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BEGIN:VEVENT
SUMMARY:Hipolito Treffinger (University of Leicester\, UK)
DTSTART:20200514T120000Z
DTEND:20200514T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/1
DESCRIPTION:Title: Representation theoretic aspects of scattering diagrams\nby Hipo
lito Treffinger (University of Leicester\, UK) as part of Longitudinal Alg
ebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe notion o
f algebraic scattering diagram associated to any finite dimensional algebr
a was recently introduced by Bridgeland as an algebraic construction of th
e celebrated cluster scattering diagrams of Gross\, Hacking\, Keel and Kon
tsevich. In this talk\, after briefly recalling the construction of scatte
ring diagrams given by Bridgeland\, we will show how the homological aspec
ts of the module category determine several properties of the support of t
he scattering diagrams. In particular\, we will show that chambers in the
scattering diagram of an algebra are in one-to-one correspondence with ce
rtain torsion pairs in its module category. This is joint work with Thomas
Brustle and David Smith. Based on this characterisation\, we will discuss
how the study of torsion pairs in the module category of algebras can pla
y a key role in the calculation of Donaldson-Thomas invariants for certain
Calabi-Yau threefolds.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHES\, France)
DTSTART:20200521T120000Z
DTEND:20200521T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/2
DESCRIPTION:Title: Gluing relative stability conditions along pushouts\nby Alex Tak
eda (IHES\, France) as part of Longitudinal Algebra and Geometry Open ONli
ne Seminar (LAGOON)\n\n\nAbstract\nIn this talk I will discuss the results
of arXiv:1811.10592 and some later developments\, concerning how to produ
ce Bridgeland stability conditions on certain categories from using a loca
l-to-global principle. The example of particular interest will be the topo
logical Fukaya category of a marked surface\, and the description of the l
ocal data is inspired by the construction of stability conditions on such
categories using quadratic differentials by Haiden\, Katzarkov and Kontsev
ich. As an application of this method\, we show that one can understand al
l the components of the stability space of such categories\, and that in s
uitable cases the whole space is described by these HKK stability conditio
ns.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Université Paris Diderot - Paris 7\, France)
DTSTART:20200528T120000Z
DTEND:20200528T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/3
DESCRIPTION:Title: Grassmannian braiding categorified\nby Bernhard Keller (Universi
té Paris Diderot - Paris 7\, France) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nChris Fraser has disc
overed an action of the extended affine braid group on d strands on the Gr
assmannian cluster algebra of k-subspaces in n-space\, where d is the leas
t common divisor of k and n. We lift this action to the corresponding clus
ter category first constructed by Geiss-Leclerc-Schröer in 2008. For this
\, we use Jensen-King-Su's description of this category as a singularity c
ategory in the sense of Buchweitz/Orlov. We conjecture an action of the sa
me braid group on the cluster algebra associated with an arbitrary pair of
Dynkin diagrams whose Coxeter numbers are k and n. This is a report on on
going joint work with Chris Fraser.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Balazs Szendroi (University of Oxford\, UK)
DTSTART:20200604T120000Z
DTEND:20200604T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/4
DESCRIPTION:Title: Hilbert schemes of points on singular surfaces: combinatorics\, geom
etry\, and representation theory\nby Balazs Szendroi (University of Ox
ford\, UK) as part of Longitudinal Algebra and Geometry Open ONline Semina
r (LAGOON)\n\n\nAbstract\nGiven a smooth algebraic surface S over the comp
lex numbers\, the Hilbert scheme of points of S is the starting point for
many investigations\, leading in particular to generating functions with m
odular behaviour and Heisenberg algebra representations. I will explain as
pects of a similar story for surfaces with rational double points\, with l
inks to algebraic combinatorics and the representation theory of affine Li
e algebras. I will in particular recall our 2015 conjecture concerning the
generating function of the Euler characteristics of the Hilbert scheme fo
r this singular case\, and aspects of more recent work that lead to a very
recent proof of the conjecture by Nakajima. Joint work with Gyenge and Ne
methi\, respectively Craw\, Gammelgaard and Gyenge.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiu Yu (Tsinghua University Beijing\, China)
DTSTART:20200611T120000Z
DTEND:20200611T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/5
DESCRIPTION:Title: Graded decorated marked surfaces: Calabi-Yau-X categories of gentle
algebras\nby Qiu Yu (Tsinghua University Beijing\, China) as part of L
ongitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstrac
t\nMotivated by q-deforming of stability conditions and categories\, we st
udy the Calabi-Yau-X categories of gentle algebras from graded decorated m
arked surfaces. The string model in this case unifies the Calabi-Yau-3 cas
e in the prequels and the usual/Calabi-Yau-infinity case (via Lagrangian i
mmersion). This is a joint work with Akishi Ikeda and Yu Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wendy Lowen (University of Antwerp\, Belgium)
DTSTART:20200625T120000Z
DTEND:20200625T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/6
DESCRIPTION:Title: Linear quasi-categories as templicial modules\nby Wendy Lowen (U
