of $K$-$k$-Schur functions and k-Schur functions via the
Pieri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized
functions. The rule is described explicitly in the cases of $K$-$k$-Schur
functions and $k$-Schur functions\, with concrete descriptions and algori
thms for coefficients. Our work recovers the result of Bandlow\, Schilling
\, and Zabrocki for $k$-Schur functions\, and explains it as a degeneratio
n of the rule for $K$-$k$-Schur functions. In particular\, many other spec
ial cases promise to be detailed in the future. - This talk will be on Zoo
m only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Williams (Harvard)
DTSTART:20230605T120000Z
DTEND:20230605T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/117
DESCRIPTION:Title: The amplituhedron and cluster algebras\nby Laur
en Williams (Harvard) as part of Paris algebra seminar\n\n\nAbstract\nI wi
ll give a gentle introduction to the amplituhedron\, a geometric object th
at was introduced in the context of scattering amplitudes in N=4 super Yan
g Mills. I'll then explain some of the connections of the amplituhedron t
o cluster algebras.\n\nThis talk will take place in hybrid mode at the Ins
titut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (IHES)
DTSTART:20230130T130000Z
DTEND:20230130T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/118
DESCRIPTION:Title: Coxeter quiver representations in fusion categories
and Gabriel’s theorem\nby Edmund Heng (IHES) as part of Paris algeb
ra seminar\n\n\nAbstract\nOne of the most celebrated theorems in the theor
y of quiver representations is undoubtedly Gabriel’s theorem\, which rev
eals a deep connection between quiver representations and root systems ari
sing from Lie algebras. In particular\, Gabriel’s theorem shows that the
finite-type quivers are classified by the ADE Dynkin diagrams and the ind
ecomposable representations are in bijection with the underlying positive
roots. Following the works of Dlab—Ringel\, the classification can be ge
neralised to include all the other Dynkin diagrams (including BCFG) if one
considers the more general notion of valued quivers (K-species) represent
ations instead.\n\nWhile the theories above relate (valued) quiver represe
ntations to root systems arising from Lie algebras\, the aim of this talk
is to generalise Gabriel’s theorem in a slightly different direction usi
ng root systems arising in Coxeter theory. Namely\, we shall introduce a n
ew notion of Coxeter quivers and their representations built in (other) fu
sion categories\, where we have a generalised Gabriel’s theorem as follo
ws: a Coxeter quiver has finitely many indecomposable representations if a
nd only if its underlying graph is a Coxeter-Dynkin diagram — including
the non-crystallographic types H and I. Using a similar notion of reflecti
on functors as introduced by Bernstein—Gelfand—Ponomarev\, we shall al
so show that the isomorphism classes of indecomposable representations of
a Coxeter quiver are in bijection with the positive roots associated to th
e root system of the underlying Coxeter graph. --\nThis talk will take pla
ce in hybrid mode at the IHP.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Shanghai Jiao Tong)
DTSTART:20230220T130000Z
DTEND:20230220T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/119
DESCRIPTION:Title: Bracelets are theta functions for surface cluster a
lgebras\nby Fan Qin (Shanghai Jiao Tong) as part of Paris algebra semi
nar\n\n\nAbstract\nThe skein algebra of a marked surface admits the basis
of bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-W
illiams. As a cluster algebra\, it also admits the theta basis from the cl
uster scattering diagram by Gross-Hacking-Keel-Kontsevich. In a joint work
with Travis Mandel\, we show that the two bases coincide except for the o
nce-punctured torus. Our results extend to quantum cluster algebras with c
oefficients arising from the surface even in punctured cases. Long-standin
g conjectures on strong positivity and atomicity follow as corollaries.\n\
nExceptionally\, this talk will take place in hybrid mode in room 1013 of
the Sophie Germain building (8\, place Aurélie Nemours\, 75013 Paris).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/11
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wille Liu (Taipei)
DTSTART:20230213T130000Z
DTEND:20230213T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/120
DESCRIPTION:Title: Translation functors for trigonometric double affin
e Hecke algebras\nby Wille Liu (Taipei) as part of Paris algebra semin
ar\n\n\nAbstract\nThe double affine Hecke algebra was introduced by Chered
nik around 1995 as a tool in his study of Macdonald polynomials. Its degen
erate version\, called trigonometric double affine Hecke algebra (TDAHA)\,
has also turned out to be linked to different areas\, notably to the repr
esentation theory of $p$-adic groups.\n\nGiven a root system\, the TDAHA $
H_c$ depends on a family of complex parameters $c$. Given two families of
parameters $c$ and $c'$ whose difference takes integer values\, there exis
ts a triangle equivalence between the bounded derived categories of the co
rresponding TDAHAs\, which we call translation functor. The objective of t
his talk is to explain the construction of this functor. \n\nThis talk wil
l be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Osaka Metropolitan)
DTSTART:20230227T130000Z
DTEND:20230227T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/121
DESCRIPTION:Title: Maximal self-orthogonal modules and a new generaliz
ation of tilting modules\nby Haruhisa Enomoto (Osaka Metropolitan) as
part of Paris algebra seminar\n\n\nAbstract\nWe study self-orthogonal modu
les\, i.e.\, modules T such that Ext^i(T\, T) = 0 for all i > 0. We introd
uce projectively Wakamatsu-tilting modules (pW-tilting modules) as a gener
alization of tilting modules. If A is a representation-finite algebra\, ev
ery self-orthogonal A-module can be completed to a pW-tilting module\, and
the following classes coincide: pW-tilting modules\, Wakamatsu tilting mo
dules\, maximal self-orthogonal modules\, and self-orthogonal modules T wi
th |T| = |A|. We also prove that every self-orthogonal module over a repre
sentation-finite Iwanaga-Gorenstein algebra has finite projective dimensio
n. We finally explain some open conjectures on self-orthogonal modules.\n\
nThis talk will be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keyu Wang (Paris Cité)
DTSTART:20230206T130000Z
DTEND:20230206T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/122
DESCRIPTION:Title: QQ˜ -systems for twisted quantum affine algebras\nby Keyu Wang (Paris Cité) as part of Paris algebra seminar\n\n\nAbstr
act\nAs a part of Langlands duality\, certain equations were found in two
different areas of mathematics. They are known as Baxter’s TQ systems an
d the QQ type systems\, as they trace back to Baxter’s study on integrab
le models in the 1970s. During the same decade\, similar systems of equati
ons were discovered in the area of ordinary differential equations (ODE) b
y Sibuya\, Voros and others. Today\, this remarkable correspondence is rea
lized as a duality between representation theory of nontwisted quantum aff
ine algebras (QAA) and the theory of opers for their Langlands dual Lie al
gebras.\n\nWe are interested in this duality when the roles of the affine
Lie algebra and its dual are exchanged. When the nontwisted QAA is of type
BCFG\, its dual will be a twisted QAA. To exchange their roles amounts to
studying representations of twisted QAAs.\n\nIn this talk\, we will begin
by reviewing this story. We will explain the representation theory of twi
sted QAAs and their Borel algebras. We will explain the expected relations
hip between twisted and nontwisted types\, and we will establish TQ system
s and QQ^{~} systems for twisted QAAs.\n\nThis talk will take place in hyb
rid mode at the IHP.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Yekutieli (Ben Gurion University)
DTSTART:20230403T120000Z
DTEND:20230403T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/123
DESCRIPTION:Title: An Algebraic Approach to the Cotangent Complex\
nby Amnon Yekutieli (Ben Gurion University) as part of Paris algebra semin
ar\n\n\nAbstract\nLet $B/A$ be a pair of commutative rings. We propose an
algebraic approach to the cotangent complex $L_{B/A}$. Using commutative s
emi-free DG ring resolutions of B relative to A\, we construct a complex o
f $B$-modules $LCot_{B/A}$. This construction works more generally for a p
air $B/A$ of commutative DG rings.\n\nIn the talk\, we will explain all th
ese concepts. Then we will discuss the important properties of the DG $B$-
module $LCot_{B/A}$. It time permits\, we'll outline some of the proofs.\n
\nIt is conjectured that for a pair of rings $B/A$\, our $LCot_{B/A}$ coin
cides with the usual cotangent complex $L_{B/A}$\, which is constructed by
simplicial methods. We shall also relate $LCot_{B/A}$ to modern homotopic
al versions of the cotangent complex.\n\n\nSlides: https://sites.google.co
m/view/amyekut-math/home/lectures/cotangent\n\n(updated 18 March 2023)\n\n
\nThis talk will be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luc Pirio (Versailles)
DTSTART:20230306T130000Z
DTEND:20230306T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/124
DESCRIPTION:Title: Hyperlogarithmic functional identities on del Pezzo
surfaces\nby Luc Pirio (Versailles) as part of Paris algebra seminar\
n\n\nAbstract\nFor any d in {1\,…\,6}\, we prove that the web of conics
on a del Pezzo surface of degree d carries a functional identity HLog(7-d)
whose components are antisymmetric hyperlogarithms of weight 7-d. Our app
roach is uniform with respect to d and relies on classical results about t
he action of the Weyl group on the set of lines on the del Pezzo surface.
These hyperlogarithmic functional identities HLog(7-d) are natural genera
lizations of the classical 3-term and (Abel's) 5-term identities of the l
ogarithm and the dilogarithm\, which are the identities HLog(1) and HLog(2
) corresponding to the cases d=6 and d=5 respectively.\n\nIf time allows\,
I will give a list of many nice properties enjoyed by the 5-term identity
of the dilogarithm and will explain that most of these properties (such a
s being of cluster type) have natural generalizations which are satisfied
by the weight 3 hyperlogarithmic identity HLog(3).\n\nThe talk will be mai
nly based on the preprint arXiv:2301.06775 written with Ana-Maria Castrave
t.\n\nExceptionally\, this talk will take place in hybrid mode in room 101
3 of the Sophie Germain building (8\, place Aurélie Nemours\, 75013 Paris
).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Holstein (Hamburg)
DTSTART:20230313T130000Z
DTEND:20230313T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/125
DESCRIPTION:Title: Enriched Koszul duality for dg categories\nby J
ulian Holstein (Hamburg) as part of Paris algebra seminar\n\n\nAbstract\nT
he category of dg categories is related by Koszul duality to a certain cat
egory of colagebras\, so-called pointed curved coalgebras. In this talk we
wil review this Quillen equivalence and observe that it is in fact quasi-
monoidal. By constructing internal homs of pointed curved coalgebras we ca
n then construct a concrete closed monoidal model for dg categories. In pa
rticular this gives natural descriptions of mapping spaces and internal ho
ms between dg categories. This is joint work with A. Lazarev.\n\nException
ally\, this talk will take place in hybrid mode in room 1013 of the Sophie
Germain building (8\, place Aurélie Nemours\, 75013 Paris).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Bochum)
DTSTART:20230320T130000Z
DTEND:20230320T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/126
DESCRIPTION:Title: Expander representations\nby Markus Reineke (Bo
chum) as part of Paris algebra seminar\n\n\nAbstract\nDimension expanders\
, introduced by Wigderson and Lubotzky-Zelmanov\, are a linear algebra ana
logue of the notion of expander graphs. We interpret this notion in terms
of quiver representations\, as a quantitative variant of stability. We use
Schofield’s recursive description of general subrepresentations to re-d
erive existence of dimension expanders and to determine optimal expansion
coefficients.\n\nThe talk will take place in hybrid mode at the IHP.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Koshevoy (IHES)
DTSTART:20230327T120000Z
DTEND:20230327T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/127
DESCRIPTION:Title: Polyhedral parametrization of canonical bases\n
by Gleb Koshevoy (IHES) as part of Paris algebra seminar\n\n\nAbstract\nPa
rametrizations of the canonical bases\, string basis and theta basis\, ca
n be obtained by the tropicalization of the Berenstein-Kazhdan decoration
function and the Gross-Hacking-Keel-Kontsevich potential respectively. Fo
r a classical Lie algebra and a reduced decomposition $\\mathbf i$\, the
decorated graphs are constructed algorithmically\, vertices of such graph
s are labeled by monomials which constitute the set of monomials of the Be
renstein-Kazhdan potential. Due to this algorithm we obtain a characteri
zation of $\\mathbf i$-trails introduced by Berenstein and Zelevinsky. Our
algorithm uses multiplication and summations only\, its complexity is li
near in time of writing the monomials of the potential. For SL_n\, there i
s an algorithm due to Gleizer and Postnikov which gets all monomials of th
e Berenstein-Kazhdan potential using combinatorics of wiring diagrams. For
this case\, our algorithm uses simpler combinatorics and is faster than t
he Gleizer-Postnikov algorithm. The cluster algorithm due to Genz\, Schuma
nn and me is polynomial in time but it uses divisions of polynomials of se
veral variables.\nIf time permits I will report on applications of decorat
ed graphs to analysis of the Newton polytopes of F-polynomials related to
the Gross-Hacking-Keel-Kontsevich potentials. The talk is based on joint
works with Volker Genz and Bea Schumann and with Yuki Kanakubo and Toshiki
Nakashima.\n\nThis talk will take place in hybrid mode at the IHP.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Vasserot (Paris Cité)
DTSTART:20230417T120000Z
DTEND:20230417T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/128
DESCRIPTION:Title: Critical convolution algebras and quantum loop grou
ps\nby Eric Vasserot (Paris Cité) as part of Paris algebra seminar\n\
n\nAbstract\nWe introduce a new family of algebras attached to quivers wit
h potentials\, using critical K-theory and critical Borel-Moore homology.
They generalize the convolution algebras attached to quivers by Nakajima.
We give some applications to cohomological and K-theoretical Hall algebras
\, to shifted quantum loop groups\, and to Kirillov-Reshetikhin and prefun
damental representations. \n\nThis talk will take place in hybrid mode at
the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Owen Garnier (Amiens)
DTSTART:20230424T120000Z
DTEND:20230424T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/129
DESCRIPTION:Title: Homology of a category and the Dehornoy-Lafont orde
r complex\nby Owen Garnier (Amiens) as part of Paris algebra seminar\n
\n\nAbstract\nThe work of Squier and Kobayashi proves that the homology of
a monoid can be computed using a so called complete rewriting system\, wh
ich acts as a convenient presentation of the monoid.\n\nLater\, Dehornoy a
nd Lafont noted that such a convenient presentation arises in particular w
hen considering monoids satisfying combinatorial assumptions regarding exi
stence of lcms. This gave rise to the so called Dehornoy-Lafont order comp
lex\, which was used to compute the homology of complex braid groups by Ca
llegaro and Marin.\n\nAfter giving a quick summary of these works\, I will
present a generalization of this latter complex to the case of a category
which again satisfies convenient combinatorial assumptions. \n\nOf course
\, as my "true" goal is to compute the homology of a group using some asso
ciated category\, I will also give a link between the homology of a catego
ry\, that of its enveloping groupoid\, and that of a group which is equiva
lent to the said groupoid.\n\nLastly\, I will explain an application to th
e case of the complex braid group $B_{31}$\, which is studied through its
associated Garside category\, and which was not directly covered by previo
us approaches.\n\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/12
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Chapoton (CNRS Strasbourg)
DTSTART:20230619T120000Z
DTEND:20230619T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/130
DESCRIPTION:Title: Posets and fractional Calabi-Yau categories\nby
Frédéric Chapoton (CNRS Strasbourg) as part of Paris algebra seminar\n\
n\nAbstract\nIn combinatorics\, several famous enumeration results involve
a special kind of product formula. The very same kind of product formula
gives the Milnor number of an isolated quasi-homogenous singularity. It se
ems possible that one could relate combinatorics and singularities by mean
s of derived categories: on the one hand\, modules over incidence algebras
of partially ordered sets (posets) and on the other hand\, some kind of F
ukaya-like category that should categorify the Milnor fibration. Even if p
art of this remains very unprecise and vague\, this implies many concrete
conjectures about derived equivalences between posets. \n\nThis talk will
take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Bershtein (Moscow and IPMU)
DTSTART:20230508T120000Z
DTEND:20230508T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/131
DESCRIPTION:Title: Cluster Hamiltonian reductions: examples\nby Mi
khail Bershtein (Moscow and IPMU) as part of Paris algebra seminar\n\n\nAb
stract\nI will talk about an\, in general conjectural\, construction of a
X-cluster structure on certain Hamiltonian reduction of a X-cluster variet
y. There are two main classes of examples of such constructions: moduli sp
aces of framed local systems with special monodromies and phase spaces of
Goncharov-Kenyon integrable systems. The first class includes the phase sp
ace of open XXZ chain and Ruijsenaars integrable systems. The second class
includes integrable systems corresponding to the q-difference Painleve eq
uations.\n\nBased on works in progress and discussions with P. Gavrylenko\
, A. Marshakov\, M. Semenyakin\, A. Shapiro\, G. Schrader.\n\nThis talk wi
ll take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haibo Jin (Cologne)
DTSTART:20230515T120000Z
DTEND:20230515T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/132
DESCRIPTION:Title: A complete derived invariant and silting theory for
graded gentle algebras\nby Haibo Jin (Cologne) as part of Paris algeb
ra seminar\n\n\nAbstract\nWe show that among the derived equivalent classe
s of homologically smooth and proper graded gentle algebras there is only
one class whose perfect derived category does not admit silting objects.\n
\nAs one application we give a sufficient and necessary condition for any
homologically smooth and proper graded gentle algebra under which all pre
-silting objects in its perfect derived category may be complete into silt
ing objects.\n\nAs another application we confirm a conjecture by Lekili a
nd Polishchuk that the geometric invariants which they construct for homol
ogically smooth and proper graded gentle algebras are a complete derived i
nvariant. Hence\, we obtain a complete invariant for partially wrapped Fuk
aya categories of surfaces with stops. \n\nThis is a report on joint work
with Sibylle Schroll and Zhengfang Wang.\n\nThis talk will take place in h
ybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Positselski (Prague)
DTSTART:20230522T121500Z
DTEND:20230522T131500Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/133
DESCRIPTION:Title: The homomorphism removal and repackaging constructi
on\nby Leonid Positselski (Prague) as part of Paris algebra seminar\n\
n\nAbstract\nThis work is an attempt to understand the maximal natural gen
erality context for\nthe Koenig-Kuelshammer-Ovsienko construction in the t
heory of quasi-hereditary algebras by\nputting it into a category-theoreti
c context. Given a field k and a k-linear exact category E \nwith a chosen
set of nonzero objects F_i such that every object of E is a finitely iter
ated \nextension of some F_i\, we construct a coalgebra C whose irreducibl
e comodules L_i are indexed by the same indexing set\, and an exact functo
r from C-comod to E taking L_i to F_i such that the spaces Ext^n between L
_i in C−comod are the same as between F_i in E (for n > 0). Thus\, the a
belian category C−comod is obtained from the exact category E by removin
g all the nontrivial homomorphisms between the chosen objects F_i in E whi
le keeping the Ext spaces unchanged. The removed homomorphisms are then re
packaged into a semialgebra S over C such that the exact category E can be
recovered as the category of S-semimodules induced from finite-dimensiona
l C-comodules. The construction used Koszul duality twice: once as absolut
e and once as relative Koszul duality.\n\n\nThis talk will take place in h
ybrid format at the GAP conference at the Institut Henri Poincaré\, cf. <
a href="https://personal.psu.edu/mps16/hirsutes2023/gap2023.html">GAP.
\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine De Saint Germain (Hong Kong U.)
DTSTART:20230612T120000Z
DTEND:20230612T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/134
DESCRIPTION:Title: Cluster additive functions and acyclic cluster alge
bras\nby Antoine De Saint Germain (Hong Kong U.) as part of Paris alge
bra seminar\n\n\nAbstract\nIn his study of combinatorial features of clust
er categories and cluster-tilted algebras\, Ringel introduced an analogue
of additive functions of stable translation quivers called cluster-additiv
e functions. \n\nIn this talk\, we will define cluster-additive functions
associated to any acyclic mutation matrix\, relate them to tropical point
s of the cluster X-variety\, and realise their values as certain compatibi
lity degrees between functions on the cluster A-variety associated to the
Langlands dual mutation matrix (in accordance with the philosophy of Fock-
Goncharov). This is based on joint work with Peigen Cao and Jiang-Hua Lu.
\n\nThis talk will take place in hybrid mode at the Institut Henri Poincar
é.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Rivera (Purdue)
DTSTART:20230626T120000Z
DTEND:20230626T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/135
DESCRIPTION:Title: Loop spaces and bialgebras\nby Manuel Rivera (P
urdue) as part of Paris algebra seminar\n\n\nAbstract\nI will discuss seve
ral interlocked constructions giving rise to bialgebra structures all of w
hich have parallel algebraic and topological interpretations. The bialgebr
as considered will be of different flavors depending on the compatibility
between the product and coproduct\; for instance\, we will see examples of
Hopf\, Frobenius\, infinitesimal and Lie bialgebras. These structures app
ear when analyzing the role of loop spaces in homotopy theory and manifold
topology and reveal new results regarding the algebraic nature of geometr
ic space.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duncan Laurie (Oxford)
DTSTART:20231002T120000Z
DTEND:20231002T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/136
DESCRIPTION:Title: Quantum toroidal algebras: braid group actions\, au
tomorphisms\, and representation theory\nby Duncan Laurie (Oxford) as
part of Paris algebra seminar\n\n\nAbstract\nQuantum toroidal algebras Uq(
g_tor) occur as the Drinfeld\nquantum affinizations of quantum affine alge
bras. In particular\; they\ncontain (and are generated by) a horizontal an
d vertical copy of the\naffine quantum group. In type A\, Miki obtained an
automorphism of\nUq(g_tor) exchanging these subalgebras\, which has since
played a\ncrucial role in the investigation of its structure and represen
tation\ntheory.\n\nIn this talk\; we shall construct an action of the exte
nded double\naffine braid group B on the quantum toroidal algebra in all u
ntwisted\ntypes. In the simply laced cases\, using this action and certain
\ninvolutions of B we obtain automorphisms and anti-automorphisms of\nUq(g
_tor) which exchange the horizontal and vertical subalgebras\, thus\ngener
alising the results of Miki. We shall then discuss potential\nextensions o
f these results\, and applications to the representation\ntheory of quantu
m toroidal algebras.\n\nThis talk will take place in hybrid mode at the In
stitut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bill Crawley-Boevey (Bielefeld)
DTSTART:20230713T120000Z
DTEND:20230713T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/137
DESCRIPTION:Title: Integral representations of quivers\nby Bill Cr
awley-Boevey (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nI
n the 1990s\, I classified rigid representations of a quiver by finitely g
enerated free modules over a principal ideal ring. I shall extend the resu
lts to representations of a quiver by finitely generated projective module
s over an arbitrary commutative ring. \n\nThis talk will kindly be shared
by the organisation of the conference \nHomological algebra and representation theor
y. It will take place in hybrid mode at Karlovasi (Samos\, Greece).\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Thomas (Heidelberg)
DTSTART:20231127T130000Z
DTEND:20231127T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/138
DESCRIPTION:Title: A q-deformation of sl2 and the Witt algebra\nby
Alexander Thomas (Heidelberg) as part of Paris algebra seminar\n\n\nAbstr
act\nI will present new q-deformations of Lie algebras linked to the modul
ar group and the q-rational numbers as defined by Morier-Genoud and Ovsien
ko. In particular\, I will describe deformations of sl2 and the Witt algeb
ra. These deformations are realized as differential operators acting on th
e hyperbolic plane\, giving new insights into q-rationals. \n\nThis talk w
ill take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norihiro Hanihara (IPMU)
DTSTART:20231023T120000Z
DTEND:20231023T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/139
DESCRIPTION:Title: Silting-cluster tilting correspondences\nby Nor
ihiro Hanihara (IPMU) as part of Paris algebra seminar\n\n\nAbstract\nClus
ter categories are fundamental objects in representation theory\, includin
g such topics as cluster algebras\, tilting theory\, singularity theory. T
he theory of Amiot\, Guo\, and Keller shows that tilting/silting objects i
n derived categories (of a finite dimensional algebra or of a Calabi-Yau d
g algebra) give rise to cluster tilting objects in the cluster category. W
e study such correspondences between silting objects and cluster tilting o
bjects. We propose a conjecture on the liftability of cluster tilting obje
cts in the cluster category to silting objects\, and discuss some evidence
for it. This is based on a joint work with Osamu Iyama.\n\nThis talk will
take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/13
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Se-jin Oh (Sungkyunkwan U.)