niversity of Antwerp\, Belgium) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\n(joint work with Arne Merte
ns) We introduce a notion of enriched infinity categories over a given mon
oidal category\, in analogy with quasi-categories over the category of set
s. We make use of certain colax monoidal functors\, which we calltemplicia
l objects\, as a replacement of simplicial objects that respects the monoi
dal structure. We relate the resulting enriched quasi-categories to nonass
ociative Frobenius monoidal functors\, allowing us to prove that the free
templicial module over an ordinary quasi-category is a linear quasi-catego
ry. To any dg category we associate a linear quasi-category\, the linear d
g nerve\, which enhances the classical dg nerve\, and we argue that linear
quasi-categories can be seen as relaxations of dg-categories.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Nakajima (Kavli IPMU\, Tokyo\, Japan)
DTSTART:20200702T120000Z
DTEND:20200702T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/7
DESCRIPTION:Title: Euler numbers of Hilbert schemes of points on simple surface singula
rities and quantum dimensions of standard modules of quantum affine algebr
as\nby Hiraku Nakajima (Kavli IPMU\, Tokyo\, Japan) as part of Longitu
dinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nBal
azs explained his conjecture with Gyenge and Nemethi on\nEuler numbers of
Hilbert schemes on June 4. I proved it by showing that\nquantum dimensions
of standard modules of quantum affine algebras are\nalways 1. This remark
able property is the simplest case of a conjecture\non quantum dimensions
of Kirillov-Reshetikhin modules proposed by Kuniba\nin 93\, which is still
open for E7\,8 in general. In this talk\, I will\nemphasize on representa
tion theoretic aspects to minimize overlaps with\nBalazs' talk.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM Oaxaca\, Mexico)
DTSTART:20200618T150000Z
DTEND:20200618T160000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/8
DESCRIPTION:Title: Families of Gröbner degenerations\nby Lara Bossinger (UNAM Oaxa
ca\, Mexico) as part of Longitudinal Algebra and Geometry Open ONline Semi
nar (LAGOON)\n\n\nAbstract\nIn this talk I will present a construction of
one flat family that combines many Gröbner degenerations. More precisely\
, for a (weighted) homogeneous ideal we consider a maximal cone in its Gr
öbner fan. Associated to that cone we define a flat family that contains
various special fibers associated to the initial degenerations of the cone
and all its faces. This construction has several interesting applications
. Most surprisingly\, it recovers the recursive construction of universal
coefficients for cluster algebras in a non-recursive way for the Grassmann
ians Gr(2\,n) and Gr(3\,6). If time permits I will present another applica
tion explaining how to recover Kaveh-Manon's toric equivariant families ar
ising from a collection of nice cones in the tropicalization of an ideal.
This talk is based on joint work in progress with F. Mohammadi and A. Náj
era Chávez.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Polishchuk (University of Oregon\, USA)
DTSTART:20200709T150000Z
DTEND:20200709T160000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/9
DESCRIPTION:Title: Geometry of the Associative Yang-Baxter equation\nby Alexander P
olishchuk (University of Oregon\, USA) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will describe the
connection\, discovered jointly with Yanki Lekili\, between Associative Ya
ng-Baxter equation (AYBE) and pairs of 1-spherical objects in A-infinity c
ategories. I will then explain how such pairs arise from noncommutative or
ders over singular curves\, in particular\, how to get all nondegenerate t
rigonometric solutions of the AYBE in this way. If time allows\, I will ta
lk about the Lie analog of this story for the classical Yang-Baxter equati
on.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Universität Bochum\, Germany)
DTSTART:20200716T120000Z
DTEND:20200716T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/10
DESCRIPTION:Title: Fano quiver moduli\nby Markus Reineke (Universität Bochum\, Ge
rmany) as part of Longitudinal Algebra and Geometry Open ONline Seminar (L
AGOON)\n\n\nAbstract\nWe construct a large class of quiver moduli spaces w
ith are Fano varieties\, by studying global sections of line bundles on qu
iver moduli and identifying a special class of stabilities. We discuss sev
eral classes of examples (e.g. toric varieties\, point configuration space
s\, Kronecker moduli).\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:2020 Categorifications in Representation Theory
DTSTART:20200917T120000Z
DTEND:20200917T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/11
DESCRIPTION:Title: Categorifications in Representation Theory Conference at Leicester
(Sep 15-17)\nby 2020 Categorifications in Representation Theory as par
t of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Schaposnik (University of Illinois at Chicago\, USA)
DTSTART:20200723T120000Z
DTEND:20200723T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/12
DESCRIPTION:Title: On Generalized Hyperpolygons\nby Laura Schaposnik (University o
f Illinois at Chicago\, USA) as part of Longitudinal Algebra and Geometry
Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk we will introduce
generalized hyperpolygons\, which arise as Nakajima-type representations
of a comet-shaped quiver\, following a recent work joint with Steven Rayan
. After showing how to identify these representations with pairs of polygo
ns\, we shall associate to the data an explicit meromorphic Higgs bundle o
n a genus g Riemann surface\, where g is the number of loops in the comet.