DTSTART:20231016T120000Z
DTEND:20231016T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/140
DESCRIPTION:Title: A noncommutative algebra arising from the $t$-quant
ized Cartan matrix\nby Se-jin Oh (Sungkyunkwan U.) as part of Paris al
gebra seminar\n\n\nAbstract\nThe quantum Cartan matrix appears ubiquitousl
y as a key combinatorial ingredient in the representation theory of quantu
m affine algebras. Through the generalized Schur-Weyl duality\, it also pl
ays a central role in the one of quiver Hecke algebras and the quantum uni
potent coordinate ring of (skew-)symmetric finite type. Even though there
are quiver Hecke algebras and quantum unipotent coordinate rings of non (s
kew-)symmetric finite type\, there is no counterpart in representation the
ory as far as I and my collaborators understand.\nIn this talk\, I introdu
ce a non-commutative ring over $\\Q(q^{1/2}$)\, which is expected to be a
quantum Grothendieck ring for a Hernandez-Leclerc category\, if such a rep
resentation theory exists\, by using the t-quantized Cartan matrix. When w
e consider its heart subalgebra\, the algebra is isomorphic to the quantu
m unipotent coordinate ring of any finite type.\nThis talk is mainly based
on joint work with Kashiwara\, Jang and Lee.\n\nThis talk will take place
on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Shanghai Jiaotong)
DTSTART:20231009T120000Z
DTEND:20231009T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/141
DESCRIPTION:Title: Analogs of dual canonical bases for cluster algebra
s from Lie theory\nby Fan Qin (Shanghai Jiaotong) as part of Paris alg
ebra seminar\n\n\nAbstract\nThe (quantized) coordinate rings of many inter
esting varieties from Lie theory are (quantum) cluster algebras. We constr
uct the common triangular bases for these algebras. Such bases provide ana
logs of the dual canonical bases\, whose existence has been long expected
in cluster theory. For symmetric Cartan matrices\, they are positive and a
dmit monoidal categorification after base change. We employ a unified appr
oach based on cluster algebra operations. Our results apply to algebraic g
roups\, double Bott-Samelson cells\, and braid varieties\, etc. Additional
ly\, we find applications in representations of quantum affine algebras.\n
\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (IMJ-PRG)
DTSTART:20231106T130000Z
DTEND:20231106T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/142
DESCRIPTION:Title: Relative Calabi-Yau structures and extriangulated c
luster categories\nby Merlin Christ (IMJ-PRG) as part of Paris algebra
seminar\n\n\nAbstract\nWe will begin with an introduction to relative Cal
abi-Yau structures in the sense of Brav-Dyckerhoff\, generalizing the noti
on of a Calabi-Yau triangulated (or dg-) category to functors. Via so-call
ed relative theory\, Calabi-Yau functors give rise to extriangulated categ
ories\, which are Frobenius 2-Calabi-Yau. We apply this to examples of clu
ster categories of surfaces\, categorifying the surface cluster algebras w
ith coefficients in the boundary arcs. This talk is mostly based on my pre
print arXiv:2209.06595. \n\nThis talk will take place in hybrid mode at th
e Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Francone (Lyon)
DTSTART:20231113T130000Z
DTEND:20231113T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/143
DESCRIPTION:Title: Minimal monomial lifting of cluster algebras and br
anching problems\nby Luca Francone (Lyon) as part of Paris algebra sem
inar\n\n\nAbstract\nThe minimal monomial lifting is a sort of homogenisati
on technique\, whose goal is to identify a cluster algebra structure on ce
rtain "suitable for lifting" schemes\, compatibly with a base cluster stru
cture on a distinguished subscheme. This technique allows to recover\, by
geometric methods\, some well known cluster structures. In this talk\, we
will present this technique and discuss applications to branching problems
in representation theory of complex reductive groups.\n\nThis talk will t
ake place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wahei Hara (IPMU)
DTSTART:20231120T130000Z
DTEND:20231120T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/144
DESCRIPTION:Title: Spherical objects in dimension two and three\nb
y Wahei Hara (IPMU) as part of Paris algebra seminar\n\n\nAbstract\nIn thi
s talk\, we discuss the classification problem of spherical “like” obj
ects in various geometric settings including the minimal resolution of an
ADE surface singularity and a 3-fold flopping contraction. The classificat
ion of spherical objects is related to questions about the autoequivalence
groups or Bridgeland stability conditions\, but in 3-fold settings\, this
is not always a correct problem to ask. In the first half of the talk\, w
e discuss what kind of objects should be classified\, and in the second ha
lf\, a sketch of the proof will be explained. Our new technique can also b
e applied to the heart of a bounded t-structure\, and classifies all t-str
uctures of the associated null category. As a corollary\, the connectednes
s of the space of stability conditions follows. This is all joint work wit
h Michael Wemyss.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Berggren (Kentucky)
DTSTART:20231204T130000Z
DTEND:20231204T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/145
DESCRIPTION:Title: Consistent Dimer Models on Surfaces with Boundary\nby Jonah Berggren (Kentucky) as part of Paris algebra seminar\n\n\nAbs
tract\nA dimer model is a quiver with faces embedded in a surface. Dimer m
odels on the disk and torus are particularly well-studied\, though these t
heories have remained largely separate. Various “consistency conditions
” may be imposed on dimer models on the disk or torus with implications
relating to 3-Calabi-Yau properties and categorification.\n \nWe extend ma
ny of these definitions and results to the setting of general surfaces wit
h boundary. We show that the completed dimer algebra of a “strongly cons
istent” dimer model is bimodule internally 3-Calabi-Yau with respect to
its boundary idempotent. As a consequence\, the Gorenstein-projective modu
le category of the completed boundary algebra of a suitable dimer model ca
tegorifies the cluster algebra given by its underlying ice quiver. We give
a class of examples of annulus models satisfying the requisite conditions
. \n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (MIT)
DTSTART:20231218T130000Z
DTEND:20231218T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/146
DESCRIPTION:Title: Cluster structures on braid and Richardson varietie
s\nby Melissa Sherman-Bennett (MIT) as part of Paris algebra seminar\n
\n\nAbstract\nIn 2014\, Leclerc gave a construction of a conjectural clust
er structure on open Richardson varieties in types ADE. His construction w
as categorical in nature\, involving preprojective algebra modules. His co
njecture inspired work on cluster structures on braid varieties in arbitra
ry type\, which generalize open Richardsons. Two cluster structures on bra
id varieties were recently constructed. The first one\, based on ideas and
techniques from symplectic topology\, is due to Casals-Gorsky-Gorsky-Le-S
hen-Simental. I will discuss the other\, which is joint work with Galashin
\, Lam and Speyer. Our main geometric tool is the Deodhar decomposition. I
n type A\, our quivers are given by "3D plabic graphs"\, which generalize
Postnikov's plabic graphs for the Grassmannian. Time permitting\, I will a
lso discuss related work with Serhiyenko\, where we show that for type A R
ichardsons\, Leclerc's conjectural categorical construction does in fact g
ive a cluster structure\, with quivers again given by 3D plabic graphs.\n\
nThis talk will be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JiaRui Fei (Shanghai Jiao Tong)
DTSTART:20231211T130000Z
DTEND:20231211T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/147
DESCRIPTION:Title: Crystal Structure of Upper Cluster Algebras\nby
JiaRui Fei (Shanghai Jiao Tong) as part of Paris algebra seminar\n\n\nAbs
tract\nWe describe the upper seminormal crystal structure for the $\\mu$-s
upported $\\delta$-vectors for any quiver with potential with reachable fr
ozen vertices\, or equivalently for the tropical points of the correspondi
ng cluster $\\mathcal{X}$-variety. We show that the crystal structure can
be algebraically lifted to the generic basis of the upper cluster algebra.
This can be viewed as an additive categorification of the crystal structu
re arising from cluster algebras. We introduce the biperfect bases and the
strong biperfect bases in the cluster algebra setting and give a descript
ion of all strong biperfect bases.\n\nThis talk will be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Asplund (Stony Brook U.)
DTSTART:20240115T130000Z
DTEND:20240115T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/148
DESCRIPTION:Title: Relative Ginzburg algebras and Chekanov-Eliashberg
dg-algebras\nby Johan Asplund (Stony Brook U.) as part of Paris algebr
a seminar\n\n\nAbstract\nThe Chekanov-Eliashberg dg-algebra yields a power
ful isotopy invariant of (possibly singular) Legendrian submanifolds in a
class of contact manifolds\, and is also intimately related to Fukaya cate
gories of a class of non-compact symplectic manifolds. The goal for this t
alk is to explain how the relative Ginzburg algebra associated to any ice
quiver with trivial potential is quasi-isomorphic to some Chekanov-Eliashb
erg dg-algebra. The proof is constructive. I will give a gentle introducti
on to Chekanov-Eliashberg dg-algebras and will discuss how the relation to
relative Ginzburg algebras is interesting to contact and symplectic geome
ters.\n\nThis talk will be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Beijing Normal)
DTSTART:20240122T130000Z
DTEND:20240122T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/149
DESCRIPTION:Title: Applications of the freezing operators on cluster a
lgebras\nby Fan Qin (Beijing Normal) as part of Paris algebra seminar\
n\n\nAbstract\nWe utilize freezing operators to establish connections amon
g distinct (quantum) upper cluster algebras. This approach enables us to c
ompare the quantized coordinate rings of different varieties. We prove tha
t these operators send localized (quantum) cluster monomials to localized
(quantum) cluster monomials. Furthermore\, in many instances\, they also p
reserve bases. Remarkably\, the bases constructed via freezing operators c
oincide with those obtained via localization.\n\nThis talk will take place
in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/14
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (U. of British Columbia)
DTSTART:20240311T130000Z
DTEND:20240311T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/150
DESCRIPTION:Title: Categorical cluster structure of Coulomb branches\nby Sabin Cautis (U. of British Columbia) as part of Paris algebra semi
nar\n\n\nAbstract\nCoulomb branches are certain moduli spaces arising in s
upersymmetric field theory. They include as special cases many spaces of i
ndependent interest such as double affine Hecke algebras\, certain open Ri
chardson varieties\, multiplicative Nakajima quiver varieties etc. In the
four-dimensional case\, one expects that their coordinate rings can be cat
egorified by abelian monoidal categories carrying a cluster structure.\n\n
After reviewing the mathematical construction of these Coulomb branches we
will explain how these categories are constructed and why the cluster str
ucture appears. This is joint work with Harold Williams. \n\n\n\nThis talk
will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Till Wehrhan (Bonn)
DTSTART:20240129T130000Z
DTEND:20240129T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/151
DESCRIPTION:Title: Chevalley-Monk formulas for bow varieties\nby T
ill Wehrhan (Bonn) as part of Paris algebra seminar\n\n\nAbstract\nThe the
ory of stable envelopes\, introduced by Maulik and Okounkov\, provides a f
ascinating interplay between the geometry of holomorphic symplectic variet
ies and integrable systems. We apply this theory to bow varieties which fo
rm a rich family of holomorphic symplectic varieties including type A Naka
jima quiver varieties. We then discuss a formula for the multiplication of
torus equivariant first Chern classes of tautological bundles of bow vari
eties with respect to the stable envelope basis. This formula naturally ge
neralizes the classical Chevalley-Monk formula and can be expressed in ter
ms of moves on skein-type diagrams that label the stable envelope basis. \
n\nThis talk will take place in hybrid mode at the Institut Henri Poincar
é.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dirceu Bagio (Fed. U. of Santa Catarina)
DTSTART:20240108T130000Z
DTEND:20240108T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/152
DESCRIPTION:Title: Tameness of a restricted enveloping algebra\nby
Dirceu Bagio (Fed. U. of Santa Catarina) as part of Paris algebra seminar
\n\n\nAbstract\nWe will describe a 5-dimensional Lie algebra over an algeb
raically\nclosed field of characteristic 2 and show that its restricted en
veloping algebra is special biserial\, hence tame. We obtain an explicit d
escription of all of its families of finite-dimensional indecomposable mod
ules using Crawley-Boevey's description via strings and bands of the indec
omposable modules over a special biserial algebra. This is joint work with
N. Andruskiewitsch\, S. D. Flora and D. Flores.\n\nThis talk will take pl
ace in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Janssens (UCLouvain)
DTSTART:20240212T130000Z
DTEND:20240212T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/153
DESCRIPTION:Title: Group invariants observed through a representation-
theoretical lens\nby Geoffrey Janssens (UCLouvain) as part of Paris al
gebra seminar\n\n\nAbstract\nThe leitfaden of this talk will be the genera
l problem of determining which invariants of a finite group G are determin
ed by which piece of the representation category of G over a commutative r
ing R. In the first part of the talk\, we will recall the information enco
ded by the monoidal category of complex representations and its (braided)
auto-equivalences. By doing so we will stumble on a question concerning th
e connection between two types of rigidity associated to G. The first is g
iven by the group of class-preserving outer automorphisms of G and the sec
ond is a birational invariant of the quotient variety V/G\, where V is a f
aithful representation of G. The aim of the second part of the talk will b
e to present some new perspective on them. Thereafter\, in the last part\,
we will explain how the situation changes when taking R to be a number fi
eld or its ring of integers. In particular\, the role of the theory of ari
thmetic groups will be emphasized. All along the talk\, we will mention so
me open questions and some recent contributions.\n\nThis talk will take pl
ace in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (USTC Hefei)
DTSTART:20240205T130000Z
DTEND:20240205T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/154
DESCRIPTION:Title: Exact dg categories and higher Auslander correspond
ences\nby Xiaofa Chen (USTC Hefei) as part of Paris algebra seminar\n\
n\nAbstract\nExact dg categories allow to enhance extriangulated categorie
s and\nto perform constructions like functor categories or tensor products
\nfor which the extriangulated structure alone does not suffice.\nIn parti
cular\, they yield a new approach to and a generalization\nof higher versi
ons of Auslander correspondences as established\nby Iyama and by Iyama-Sol
berg\, for example. In this talk\, I will give \nan introduction to exact
dg categories and sketch their application\nto correspondences on the exam
ple of 0-Auslander categories. \nWe will see in particular that the framew
ork of exact dg\ncategories allows to enhance the correspondences to equiv
alences\nof infinity-groupoids.\n\nThis talk will take place on Zoom only.
\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (Tsinghua)
DTSTART:20240226T130000Z
DTEND:20240226T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/156
DESCRIPTION:Title: On cluster braid groups\nby Yu Qiu (Tsinghua) a
s part of Paris algebra seminar\n\n\nAbstract\nWe introduce cluster braid
groups\, with motivations coming from the study of stability conditions on
triangulated categories. In the Coxeter-Dynkin case\, they are naturally
isomorphic to the corresponding Artin braid groups (1407.5986 and 2310.028
71). In the surface case\, they are naturally isomorphic to braid twist gr
oups (1407.0806\, 1703.10053 and 1805.00030). If time permits\, I will men
tion an application to quadratic differentials.\n\nThis talk will take pla
ce on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Lancaster)
DTSTART:20240318T130000Z
DTEND:20240318T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/157
DESCRIPTION:Title: Donaldson--Thomas invariants for the Bridgeland--Sm
ith correspondence\nby Nicholas Williams (Lancaster) as part of Paris
algebra seminar\n\n\nAbstract\nCelebrated work of Bridgeland and Smith sho
ws a correspondence between quadratic differentials on Riemann surfaces an
d stability conditions on certain 3-Calabi--Yau triangulated categories. P
art of this correspondence is that finite-length trajectories of the quadr
atic differential correspond to stable objects of phase 1. Speaking roughl
y\, these stable objects are then counted by an associated Donaldson--Thom
as invariant. Work of Iwaki and Kidwai predicts particular values for thes
e Donaldson--Thomas invariants according to the different types of finite-
length trajectories\, based on the output of topological recursion. We sho
w that the category recently studied by Christ\, Haiden\, and Qiu produces
Donaldson--Thomas invariants matching these predictions. This is joint wo
rk with Omar Kidwai.\n\nThis talk will take place in hybrid mode at the In
stitut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich (Hamburg)
DTSTART:20240513T120000Z
DTEND:20240513T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/158
DESCRIPTION:Title: A braided monoidal (infinity\,2)-category from link
homology\nby Paul Wedrich (Hamburg) as part of Paris algebra seminar\
n\n\nAbstract\nAn early highlight of quantum topology was the observation
that the Jones polynomial -- and many other knot and link invariants -- ar
ise from braided monoidal categories of quantum group representations. In
hindsight\, this can be understood as underlying reason for the existence
of associated topological quantum field theories (TQFTs) in 3 and 4 dimens
ions.\n\nNot much later\, Khovanov discovered a link homology theory that
categorifies the Jones polynomial. It associates graded chain complexes to
links\, from which the Jones polynomials can be recovered. It was therefo
re speculated that Khovanov homology and its variants may themselves be ex
pressible in terms of certain braided monoidal 2-categories and that there
should exist associated TQFTs in 4 and 5 dimensions that may be sensitive
to smooth structure.\n\nA major challenge in fully realizing this dream i
s the problem of coherence: Link homology theories live in the world of ho
mological algebra\, where constructing a braided monoidal structure in pri
nciple requires an infinite amount of higher and higher homological cohere
nce data. In this talk\, I will sketch a proposed solution to this problem
\, joint with Leon Liu\, Aaron Mazel-Gee\, David Reutter\, and Catharina S
troppel\, and explain how we use the language of infinity-categories to bu
ild an E2-monoidal (infinity\,2)-category which categorifies the Hecke bra
ided monoidal category underlying the HOMFLYPT link polynomial.\n\n\nThis
talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Voloshyn (Pohang)
DTSTART:20240408T120000Z
DTEND:20240408T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/159
DESCRIPTION:Title: Generalized cluster structures on the special linea
r group\nby Dmitriy Voloshyn (Pohang) as part of Paris algebra seminar
\n\n\nAbstract\nThe Gekhtman-Shapiro-Vainshtein conjecture (the GSV conjec
ture) states that for any any given simple complex algebraic group G and a
ny Poisson bracket from the Belavin-Drinfeld class\, there exists a compat
ible generalized cluster structure. In this talk\, I will review the proce
ss of constructing compatible generalized cluster structures\, as well as
the current state-of-the-art on the GSV conjecture. After that\, I will de
scribe a construction of generalized cluster structures on SL_n compatible
with Poisson brackets induced from the Poisson dual of SL_n endowed with
the Poisson structure determined by a BD triple of\ntype A_{n-1}. I will a
lso describe the associated family of birational quasi-isomorphisms. The t
alk will be based on the preprint arXiv:2312.04859 (joint work with M. Gek
htman). \n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/15
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hussein Mourtada (U. Paris Cité)
DTSTART:20240325T130000Z
DTEND:20240325T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/160
DESCRIPTION:Title: Singularities of algebraic varieties and integer pa
rtitions\nby Hussein Mourtada (U. Paris Cité) as part of Paris algebr
a seminar\n\n\nAbstract\nI will talk about a link between arc spaces of si
ngularities\, which are algebro-geometric objects\, and identities of inte
ger partitions.\n\nThis link allows us to discover new partition identitie
s in the spirit of the work of Ramanujan. The talk is accessible to a wide
audience. \n\nThis talk will take place in hybrid mode at the Institut He
nri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Cruz (Stuttgart)
DTSTART:20240422T120000Z
DTEND:20240422T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/161
DESCRIPTION:Title: Relative Auslander-Gorenstein pairs\nby Tiago C
ruz (Stuttgart) as part of Paris algebra seminar\n\n\nAbstract\nA famous r
esult in representation theory is Auslander’s correspondence which conne
cts finite-dimensional algebras of finite representation-type with Ausland
er algebras. Over the years\, many generalisations of Auslander algebras h
ave been proposed: for instance n-Auslander algebras (by Iyama)\, n-minima
l Auslander–Gorenstein algebras (by Iyama and Solberg)\, among others. A
ll of the concepts above require the existence of a faithful projective-in
jective module and use classical dominant dimension. Now replace the faith
ful projective-injective module with a self-orthogonal module and classica
l dominant dimension with relative dominant dimension with respect to a mo
dule and you get a relative Auslander-Gorenstein pair.\n\nIn this talk\, w
e introduce relative Auslander-Gorenstein pairs. Further\, we will charact
erise relative Auslander pairs (those whose underlying algebras have finit
e global dimension) by the existence and uniqueness of tilting-cotilting m
odules having the highest values of relative dominant and codominant dimen
sion with respect to the self-orthogonal module. At the end\, we discuss e
xplicit examples of relative Auslander pairs. (This is joint work with Chr
ysostomos Psaroudakis.)\n\nThis talk will take place in hybrid mode at the
Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Robalo (Sorbonne U.)
DTSTART:20240429T120000Z
DTEND:20240429T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/162
DESCRIPTION:Title: Choices of HKR isomorphisms and exponential maps\nby Marco Robalo (Sorbonne U.) as part of Paris algebra seminar\n\n\nAbs
tract\nIn this talk\, I will explain a computation describing the space of
choices of functorial HKR isomorphisms as choices of exponential maps fro
m the additive to the multiplicative formal group. This computation uses t
he construction of a filtered circle obtained in collaboration with with M
oulinos and Toën\, which combines the HKR filtration and the circle actio
n on Hochschild homology even when the characteristic of the base field is
positive. We will review the construction of the filtered circle and the
relation with Witt vectors.\n\nThis talk will take place in hybrid mode a
t the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke
DTSTART:20240506T120000Z
DTEND:20240506T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/163
DESCRIPTION:Title: Floer potentials\, cluster algebras and quiver repr
esentations\nby Markus Reineke as part of Paris algebra seminar\n\n\nA
bstract\nWe interpret Floer potentials (encoding certain Gromov-Witten inv
ariants) of "exotic" monotone Lagrangian tori in dle Pezzo surfaces as clu
ster characters of representations of certain quivers with potential.\n\nT
his talk will be on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Paris)
DTSTART:20240304T130000Z
DTEND:20240304T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/164
DESCRIPTION:Title: Complexes of stable infinity-categories and pervers
e schobers\nby Merlin Christ (Paris) as part of Paris algebra seminar\
n\n\nAbstract\nA complex of stable infinity-categories is a categorificati
on of a chain complex\, meaning a sequence of stable infinity-categories t
ogether with a differential that squares to the zero functor. Examples of
such categorical complexes arise for instance via a categorification of th
e totalization construction\, which produces a categorical complex from a
categorical multi-complex\, such as a commuting cube of stable infinity-ca
tegories. We will then explain how categorified perverse sheaves\, also kn
own as perverse schobers\, on C^n (with a certain stratification) can be d
escribed in terms of categorical cubes and categorical complexes of spheri
cal functors\, and what categorical totalization means in this case geomet
rically. This talk is based on joint work with T. Dyckerhoff and T. Walde.
\n\nThis talk will take place in hybrid mode at the Institut Henri Poinca
ré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pauksztello (Lancaster)
DTSTART:20240527T120000Z
DTEND:20240527T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/165
DESCRIPTION:Title: Convex geometry for (co)fans of abelian categories<
/a>\nby David Pauksztello (Lancaster) as part of Paris algebra seminar\n\n
\nAbstract\nArising in cluster theory\, the g-vector fan is a convex geome
tric invariant encoding the mutation behaviour of clusters. In representat
ion theory\, the g-vector fan encodes the mutation theory of support tau-t
ilting objects or\, equivalently\, two-term silting objects. In this talk\
, we will describe a generalisation of the g-vector fan which in some sens
e “completes” the g-vector fan: the heart fan of an abelian category.
This convex geometric invariant encodes many important homological propert
ies: e.g. one can detect from the convex geometry whether an abelian categ
ory is length\, whether it has finitely many torsion pairs\, and whether a
given Happel-Reiten-Smaloe tilt is length. This talk will be a report on
joint work with Nathan Broomhead\, David Ploog and Jon Woolf.\n\nThis talk
will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (Glasgow)
DTSTART:20240617T120000Z
DTEND:20240617T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/166
DESCRIPTION:Title: Categorical cluster ensembles\nby Matthew Press
land (Glasgow) as part of Paris algebra seminar\n\n\nAbstract\nIn their ge
ometric approach to cluster theory\, Fock–Goncharov and Gross–Hacking
–Keel construct cluster varieties beginning with a seed datum. This cons
ists of a lattice which contains various distinguished sublattices\, has a
preferred basis\, and carries a partially defined bilinear form. A proces
s of mutation allows one to construct more such seed data\, and birational
gluing maps between the tori dual to the lattices\, leading to two cluste
r varieties known as A and X. By enhancing the initial data to a cluster e
nsemble\, in which the bilinear form is extended to the whole lattice\, on
e also obtains a map from A to X.\nIn this talk\, based on joint work with
Jan Grabowski\, I will explain how one can obtain a seed datum\, and in m
any cases a full cluster ensemble\, from each cluster-tilting subcategory
of an appropriate 2-Calabi–Yau category. Furthermore\, I will explain ho
w the seed data of different cluster-tilting subcategories are related\, g
eneralising the relationship between a seed datum and its mutations.\n\nTh
is talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Théo Pinet (Paris Cité)
DTSTART:20240624T120000Z
DTEND:20240624T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/167
DESCRIPTION:Title: Inflations for representations of shifted quantum a
ffine algebras\nby Théo Pinet (Paris Cité) as part of Paris algebra
seminar\n\n\nAbstract\nThe only finite-dimensional simple Lie algebra admi
tting a 2-dimensional irreducible representation is sl(2). The restriction
functors arising from Dynkin diagram inclusions in (classical) Lie theory
are thus in general not essentially surjective on finite-dimensional simp
le modules. The goal of this talk is to specify whether or not this "surje
ctivity defect" remains in the case of Finkelberg-Tsymbaliuk's shifted qua
ntum affine algebras (SQAAs).\n\nSQAAs are infinite-dimensional associativ
e algebras parametrized by a simple finite-dimensional Lie algebra and a c
oweight in the corresponding coweight lattice. They appear naturally in th
e study of Coulomb branches\, of quantum integrable systems and of cluster
algebras. In this presentation\, we will give a brief introduction to the
vast representation theory of SQAAs and will state some results about the
existence of remarkable modules\, that we call "inflations"\, which are c
onstructed as special preimages for different canonical restriction functo
rs (associated here also to Dynkin diagram inclusions). We will finally\,
if time permits\, discuss potential applications of our results to the stu
dy of cluster structures on Grothendieck rings. \n\nThis talk will take pl
ace in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Rognerud (Paris Cité)
DTSTART:20240603T120000Z
DTEND:20240603T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/168
DESCRIPTION:Title: The fractionally Calabi-Yau combinatorics of the Ta
mari lattice\nby Baptiste Rognerud (Paris Cité) as part of Paris alge
bra seminar\n\n\nAbstract\nA poset is said to be fractionally Calabi-Yau i
f the bounded derived category of its incidence algebra over a field is fr
actionally Calabi-Yau. In other words\, a power of the Serre functor is is
omorphic to a shift. When going from a poset to its derived category\, one
looses almost all the combinatorics of the poset. However in some favora
ble cases\, part of the combinatorics is encoded in the Serre functor.\n\n
In this talk\, I will present the combinatorics of the Serre functor of th
e Tamari lattice. This leads to a more algebraic proof of its fractional C
alabi-Yau property. It is also the first step toward a generalization to a
larger family of posets. \n\nThis talk will take place in hybrid mode at
the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyang Liu (USTC\, Hefei)
DTSTART:20240610T120000Z
DTEND:20240610T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/169
DESCRIPTION:Title: Singularity categories via McKay quivers with poten
tial\nby Junyang Liu (USTC\, Hefei) as part of Paris algebra seminar\n
\n\nAbstract\nIn 2018\, Kalck and Yang showed that the singularity categor
ies associated with 3-dimensional Gorenstein quotient singularities are tr
iangle equivalent (up to direct summands) to small cluster categories asso
ciated with McKay quivers with potential. I introduce graded McKay quivers
with potential and generalize Kalck-Yang's theorem to arbitrary dimension
s. The singularity categories I consider occur as stable categories of cat
egories of maximal Cohen-Macaulay modules. I refine my description of the
singularity categories by showing that these categories of maximal Cohen-M
acaulay modules are equivalent to Higgs categories in the sense of Wu. Mor
eover\, I describe the singularity categories in the non-Gorenstein case.
\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/16
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Vienna)
DTSTART:20240701T120000Z
DTEND:20240701T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/170
DESCRIPTION:Title: Deep points in cluster varieties\nby Mikhail Go
rsky (Vienna) as part of Paris algebra seminar\n\n\nAbstract\nMany importa
nt algebraic varieties\, such as open positroid strata in Grassmannians\,
Richardson varieties\, or augmentation varieties of certain Legendrian lin
ks\, are known to carry cluster structures. In particular\, each such vari
ety is covered\, up to codimension 2\, by a collection of overlapping open
tori. In this talk\, I will discuss the ``deep locus'' of a cluster varie
ty\, that is\, the complement to the union of all cluster toric charts. I
will explain a conjectural relation between the deep locus and the natural
torus action compatible with the cluster structure. For many positroid st
rata in Gr(2\,n) and Gr(3\,n)\, and for cluster varieties of types ADE\, t
his relation is made precise: we show that the deep locus consists precise
ly of the points with non-trivial stabilizer for this action. If time perm
its\, I will explain how these results can be applied in the context of ho
mological mirror symmetry and say a few words on the geometry of deep loci
. The talk is based on joint work with Marco Castronovo\, José Simental\,
and David Speyer (arXiv:2402.16970).\n\n\nThis talk will be on Zoom only.
\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isambard Goodbody (Glasgow)
DTSTART:20240930T120000Z
DTEND:20240930T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/171
DESCRIPTION:Title: Reflexivity and Hochschild Cohomology\nby Isamb
ard Goodbody (Glasgow) as part of Paris algebra seminar\n\n\nAbstract\nRef
lexivity is about a duality between two kinds of derived categories appear
ing in algebra and geometry. The motivating examples are the bounded deriv
ed category of a finite dimensional algebra vs its perfect complexes and t
he bounded derived category of a projective scheme vs its perfect complexe
s. In the smooth case\, these categories coincide but even in the non-smoo
th case these two categories share some common information. In this talk I
'll provide a conceptual justification for this phenomenon. The main resul
t is a monoidal characterisation of reflexive DG-categories as introduced
by Kuznetsov and Shinder. As applications of this new perspective one can
prove invariance results for Hochschild cohomology\, derived Picard groups
and a bijection between semi-orthogonal decompositions. \n\nThis talk wil
l take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanskiy (MIT)
DTSTART:20241014T120000Z
DTEND:20241014T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/172
DESCRIPTION:Title: Quantum loop group and coherent Satake category
\nby Ilya Dumanskiy (MIT) as part of Paris algebra seminar\n\n\nAbstract\n
The category of equivariant perverse sheaves on the affine Grassmannian ha
s a coherent counterpart\, called the coherent Satake category. Cautis and
Williams proved for GL and conjectured for other types that this category
has a cluster structure. I will talk about work in progress towards the p
roof of this conjecture for simply-laced types. Our approach is based on r
elating the coherent Satake category with the category of finite-dimension
al modules over the affine quantum group. The bridge between these two cat
egories is provided by the notion of Feigin-Loktev fusion product for modu
les over the current algebra. In particular\, it helps to construct cluste
r short exact sequences of perverse coherent sheaves using the existence o
f exact sequences of modules over the quantum affine group.\n\nThis talk w
ill take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (IHES)
DTSTART:20241007T120000Z
DTEND:20241007T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/173
DESCRIPTION:Title: Fusion categories as quantum symmetries: on Bridgel
and stability conditions\nby Edmund Heng (IHES) as part of Paris algeb
ra seminar\n\n\nAbstract\nClassically\, finite symmetries are captured by
the action of a finite group. Moving to the quantum world\, one has to all
ow for possibly non-invertible symmetries\, which are instead captured by
the action of a more general algebraic structure\, known as a fusion categ
ory. Such symmetries are actually ubiquitous in mathematics\; for example\
, given a category with an action of a finite group G (e.g. A-mod\, Coh(X)
)\, its G-equivariant category (A#G-mod\, Coh(X//G) resp.) has instead the
action of the category of G-representations rep(G)\, which has the struct
ure of a fusion category. There are also other more “exotic” fusion ca
tegories\, which nonetheless capture “hidden” symmetries on familiar (
non-“exotic”) categories. \nThe aim of this talk is to discuss the app
lication of fusion categorical symmetries to the study of Bridgeland stabi
lity conditions. I will discuss how the fusion-equivariant stability condi
tions — a generalisation of G-invariant stability conditions (i.e. G-fix
ed points) — form a closed submanifold of the Bridgeland stability manif
old. Moreover\, we will see the following duality result inspired by a cat
egorical Morita duality: let D be a triangulated category with a G-action\
, so that its G-equivariant category D^G has a rep(G)-action. The manifold
of G-invariant stability conditions (associated to D) is homeomorphic to
the manifold of rep(G)-equivariant stability conditions (associated to D^G
). - This is part of joint work with Hannah Dell and Anthony Licata.\n\nTh
is talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myungho Kim (Kyung Hee University)
DTSTART:20241104T130000Z
DTEND:20241104T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/174
DESCRIPTION:Title: Exchange matrices of $\\bold i$-boxes\nby Myung
ho Kim (Kyung Hee University) as part of Paris algebra seminar\n\n\nAbstra
ct\nAdmissible chains of $\\bold i$-boxes are important combinatorial tool
s in the monoidal categorification of cluster algebras via representations
of quantum affine algebras\, since they provide some seeds of the cluster
algebra. For a given sequence $\\bold i$ with indices ranging over the in
terval [a\,b]\, we define a subinterval [x\,y] of [a\,b] as an $\\bold i$-
box if the color of $\\bold i$ at x matches the color at y. Two $\\bold i$
-boxes are said to commute if the extension of one of the $\\bold i$-boxes
by one step to the left and one step to the right properly contains the o
ther $\\bold i$-box. A maximal commuting family of $\\bold i$-boxes yields
a seed in the category of finite-dimensional modules over the quantum aff
ine algebra\, and any such family can be constructed from an admissible ch
ain. In this talk\, I will introduce the notion of $\\bold i$-boxes and p
resent recent results on the exchange matrices of a maximal commuting fami
ly of $\\bold i$-boxes. This is a joint work with Masaki Kashiwara.\n\nThi
s talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (Cologne)
DTSTART:20250113T130000Z
DTEND:20250113T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/175
DESCRIPTION:Title: Deformations of gentle algebras and gluing of Fukay
a categories of surfaces\nby Severin Barmeier (Cologne) as part of Par
is algebra seminar\n\n\nAbstract\nGentle algebras can be obtained by gluin
g quivers of type A with square-zero relations along vertices. This observ
ation has a beautiful geometric incarnation: partially wrapped Fukaya cate
gories of smooth surfaces can be obtained by gluing derived categories of
type A quivers. In this talk\, I will explain how this can be generalized
to surfaces with orbifold singularities and how this relates to A∞ defor
mations of graded gentle algebras. This interplay between the geometry of
surfaces and algebraic deformation theory has two fascinating consequences
. On the one hand\, it leads to the proof of (a singular surface version o
f) a conjecture of Kontsevich on the local-to-global properties of Fukaya
categories of noncompact manifolds. On the other hand\, it sheds light on
the relationship between deformations of Fukaya categories and partial com
pactifications (as advocated in Seidel's ICM 2002 address) in the presence
of stop data. This talk is based on https://arxiv.org/abs/2407.16358 join
t with Sibylle Schroll and Zhengfang Wang.\n\nThis talk will take place in
hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Neville (Michigan)
DTSTART:20241021T120000Z
DTEND:20241021T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/176
DESCRIPTION:Title: Cyclically ordered quivers\nby Scott Neville (M
ichigan) as part of Paris algebra seminar\n\n\nAbstract\nQuivers and their
mutations play a fundamental role in the theory of cluster algebras. We f
ocus on the problem of deciding whether two given quivers are mutation equ
ivalent to each other. Our approach is based on introducing an additional
structure of a cyclic ordering on the set of vertices of a quiver. This le
ads to new powerful invariants of quiver mutation. These invariants can be
used to show that various quivers are not mutation acyclic\, i.e.\, they
are not mutation equivalent to an acyclic quiver. This talk is partially b
ased on joint work with Sergey Fomin [arXiv:2406.03604]. \n\nThis talk wil
l take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Ovenhouse (Yale)
DTSTART:20241209T130000Z
DTEND:20241209T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/177
DESCRIPTION:Title: Higher q-Rational Numbers\nby Nick Ovenhouse (Y
ale) as part of Paris algebra seminar\n\n\nAbstract\nThe classical q-integ
ers were generalized to rational numbers by Morier-Genoud and Ovsienko by
q-deforming the continued fraction expressions. These "q-rationals" have s
everal nice properties\, and are related to many interesting things (such
as cluster algebras\, hyperbolic geometry\, and Jones polynomials). I will
discuss how one natural generalization of the q-rationals is given by rat
ios of generating functions for "P-partitions" on certain types of posets\
, and that some of the properties of q-rationals hold more generally in th
is case. We are able to use this to give some quantizations of cubic (and
other algebraic) numbers\, generalizing a result of Morier-Genoud and Lecl
ere on quadratic irrationals.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Beijing Normal U.)
DTSTART:20241202T130000Z
DTEND:20241202T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/178
DESCRIPTION:Title: Based cluster algebras of infinite rank and their a
pplications to double Bott-Samelson cells\nby Fan Qin (Beijing Normal
U.) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce based clu
ster algebras of infinite rank. By extending cluster algebras arising from
double Bott-Samelson cells to the infinite rank setting\, we recover cert
ain infinite rank cluster algebras connected to monoidal categories of rep
resentations of (shifted) quantum affine algebras. Several conjectures fol
low as a result.\n\nThis talk will take place in hybrid mode at the Instit
ut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (Tsinghua)
DTSTART:20241125T130000Z
DTEND:20241125T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/179
DESCRIPTION:Title: Skein algebras and quantized Coulomb branches\n
by Dylan Allegretti (Tsinghua) as part of Paris algebra seminar\n\n\nAbstr
act\nCharacter varieties of surfaces are fundamental objects in modern mat
hematics\, appearing in low-dimensional topology\, representation theory\,
and mathematical physics\, among other areas. Given a reductive algebraic
group G\, the G-character variety of a surface is a moduli space parametr
izing G-local systems on the surface.\n\nCharacter varieties of surfaces a
re expected to arise in physics as Coulomb branches of certain quantum fie
ld theories. A Coulomb branch is a kind of moduli space that was recently
given a precise mathematical definition in the work of Braverman\, Finkelb
erg\, and Nakajima.\n\nIn this talk\, I will focus on the SL(2\,C)-charact
er variety of a surface. It has a quantization given by a noncommutative a
lgebra called the Kauffman bracket skein algebra. I will describe a precis
e relationship between skein algebras and quantized Coulomb branches\, con
firming the physics prediction in some cases. This is joint work with Peng
Shan.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/17
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Hanson (North Caroline State U.)
DTSTART:20241118T130000Z
DTEND:20241118T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/180
DESCRIPTION:Title: Mutation of tau-exceptional sequences\nby Eric
Hanson (North Caroline State U.) as part of Paris algebra seminar\n\n\nAbs
tract\nBy the work of Crawley-Boevey and Ringel\, the set of complete exce
ptional sequences over a finite-dimensional hereditary algebra admits a tr
ansitive braid group action. This can also be viewed as a "mutation theory
" for exceptional sequences. In this talk\, we discuss recent joint work w
ith Aslak Buan and Bethany Marsh which extends this into a mutation theory
for (complete) tau-exceptional sequences over an arbitrary finite-dimensi
onal algebra. In addition to giving the formulas for this mutation\, we di
scuss the existence of non-mutable sequences\, the problem of transitivity
\, and the (lack of) braid relations. \n\nThis talk will be on Zoom only.\
n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern)
DTSTART:20250512T120000Z
DTEND:20250512T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/181
DESCRIPTION:Title: Bethe subalgebras in type A\, tame representations\
, and a cactus group action\nby Iva Halacheva (Northeastern) as part o
f Paris algebra seminar\n\n\nAbstract\nThe Bethe subalgebras of the Yangia
n Y(gl(n)) are a family of maximal commutative subalgebras that generalize
the Gelfand-Tsetlin algebras. Moreover\, they are indexed by points of th
e Deligne-Mumford compactification of the moduli space M(0\,n+2). We consi
der points C in the real locus of this parameter space. For a fixed tame r
epresentation of Y(gl(n))\, the Bethe subalgebra B(C) corresponding to any
real point C acts with simple spectrum\, resulting in an unramified cover
ing of the parameter space whose fiber over C is the set of eigenlines for
the action of B(C). I will discuss how to identify each fiber with a coll
ection of Gelfand-Tsetlin keystone patterns\, carrying a gl(n)-crystal str
ucture\, as well as the monodromy action for the covering realized by the
mirabolic cactus group. Large parts of this construction are expected to g
eneralize to arbitrary semisimple Lie algebras. This is joint work with An
fisa Gurenkova and Leonid Rybnikov.\n\nThis talk will take place in hybrid
mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss (UNAM)
DTSTART:20250120T130000Z
DTEND:20250120T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/182
DESCRIPTION:Title: Representations of shifted quantum affine algebras
and cluster algebras\nby Christof Geiss (UNAM) as part of Paris algebr
a seminar\n\n\nAbstract\nThis is a report on an ongoing joint project wit
h David Hernandez (Université Paris Cité) and Bernard Leclerc (Universi
té de Caen). We define for each Cartan matrix of finite type a skew symm
etric cluster algebra A of infinite rank in terms of an almost periodic qu
iver. By choosing an initial seed\, where the cluster variables are certa
in formal power series\, which fulfill the q-difference equations of a QQ
-system\, we can identify an adequate completion of A with the Grothendiec
k ring of the category\nO_Z of the corresponding (untwisted) shifted quant
um affine algebras. We conjecture that under this identification the clus
ter monomials become the q-characters of the real simple representations i
n this category. \n\nThis talk will take place in hybrid mode at the Insti
tut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Huang (Sun Yat Sen U.)
DTSTART:20241216T130000Z
DTEND:20241216T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/183
DESCRIPTION:Title: Non-commutative surfaces\, symmetry and positivity<
/a>\nby Min Huang (Sun Yat Sen U.) as part of Paris algebra seminar\n\n\nA
bstract\nThe aim of my talk (based on joint work in progress with Arkady B
erenstein and Vladimir Retakh) is to introduce and study certain noncommut
ative cluster algebras A from marked orbifolds. They are non-commutative v
ersions of the generalized cluster algebras defined by Chekhov and Shapiro
. These algebras admit noncommutative clusters\, i.e.\, embeddings of a gi
ven group G which is either free or one-relator (we call it a triangle gro
up) into the multiplicative monoid A×. The clusters are parametrized by t
riangulations of the orbifold and exhibit a noncommutative Laurent Phenome
non\, which asserts that generators of the algebra can be written as sums
of the images of elements of G for any noncommutative cluster. In particul
ar\, if the surface is unpunctured\, then our algebra A can be specialized
to the ordinary quantum cluster algebra\, and the noncommutative Laurent
Phenomenon becomes the (positive) quantum one. \n\nThis talk will take pla
ce in hybrid mode in Conference Hall B of the New York University Abu Dhab
i.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregg Musiker (U. of Minnesota)
DTSTART:20250210T130000Z
DTEND:20250210T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/184
DESCRIPTION:Title: Super Fibonacci and Super Markov Numbers\nby Gr
egg Musiker (U. of Minnesota) as part of Paris algebra seminar\n\n\nAbstra
ct\nIn this talk\, I will describe joint work with N. Ovenhouse and S. Zha
ng providing combinatorial formulas for super lambda lengths in the contex
t of decorated super Teichmueller space of a marked disc or an annulus.
The latter leads to a notion of Super Fibonacci Numbers\, as will be discu
ssed. The talk will then describe recent research applying these methods
instead on the once-punctured torus and how this leads to Super Markov Num
bers where associated combinatorial formulas are no longer positive genera
ting functions but instead involve signed enumeration.\n\nThis talk will t
ake place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstanze Rietsch (King's College London)
DTSTART:20250203T130000Z
DTEND:20250203T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/185
DESCRIPTION:Title: A Tropical Edrei theorem\nby Konstanze Rietsch
(King's College London) as part of Paris algebra seminar\n\n\nAbstract\nA
classical theorem proved by Edrei in the 1950's (building on work with Ais
sen\, Schoenberg and Whitney) gives a parametrisation for infinite upper-t
riangular totally positive Toeplitz matrices using pairs of sequences of p
ositive real parameters with finite sum. These infinite Toeplitz matrices
(and their parameters) are central for understanding characters of the inf
inite symmetric group\, as was discovered by Thoma\, who reproved Edrei's
theorem in the 1960's. There is also a totally different (totally positive
) theorem about Toeplitz matrices that relates to quantum cohomology of fl
ag varieties and mirror symmetry [R\,06]. This talk will be about new trop
ical versions of these parametrisation results and the relationship betwee
n them. This work builds on results of Judd and Ludenbach and relates also
to Lusztig's parametrisation of his canonical basis.\n\nThis talk will ta
ke place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niels Kowalzig (Rome 2)
DTSTART:20250303T130000Z
DTEND:20250303T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/186
DESCRIPTION:Title: Higher structures on homology groups\nby Niels
Kowalzig (Rome 2) as part of Paris algebra seminar\n\n\nAbstract\nWe duali
se the classical fact that an operad with multiplication leads to cohomolo
gy\ngroups which form a Gerstenhaber algebra to the context of cooperads:
as a result\, a cooperad\nwith comultiplication induces a homology theory
that is endowed with the structure of a Gerstenhaber coalgebra\, that is\,
it comes with a (graded cocommutative) coproduct which is compatible with
a cobracket in a dual Leibniz sense. As an application\, one obtains Gers
tenhaber coalgebra structures on Tor groups over bialgebras or Hopf algebr
as\, as well as on Hochschild homology for Frobenius algebras. Joint work
with Francesca Pratali.\n\n\nThis talk will take place in hybrid mode at t
he Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongjian Wu (Tsinghua U.)
DTSTART:20250217T130000Z
DTEND:20250217T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/187
DESCRIPTION:Title: Relative Bridgeland Stability Conditions\nby Do
ngjian Wu (Tsinghua U.) as part of Paris algebra seminar\n\n\nAbstract\nTh
e notion of a stability condition on a triangulated category was introduce
d by Bridgeland\, based on the study of slope stability of vector bundles
over curves and the Π-stability of D-branes in string theory. The theory
of stability conditions has since played an important role in many branche
s of mathematics\, such as mirror symmetry\, Donaldson-Thomas invariants a
nd cluster theory.\n\nIn this talk\, I will provide an overview of the the
ory of Bridgeland stability conditions. Following this\, I will introduce
the notion of relative stability conditions on triangulated categories and
illustrate the deformation property of the spaces of relative stability c
onditions. The motivation for this concept arises from the link between Br
idgeland stability and deformed Hermitian-Yang-Mills metrics. The talk is
based on joint work with Bowen Liu. \n\nThis talk will take place in hybri
d mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Lehmann (Antwerp)
DTSTART:20250224T130000Z
DTEND:20250224T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/188
DESCRIPTION:Title: Curved algebras and deformations of triangulated ca
tegories\nby Alessandro Lehmann (Antwerp) as part of Paris algebra sem
inar\n\n\nAbstract\nIs well known that the deformation theory of dg-algebr
as — and by extension\, triangulated categories — has some pathologica
l aspects\, due to the existence of curved deformations\; this is the so-c
alled curvature problem. I will discuss a construction that associates a t
riangulated category\, called the n-derived category\, to a curved deforma
tion of a dg-algebra. I’ll explain how this category can be interpreted
as a deformation of the derived category of the base algebra and how this
leads to considering a novel notion of deformation for (enhanced) triangul
ated categories. This talk is based on joint work with Wendy Lowen.\n\nThi
s talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Launois (Caen)
DTSTART:20250127T130000Z
DTEND:20250127T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/189
DESCRIPTION:Title: Derivations of quantum algebras\nby Stéphane L
aunois (Caen) as part of Paris algebra seminar\n\n\nAbstract\nIn this talk
\, I will discuss derivations of a class of noncommutative polynomial alge
bras\, the so-called quantum nilpotent algebras\, and their primitive quot
ients. This is joint work in progress with Samuel Lopes (Porto) and Isaac
Oppong (Greenwich). \n\nThis talk will take place in hybrid mode at the In
stitut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/18
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Hamburg)
DTSTART:20250317T130000Z
DTEND:20250317T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/190
DESCRIPTION:Title: Hall algebras and counting in Calabi-Yau categories
\nby Mikhail Gorsky (Hamburg) as part of Paris algebra seminar\n\n\nAb
stract\nI will discuss a replacement of the notion of homotopy cardinality
in the setting of even-dimensional Calabi-Yau categories and their relati
ve generalizations. This includes cases where the usual definition does no
t apply\, such as Z/2-graded dg categories. As an application of the defin
ition in the relative case\, we define a version of Hall algebras for odd-
dimensional Calabi-Yau categories. I will explain its relation to some pre
viously known non-intrinsic constructions of Hall algebras. Whenever a 1CY
category C is equivalent to the Z/2-graded derived category of a heredita
ry abelian category A\, our intrinsically defined Hall algebra of C realis
es the Drinfeld double of the twisted Hall algebra of A. If time permits\,
I will also briefly discuss another application in the context of invaria
nts of smooth and graded Legendrian links\, where we prove a conjecture of
Ng-Rutherford-Shende-Sivek relating ruling polynomials with augmentation
categories.The talk is based on joint work with Fabian Haiden\, arxiv:2409
.10154.\n\n\n\nThis talk will take place in hybrid mode at the Institut He
nri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Brussels)
DTSTART:20250310T130000Z
DTEND:20250310T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/191
DESCRIPTION:Title: Nichols algebras over groups\nby Leandro Vendra
min (Brussels) as part of Paris algebra seminar\n\n\nAbstract\nNichols alg
ebras appear in various areas of mathematics\, ranging from Hopf algebras
and quantum groups to Schubert calculus and conformal field theory. In thi
s talk\, I will review the main challenges in classifying Nichols algebras
over groups and discuss some recent classification theorems. In particula
r\, I will highlight a recent classification result (https://arxiv.org/abs
/2411.02304)\, achieved in collaboration with Andruskiewitsch and Heckenbe
rger\, concerning finite-dimensional Nichols algebras over solvable groups
.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Xu (Penn State)
DTSTART:20250428T120000Z
DTEND:20250428T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/192
DESCRIPTION:Title: Noncommutative Calculus for DG Manifolds\nby Pi
ng Xu (Penn State) as part of Paris algebra seminar\n\n\nAbstract\nIt is a
classical theorem that for any DG algebra $A$\, the pair of its Hochschil
d (co)homologies $(H^\\bullet (A\, A)\, H_\\bullet (A\, A))$\nadmits ric
h algebraic structures\, resembling the usual Cartan calculus\, called non
commutative calculus. DG manifolds are a useful geometric notion for descr
ibing spaces with singularities. In this talk\, I will discuss the noncomm
utative calculus for the DGA associated with a DG manifold and present a D
uflo–Kontsevich type theorem for DG manifolds. This is joint work with H
suan-Yi Liao and Mathieu Stienon.\n\nThis talk will take place in hybrid m
ode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hironori Oya
DTSTART:20250407T120000Z
DTEND:20250407T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/193
DESCRIPTION:Title: Algebraic study of quantum configuration spaces of
decorated flags\nby Hironori Oya as part of Paris algebra seminar\n\n\
nAbstract\nLet G be a simply-connected simple algebraic group over the com
plex numbers\, and U its maximal unipotent subgroup. An element of G/U is
called a decorated flag. In this talk\, we study algebraic structure of a
quantum analogue of the ring of regular functions on the configuration spa
ce of n decorated flags. I explain its relation with the quantum coordinat
e rings of G and its Borel subgroup B. It can be considered as a quantum a
nalogue of Wilson lines on the moduli space of decorated twisted G-local s
ystems on the polygons. We also discuss its quantum cluster algebra struct
ure. - This talk is based on joint work with Tsukasa Ishibashi.\n\nThis ta
lk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Koshevoy (CEMI\, Moscow)
DTSTART:20250331T120000Z
DTEND:20250331T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/194
DESCRIPTION:Title: Products of Kirillov-Reshetikhin modules and maxim
al green sequences\nby Gleb Koshevoy (CEMI\, Moscow) as part of Paris
algebra seminar\n\n\nAbstract\nWe show that a $q$-character of a Kirillov-
Reshetikhin module (KR modules) for untwisted quantum affine algebras of s
imply laced types $A_n^{(1)}$\, $D_n^{(1)}$\, $E_6^{(1)}$\, $E_7^{(1)}$\,
$E_8^{(1)}$ might be obtained from a specific cluster variable of a seed
obtained by applying a maximal green sequence to the initial (infinite) qu
iver of the Hernandez-Leclerc cluster algebra. For a collection of KR-mod
ules with nested supports\, we show an explicit construction of a cluster
seed\, which has cluster variables corresponding to the $q$-characters of
KR-modules of such a collection.\nWe prove that the product of KR-modules
of such a collection is a simple module. We also have an explicit construc
tion of cluster seeds with cluster variables corresponding to $q$-characte
rs of KR-modules of some non-nested collections. We make a conjecture that
tensor products of KR-modules for such non-nested collections are simple.
\nIf time permits\, I explain that the cluster Donaldson-Thomas transfor
mations for double Bruhat cells for $ADE$ types can be computed using $q$-
characters of KR-modules\, and new algorithm to compute $q$-characters KR-
modules. The talk is based on joint work with Y.Kanakubo and T.Nakashima.\
n\nThis talk will take place in hybrid mode at the Institut Henri Poincar
é.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Rota (Paris Saclay)
DTSTART:20250505T120000Z
DTEND:20250505T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/195
DESCRIPTION:Title: Towards Curve contractibility via non-commutative d
eformations\nby Franco Rota (Paris Saclay) as part of Paris algebra se
minar\n\n\nAbstract\nDeciding whether a subvariety of an algebraic variety
is contractible is a deep problem of algebraic geometry. Even when the su
bvariety is a single smooth rational curve C\, the question is extremely s
ubtle.\n\nIn this talk\, I will assume moreover that the ambient variety i
s a Calabi-Yau threefold.\nWhen C is contractible\, its Donovan-Wemyss con
traction algebra (which pro-represents the deformation theory of C) govern
s much of the geometry. Our expectation is that deformation theory not onl
y controls contractibility but detects it\, even when C is not known to co
ntract. To investigate the deformation theory of C\, we use technology dev
eloped by Brown and Wemyss to describe a local model for C. \n\nI will int
roduce the key ideas and tools appearing in this problem\, the leading con
jectures\, and I will describe the (partial) results I obtained so far in
collaboration with G. Brown and M. Wemyss.\n\nThis talk will take place in
hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk because of the
DTSTART:20250324T130000Z
DTEND:20250324T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/196
DESCRIPTION:Title: Viazovska-Fest\nby No talk because of the as pa
rt of Paris algebra seminar\n\n\nAbstract\nThere will be no talk because o
f the Viazovska-Fest\, cf.\n\nhttps://viazovska-fest.sciencesconf.org/?lan
g=en\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Qunell (UCLA)
DTSTART:20250602T120000Z
DTEND:20250602T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/197
DESCRIPTION:Title: 2-categorical affine symmetries and q-boson algebra
s\nby Sam Qunell (UCLA) as part of Paris algebra seminar\n\n\nAbstract
\nRepresentations of KLR (quiver Hecke) algebras categorify the positive p
art of the quantum group associated to any symmetrizable Cartan matrix. Th
is categorical perspective makes certain symmetries more natural to study.
For example\, the induction and restriction functors between categories o
f KLR algebra modules play an important role in the theory. A closer inves
tigation of these functors reveals surprising new symmetries. In this talk
\, I will explain how the induction and restriction functors for KLR algeb
ras can be used to obtain a 2-representation of the corresponding affine p
ositive part in type A. I will also describe a new categorification of a c
losely related algebra\, the q-boson algebra\, in all symmetrizable Kac-Mo
ody types.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (Glasgow)
DTSTART:20251013T120000Z
DTEND:20251013T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/198
DESCRIPTION:Title: The classification of 3-fold flops\nby Michael
Wemyss (Glasgow) as part of Paris algebra seminar\n\n\nAbstract\nI will gi
ve an overview of the analytic classification of smooth\, simple\, 3-fold
flops. There are three main aspects: (1) reducing the problem to the class
ification of certain noncommutative finite dimensional algebras\, (2) a co
mplete understanding of those algebras\, then lastly (3) building the asso
ciated geometry for each algebra in that class. The talk will focus on (1
) and (2)\, as they are the most algebraic. In the process of proving the
above results\, we also obtain various bonus (and very surprising) geomet
ric corollaries\, including to curve-counting invariants\, and also to 3-f
old crepant divisor-to-curve contractions. Part (1) is joint with Joe Kar
mazyn and Emma Lepri\, the rest is joint with Gavin Brown.\n\nThis talk wi
ll take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (Amiens)
DTSTART:20250526T120000Z
DTEND:20250526T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/199
DESCRIPTION:Title: Cohomological Mackey formula for representations of
reductive groups\nby Lucien Hennecart (Amiens) as part of Paris algeb
ra seminar\n\n\nAbstract\nI will describe the construction of induction an
d restriction morphisms on the critical cohomology associated with a funct
ion on a representation of a reductive group. The induction morphism plays
a key role in obtaining a cohomological integrality decomposition\, which
is a decomposition into finite-dimensional pieces with enumerative signif
icance. After discussing this decomposition and its geometric meaning\, I
will present a cohomological version of the Mackey formula that relates th
e induction and restriction operations.\n\nThis talk will take place in hy
brid format at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/19
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Vogel (Paris Cité)
DTSTART:20250519T120000Z
DTEND:20250519T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/200
DESCRIPTION:Title: Regular exact categories and algebraic K-theory
\nby Pierre Vogel (Paris Cité) as part of Paris algebra seminar\n\n\nAbst
ract\nWe introduce a new notion of regularity for rings and exact \ncatego
ries and we show important results in algebraic homology and\nalgebraic K-
theory. In particular we prove that any acyclic complex \nof projective mo
dules over a regular ring is contractible. We have\nalso two conjectures a
bout Whitehead groups.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Bochum)
DTSTART:20260119T130000Z
DTEND:20260119T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/201
DESCRIPTION:Title: Varieties of complexes and canonical bases of quant
um groups\nby Markus Reineke (Bochum) as part of Paris algebra seminar
\n\n\nAbstract\nWe compute the local intersection cohomology of the irredu
cible components of varieties of complexes by using Lusztig’s geometric
approach to quantum groups and explicit constructions of elements of Luszt
ig’s canonical bases.\n\nThis talk will take place in hybrid mode at the
Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Coulembier (Sydney)
DTSTART:20250929T120000Z
DTEND:20250929T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/203
DESCRIPTION:Title: Oligomorphic groups and new tensor categories\n
by Kevin Coulembier (Sydney) as part of Paris algebra seminar\n\n\nAbstrac
t\nIn the 90’s Deligne ‘classified’ symmetric tensor categories of m
oderate growth in characteristic zero and initiated the study of categorie
s of faster growth. Since then a lot of progress has been made in positive
characteristic and for categories of fast growth. In this talk we will re
view this and then introduce and combine two successful contributing theor
ies: oligomorphic groups and abelian envelopes. Joint with Andrew Snowden.
\n\nThis talk will take place in hybrid mode at the Institut Henri Poincar
é.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calvin Pfeifer (Cologne)
DTSTART:20251020T120000Z
DTEND:20251020T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/204
DESCRIPTION:Title: Serre cyclotomic algebras\nby Calvin Pfeifer (C
ologne) as part of Paris algebra seminar\n\n\nAbstract\nIn 2013\, de la Pe
ña initiated the systematic study of algebras of cyclotomic type\, that i
s finite-dimensional algebras of finite global dimension such that some po
wer of their Coxeter matrix is unipotent. For example\, fractionally Calab
i–Yau algebras have periodic Coxeter matrices. In this talk\, we propose
a class of algebras\, which we call Serre cyclotomic\, as a generalizatio
n of fractionally Calabi–Yau algebras\, and as a categorification of alg
ebras of cyclotomic type. We study dynamical properties of their Nakayama
functors and the complexity of their trivial extension algebras. Based on
recent work of Chang–Schroll\, we characterize Serre cyclotomic gentle a
lgebras. Finally\, we provide further examples coming from generalized spe
cies. Parts of this ongoing work are joint with Sibylle Schroll.\n\n\nThis
talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (IMJ-PRG)
DTSTART:20250922T120000Z
DTEND:20250922T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/205
DESCRIPTION:Title: Cluster tilting in topological Fukaya categories fo
r higher Teichmüller theory\nby Merlin Christ (IMJ-PRG) as part of Pa
ris algebra seminar\n\n\nAbstract\nThe (decorated) higher Teichmüller spa
ce of a marked surface is a space of local systems valued in a split simpl
e Lie group of a Dynkin type I. There is a corresponding cluster algebra\,
which gives rise to coordinates on the higher Teichmüller space. We will
discuss additive categorifications of these cluster algebras. We first as
sociate a (relative) 3-Calabi--Yau dg category with the surface and Dynkin
type I. This dg category arises by gluing\, along a perverse (co)sheaf of
categories. The fundamental building block is associated with the 3-gon s
urface (=the basic triangle). The 3-CY category of the basic triangle was
introduced and studied in recent work of B. Keller and M. Liu. We then dis
cuss an equivalence between the following three Frobenius exact dg/infinit
y-categories\, categorifying the cluster algebra:\n\n1) The Higgs category
associated with the 3-CY category.\n\n2) The cosingularity category of th
e 3-CY category.\n\n3) The topological Fukaya category of the surface valu
ed in the 2-periodic 1-CY cluster category of type I.\n\nThis talk will ta
ke place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Francone (Rome Tor Vergata)
DTSTART:20251006T120000Z
DTEND:20251006T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/206
DESCRIPTION:Title: Schemes of bands and their cluster structures\n
by Luca Francone (Rome Tor Vergata) as part of Paris algebra seminar\n\n\n
Abstract\nIn a recent joint work with Bernard Leclerc\, we introduce a fam
ily of infinite-dimensional affine schemes called schemes of (G\,c)-bands.
Here\, G denotes a simple\, simply laced\, and simply connected algebraic
group\, and c is a Coxeter element of its Weyl group. These schemes offer
a common geometric framework for understanding certain cluster algebras w
hich play a central role in the representation theory of (untwisted) quant
um affine algebras\, their Borel subalgebras\, and shifted quantum affine
algebras. The goal of this talk is to introduce these schemes and explore
their connections with cluster algebras and representation theory.\n\nThis
talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serge Bouc (Amiens)
DTSTART:20251103T130000Z
DTEND:20251103T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/207
DESCRIPTION:Title: On Alperin's conjecture and functorial equivalence
of blocks\nby Serge Bouc (Amiens) as part of Paris algebra seminar\n\n
\nAbstract\nAlperin's weight conjecture (1987) is one of the most importan
t\nso-called "local-global" conjectures in the block theory of finite grou
ps.\nIt relates "global" information on a block algebra of a finite group
G\n- typically\, the number of its simple modules - to information attache
d\nto "local" subgroups of G - typically\, the number of their projective
simple\nmodules. In this talk\, I will show how this conjecture can be int
erpreted\n- and proved to hold "stably" - in the category of diagonal p-pe
rmutation\nfunctors.\nThis is joint work with Deniz Yılmaz (Bilkent)\, an
d Deniz Yılmaz and Robert\nBoltje (UCSC). \n\nThis talk will take place i
n hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yingchun Zhang (Shanghai Jiao Tong)
DTSTART:20251110T130000Z
DTEND:20251110T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/208
DESCRIPTION:Title: On the Seiberg duality conjecture at the geometric
level and its applications\nby Yingchun Zhang (Shanghai Jiao Tong) as
part of Paris algebra seminar\n\n\nAbstract\nIn the first part\, I will in
troduce our work in progress on the Seiberg duality conjecture at the geom
etric level. Consider a quiver with potential. It has been proved by many
people that its quasimap I function is preserved under quiver mutation in
some sense. In this work\, we further consider the behaviour of the repres
entation scheme under quiver mutation.\nIn the second part\, I will talk a
bout an expected application of this result to the relation between cluste
r algebras and quantum cohomology rings. From a given quiver\, one can con
struct a cluster algebra. One the other hand\, one can consider the quantu
m cohomology ring of the quiver variety when it is smooth. We expect that
there is an algebra homomorphism from the cluster algebra to the quantum c
ohomology ring. \nThis is a joint work with Zijun Zhou and Yaoxiong Wen.\n
\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanpeng Li (Sichuan U.)
DTSTART:20251027T130000Z
DTEND:20251027T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/209
DESCRIPTION:Title: Cluster structures\, integrable systems and symplec
tic groupoids\nby Yanpeng Li (Sichuan U.) as part of Paris algebra sem
inar\n\n\nAbstract\nWe introduce two operations applicable to a compatible
cluster structure on a Poisson variety. (1) We present a construction of
an integrable system on the tangent space equipped with the Poisson bivect
or which is the linearization of a Poisson-cluster variety\; (2) If a Pois
son-cluster variety integrates into a symplectic groupoid\, it is a natura
l question to ask whether a compatible cluster structure exists on the tot
al space. We give a positive answer to such a question when the base varie
ties are the standard Poisson Lie groups and Schubert varieties. This is j
oint work with Yu Li and Jiang-Hua Lu.\n\nThis talk will take place on Zoo
m only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/20
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (UC Davis)
DTSTART:20251117T130000Z
DTEND:20251117T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/210
DESCRIPTION:Title: Positivity of generalized cluster algebras\nby
Lang Mou (UC Davis) as part of Paris algebra seminar\n\n\nAbstract\nI will
discuss the recent proof of positivity of generalized cluster algebras\,
in collaboration with Amanda Burcroff and Kyungyong Lee (arXiv:2503.03719)
. We prove that the generalized cluster scattering diagram\, extending the
construction of Gross-Hacking-Keel-Kontsevich\, has positive wall-functio
n coefficients\, implying Laurent positivity of cluster variables and stro
ng positivity of theta functions. The argument reduces to the rank-2 case\
, where positivity is shown to follow from a combinatorial solution to cer
tain generalized Lee–Li–Zelevinsky greedy recurrences via counting spe
cial classes of Rupel’s compatible gradings.\n\nThis talk will take plac
e on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Kleinau (Bonn)
DTSTART:20251124T130000Z
DTEND:20251124T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/211
DESCRIPTION:Title: Cambrian lattices are fractionally Calabi-Yau via 2
-cluster combinatorics\nby Markus Kleinau (Bonn) as part of Paris alge
bra seminar\n\n\nAbstract\nCambrian lattices originate in the theory of Co
xeter groups. They appear as 1-skeletons of generalised associahedra or as
lattices of torsion classes of representation finite hereditary algebras.
Rognerud has shown that Cambrian lattices of linear type A\, better known
as Tamari lattices\, are fractionally Calabi-Yau. That is a power of the
Serre functor on the derived category of their incidence algebra agrees wi
th a power of the shift.\nThe m-cluster categories are an m+1 Calabi-Yau v
ersion of cluster categories. They contain a family of m-cluster tilting o
bjects connected by a notion of mutation. In this talk I will introduce a
family of intervals in crystallographic Cambrian lattices that exhibit the
same combinatorics as 2-cluster tilting objects in 2-cluster categories.
As a consequence I will show that Cambrian lattices are fractionally Calab
i-Yau.\n\nThis talk will take place in hybrid mode at the Institut Henri P
oincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Voloshyn (Pohang)
DTSTART:20251201T130000Z
DTEND:20251201T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/212
DESCRIPTION:Title: New normal forms in Lie theory and cluster algebras
\nby Dmitriy Voloshyn (Pohang) as part of Paris algebra seminar\n\n\nA
bstract\nI will describe a new family of rational normal forms in Lie theo
ry. The family arises as a tool for constructing cluster structures on dua
l Poisson-Lie groups\, and it gives rise to some interesting combinatorics
of what I call rational Weyl group elements. The talk will be based on th
e preprint arXiv:2506.01530.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryu Tomonaga (Tokyo)
DTSTART:20251215T130000Z
DTEND:20251215T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/213
DESCRIPTION:Title: Weak del Pezzo surfaces yield 2-hereditary algebras
and 3-Calabi-Yau algebras\nby Ryu Tomonaga (Tokyo) as part of Paris a
lgebra seminar\n\n\nAbstract\nThe importance of studying d-tilting bundles
\, which are tilting bundles whose endomorphism algebras have global dimen
sion d (or less)\, on d-dimensional smooth projective varieties has been r
ecognized recently. Previous work conjectured that a smooth projective sur
face has a 2-tilting bundle if and only if is is a weak del Pezzo surface.
In our research\, we prove this conjecture affirmatively. Moreover\, this
endomorphism algebra becomes a 2-representation infinite algebra whose 3-
Calabi-Yau completion gives a non-commutative crepant resolution (NCCR) of
the corresponding Du Val del Pezzo cone\, generalizing a result of Van de
n Bergh. This talk is based on arXiv:2510.26199.\n\nThis talk will take pl
ace on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Beijing Normal)
DTSTART:20260126T130000Z
DTEND:20260126T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/214
DESCRIPTION:Title: Quantum cluster algebras over commutative rings and
quantized coordinate rings of simple algebraic groups\nby Fan Qin (Be
ijing Normal) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce
quantum cluster algebras over arbitrary commutative rings. We also presen
t a general method to construct (partially compactified) quantum cluster s
tructures on quantized coordinate rings from those defined on localization
s\, in a setting where the standard codimension-two arguments used in the
classical case are no longer available.\n\nAs an application\, we obtain n
atural quantum cluster structures on the quantized coordinate rings of all
simple algebraic groups over arbitrary commutative rings. This is based o
n a series of joint papers with Milen Yakimov and Hironori Oya.\n\nThis ta
lk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine de Saint Germain (U. of Hong Kong)
DTSTART:20251208T130000Z
DTEND:20251208T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/215
DESCRIPTION:Title: On the correspondence between root systems and clus
ter algebras\nby Antoine de Saint Germain (U. of Hong Kong) as part of
Paris algebra seminar\n\n\nAbstract\nOne of the first remarkable results
in the structure theory of cluster algebras of finite type is their classi
fication by root systems. Since its discovery by Fomin and Zelevinsky\, ma
ny more surprising connections between cluster algebras and root systems h
ave appeared. In this talk\, I will give an overview of old connections\,
mention new connections\, and propose a geometric explanation for these co
nnections. This is partly based on joint work with Jiang-Hua Lu\, availabl
e at arxiv: 2503.11391.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Hohlweg (Montréal)
DTSTART:20260309T130000Z
DTEND:20260309T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/216
DESCRIPTION:Title: Reflections on Coxeter Systems\nby Christophe H
ohlweg (Montréal) as part of Paris algebra seminar\n\n\nAbstract\nThere a
re three families of Coxeter systems: finite\, affine\, and indefinite. By
far\, the class of indefinite Coxeter systems (which includes\, for insta
nce\, hyperbolic discrete reflection groups) is the least understood. One
reason is the lack of tools to control the set of reflections\, or equival
ently\, the root system and the Coxeter arrangement. In this talk\, I will
discuss recent developments of such tools and some open problems involvin
g the notions of Garside shadows (introduced in the context of Artin–Tit
s monoids) and Shi arrangements. As an example of an application\, we will
explain their relationship with the Osajda–Przytycki biautomatic struct
ure for Coxeter systems.\n\nThis talk will take place in hybrid mode at th
e Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Mizuno (Utrecht)
DTSTART:20260223T130000Z
DTEND:20260223T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/217
DESCRIPTION:Title: Bondal–Orlov’s reconstruction theorem in noncom
mutative projective geometry\nby Yuki Mizuno (Utrecht) as part of Pari
s algebra seminar\n\n\nAbstract\nThe (derived) category of coherent sheave
s on a scheme encodes rich information about the underlying geometry. P. G
abriel showed that for noetherian schemes X and Y\, if Coh X and Coh Y are
equivalent as abelian categories\, then X and Y are isomorphic. Furthermo
re\, A. Bondal and D. Orlov proved that for smooth projective schemes X an
d Y with (anti-)ample canonical bundles\, if D^b(Coh X) and D^b(Coh Y) are
equivalent as triangulated categories\, then X and Y are isomorphic. On t
he other hand\, J.-P. Serre showed that the category of coherent sheaves o
n a projective scheme can be described as the quotient category of finitel
y generated graded modules over the homogeneous coordinate ring by the sub
category of torsion modules. Motivated by the results of Gabriel and Serre
\, the quotient category of finitely generated graded modules over a (not
necessarily commutative) graded ring by the subcategory of torsion modules
is called a noncommutative projective scheme. In this talk\, I will prese
nt an analogue of Bondal–Orlov’s reconstruction theorem in the setting
of noncommutative projective geometry.\n\nThis talk will take place in hy
brid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (USTC Hefei)
DTSTART:20260209T130000Z
DTEND:20260209T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/218
DESCRIPTION:Title: The tropical invariant and the $F$-invariant in clu
ster algebras\nby Peigen Cao (USTC Hefei) as part of Paris algebra sem
inar\n\n\nAbstract\nThe Lambda-invariant and the d-invariant are two integ
er-valued invariants introduced by Kang-Kashiwara-Kim-Oh and by Kashiwara-
Kim-Oh-Park in their study of monoidal categorification of cluster algebra
s using finite-dimensional modules over quiver Hecke algebras and quantum
affine algebras. The Lambda-invariant can be viewed as a monoidal categori
fication of the compatible Poisson structure on those cluster algebras. Th
e d-invariant is defined as half the symmetrized sum of Lambda-invariants\
, and it can be used to characterize the strong commutativity between real
simples.\n\n\nIn this talk\, we introduce the tropical invariant and the
F-invariant in cluster algebras. The tropical invariant is defined for any
cluster algebra with a compatible Poisson structure and it generalizes th
e Lambda-invariant. The F-invariant is defined as the symmetrized sum of t
he tropical invariants and it simultaneously generalizes all of the follow
ing invariants: the d-invariant\, Derksen-Weyman-Zelevinsky’s E-invarian
t\, Fu-Gyoda’s f-compatibility degree\, Fomin-Zelevinsky’s compatibili
ty degree\, and Qiu-Zhou’s f-intersection number on marked surfaces.\n\n
This talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyang Liu (U. of Tokyo)
DTSTART:20260202T130000Z
DTEND:20260202T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/219
DESCRIPTION:Title: Calabi-Yau structures on derived and singularity ca
tegories of symmetric orders\nby Junyang Liu (U. of Tokyo) as part of
Paris algebra seminar\n\n\nAbstract\nThis is a report on recent work in co
llaboration with Norihiro Hanihara (arXiv:2512.03836). We develop a differ
ential graded enhancement of Amiot's construction of Calabi-Yau structures
on Verdier quotients. Using this framework\, we establish the existence o
f a right Calabi-Yau structure on the dg singularity category associated w
ith a symmetric order. Combining this with a structure theorem in collabor
ation with Bernhard Keller\, we establish a triangle equivalence between t
he singularity category with a cluster-tilting object and the cluster cate
gory associated with a Calabi-Yau dg algebra. We also construct a left Cal
abi-Yau structure on the bounded dg derived category of a symmetric order\
, which is a non-commutative analogue of a result by Brav-Dyckerhoff.\n\nT
his talk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/21
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Cerulli (Rome)
DTSTART:20260216T130000Z
DTEND:20260216T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/220
DESCRIPTION:Title: Quivers with Polynomial Identities\nby Giovanni
Cerulli (Rome) as part of Paris algebra seminar\n\n\nAbstract\nSeventy-fi
ve years have passed since Amitsur and Levitzki proved that the algebra of
n x n matrices satisfies the standard polynomial identity of degree 2n. S
ince then\, mathematicians have investigated algebras whose elements satis
fy a polynomial identity\, meaning that every substitution of elements of
the algebra into a given noncommutative polynomial yields zero. Such algeb
ras are known as PI algebras.\n\n\n The theory of PI algebras has d
eveloped enormously over the years\, leading to deep and far-reaching resu
lts. In this talk\, we address the following natural questions: which quiv
ers have a path algebra that is PI? What can be said about the correspondi
ng T-ideal of polynomial identities? And how does the situation change whe
n relations are imposed on the path algebra?\n\n\n This is joint wo
rk with Elena Pascucci and Javier De Loera Chávez.\n\nThis talk will take
in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Chang (Shaanxi Normal U.)
DTSTART:20260323T130000Z
DTEND:20260323T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/221
DESCRIPTION:Title: Entropy of the Serre functor for partially wrapped
Fukaya categories of surfaces with stops\nby Wen Chang (Shaanxi Normal
U.) as part of Paris algebra seminar\n\n\nAbstract\nI will talk about the
categorical entropy of the Serre functor for partially wrapped Fukaya cat
egories of graded surfaces with stops\, as well as for perfect derived cat
egories of homologically smooth graded gentle algebras (to which the afore
mentioned Fukaya categories are equivalent). We prove that the entropy of
the Serre functor is a piecewise linear function determined by the winding
numbers of the surface’s boundary components and the number of stops on
each component. Specifically\, the function takes different linear forms
for non-negative and non-positive arguments\, with slopes related to the m
inimum and maximum values derived from the ratio of each boundary componen
t’s winding number to its stop count. We further derive the correspondin
g upper and lower Serre dimensions. Additionally\, for ungraded homologica
lly smooth gentle algebras\, we establish a Gromov–Yomdin-like equality\
, linking the categorical entropy of the Serre functor to the natural loga
rithm of the spectral radius of the Coxeter transformation. The talk is ba
sed on the preprint arXiv:2508.14860\, which is joint with A. Elagin and S
. Schroll.\n\nThis talk will take place in hybrid mode at the Institut Hen
ri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Canesin (Paris Cité)
DTSTART:20260316T130000Z
DTEND:20260316T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/222
DESCRIPTION:Title: An additive interpretation of the monoidal $\\Lambd
a$-invariant\nby Ricardo Canesin (Paris Cité) as part of Paris algebr
a seminar\n\n\nAbstract\nThe Lambda-invariant for quantum affine algebras
was introduced by Kashiwara-Kim-Oh-Park as an important tool in their stud
y of the monoidal categorification of cluster algebras. At the level of th
e cluster algebra\, it is related to a compatible Poisson structure\, and
it was recently shown to coincide with Peigen Cao’s tropical invariant.\
n\nIn this talk\, we interpret these invariants using the additive categor
ification of cluster algebras via Higgs categories in the sense of Yilin W
u. Whenever the relative Ginzburg algebra is proper\, we show that the Hig
gs category admits a canonical quantum structure in the sense of Grabowski
-Pressland\, and we give a homological interpretation of the corresponding
tropical invariant.\n\nFor certain finite-rank cluster algebras categorif
ied by Kashiwara-Kim-Oh-Park\, we show that the associated relative Ginzbu
rg algebra is indeed proper\, and that our additive Lambda-invariant agree
s with their monoidal one.\n\nThis is joint work in progress with Geoffrey
Janssens and Peigen Cao.\n\nThis talk will take place in hybrid mode at t
he Institut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktoria Klasz (Bonn)
DTSTART:20260511T120000Z
DTEND:20260511T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/223
DESCRIPTION:by Viktoria Klasz (Bonn) as part of Paris algebra seminar\n\n\
nAbstract\nThis talk will take place in hybrid mode at the Institut Henri
Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dani Kaufmann (MPI MIS Leipzig)
DTSTART:20260427T120000Z
DTEND:20260427T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/224
DESCRIPTION:by Dani Kaufmann (MPI MIS Leipzig) as part of Paris algebra se
minar\n\n\nAbstract\nThis talk will take place in hybrid mode at the Insti
tut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Garcia (UQAM)
DTSTART:20260302T130000Z
DTEND:20260302T140000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/225
DESCRIPTION:Title: Infinite super friezes\nby Monica Garcia (UQAM)
as part of Paris algebra seminar\n\n\nAbstract\nSuper friezes were introd
uced by S. Morier-Genoud\, V. Ovsienko\, S. Tabachnikov as a supersymmetri
c analog of classical Coxeter friezes. They show analogous properties of c
lassical friezes: they are determined by the first non-trivial even and od
d quiddity rows\, they satisfy linear recurrence relations\, and exhibit g
lide symmetry when of finite width. Moreover\, as shown by G. Musiker\, N.
Ovenhouse and S. Zhang\, all finite width super friezes arise from a deco
rated triangulation of a polygon\, where even entries correspond to $\\lam
bda$-lengths of arcs\, and odd entries to $\\mu$-invariants of triangles i
n the polygon. In this talk\, I will report on joint work with A. Burcroff
\, İ. Çanakçı\, F. Fedele and V. Klász on how to construct infinite s
uper friezes from decorated skeletal triangulations of annuli. \n\nThis ta
lk will take place on Zoom only.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anya Nordskova (IPMU Tokyo)
DTSTART:20260504T120000Z
DTEND:20260504T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/226
DESCRIPTION:by Anya Nordskova (IPMU Tokyo) as part of Paris algebra semina
r\n\n\nAbstract\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wu (Luxembourg)
DTSTART:20260615T120000Z
DTEND:20260615T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/227
DESCRIPTION:by Yilin Wu (Luxembourg) as part of Paris algebra seminar\n\n\
nAbstract\nThis talk will take place in hybrid mode at the Institut Henri
Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Tohoku and Paris Cité)
DTSTART:20260601T120000Z
DTEND:20260601T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/228
DESCRIPTION:by Shunsuke Kano (Tohoku and Paris Cité) as part of Paris al
gebra seminar\n\n\nAbstract\nThis talk will take place in hybrid mode at t
he Instiut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Silberberg (Paris Cité)
DTSTART:20260413T120000Z
DTEND:20260413T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/229
DESCRIPTION:Title: Folding of cluster algebras and quantum toroidal al
gebras\nby Lior Silberberg (Paris Cité) as part of Paris algebra semi
nar\n\n\nAbstract\nIn this talk\, I will present a relationship between th
e representation theory of the infinite rank quantum affine algebra Uq(sl_
∞) and that of the quantum toroidal algebra Uq(sl_2n\,tor). In particula
r\, I will discuss folding techniques for cluster algebras arising from in
finite quivers\, and show that the monoidal categorifications associated t
o these quantum algebras (due to Hernandez-Leclerc and Nakajima) are relat
ed by folding. I will explain how this allows us to verify a conjecture by
Hernandez in new cases.\n\nThis talk will take in hybrid mode at the Inst
itut Henri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/22
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuma Mizuno (Cork)
DTSTART:20260518T120000Z
DTEND:20260518T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/230
DESCRIPTION:by Yuma Mizuno (Cork) as part of Paris algebra seminar\n\n\nAb
stract\nThis talk will take place in hybrid mode at the Institut Henri Poi
ncaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/23
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryu Tomonaga (U. of Tokyo)
DTSTART:20260608T120000Z
DTEND:20260608T130000Z
DTSTAMP:20260404T095042Z
UID:paris-algebra-seminar/231
DESCRIPTION:by Ryu Tomonaga (U. of Tokyo) as part of Paris algebra seminar
\n\n\nAbstract\nThis talk will take place in hybrid mode at the Institut H
enri Poincaré.\n
LOCATION:https://stable.researchseminars.org/talk/paris-algebra-seminar/23
1/
END:VEVENT
END:VCALENDAR