We shall see that\, under certain assumptions on flag types\, the moduli
space of generalized hyperpolygons admits the structure of a completely in
tegrable Hamiltonian system. Time permitting\, we shall conclude the talk
by mentioning some partial results on current work on the construction of
triple branes (in the sense of Kapustin-Witten mirror symmetry)\, and dual
ities between tame and wild Hitchin systems (in the sense of Painlevé tra
nscendents).\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires\, Argentina)
DTSTART:20200903T120000Z
DTEND:20200903T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/13
DESCRIPTION:Title: A cup-cap duality in Koszul calculus\nby Andrea Solotar (Univer
sity of Buenos Aires\, Argentina) as part of Longitudinal Algebra and Geom
etry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk I will intro
duce a cup-cap duality in the Koszul calculus of N-homogeneous algebras fo
llowing https://arxiv.org/abs/2007.00627. As an application of this dualit
y\, it follows that the graded symmetry of the Koszul cap product is a con
sequence of the graded commutativity of the Koszul cup product. I will als
o comment on a conceptual approach to this problem that may lead to a proo
f of the graded commutativity\, based on derived categories in the framewo
rk of DG algebras and DG bimodules. This is joint work with Roland Berger.
\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (University of Stuttgart\, Germany)
DTSTART:20200910T120000Z
DTEND:20200910T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/14
DESCRIPTION:Title: Deformations of path algebras of quivers with relations\nby Zhe
ngfang Wang (University of Stuttgart\, Germany) as part of Longitudinal Al
gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this tal
k\, we provide a very explicit method to describe deformations of path alg
ebras of quivers with relations. This method is based on a combinatorial d
escription of an L-infinity algebra constructed from Chouhy-Solotar’s pr
ojective resolution. As an application\, we show that the variety associat
ed to monomial algebras constructed by Green-Hille-Schroll is actually giv
en by the Maurer--Cartan equation of the L-infinity algebra. This is joint
work with Severin Barmeier.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alisa Keating (University of Cambridge\, UK)
DTSTART:20200924T120000Z
DTEND:20200924T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/15
DESCRIPTION:Title: Homological mirror symmetry for log Calabi-Yau surfaces\nby Ali
sa Keating (University of Cambridge\, UK) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nGiven a log Calab
i-Yau surface Y with maximal boundary D\, I'll explain how to construct a
mirror Landau-Ginzburg model\, and sketch a proof of homological mirror sy
mmetry for these pairs when (Y\,D) is distinguished within its deformation
class (this is mirror to an exact manifold). I'll explain how to relate t
his to the total space of the SYZ fibration predicted by Gross--Hacking--K
eel\, and\, time permitting\, explain ties with earlier work of Auroux--Ka
tzarkov--Orlov and Abouzaid. Joint work with Paul Hacking.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow\, UK)
DTSTART:20201029T120000Z
DTEND:20201029T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/16
DESCRIPTION:Title: Contraction algebras\, plumbings and flops\nby Michael Wemyss (
University of Glasgow\, UK) as part of Longitudinal Algebra and Geometry O
pen ONline Seminar (LAGOON)\n\n\nAbstract\nI will explain how certain symm
etric Nakayama algebras (under the disguise of "contraction algebras") con
trol and prove theorems about geometric objects on both sides of mirror sy
mmetry. As part of this\, I will explain our symplectic geometry model\,
our algebraic geometry model\, and then how the contraction algebra relate
s them. The cohomology of objects in the underlying categories are natura
lly modules for the associated contraction algebra\, and I will explain ho
w to use this information to obtain otherwise tricky results\, such as a c
lassification of spherical (and more generally\, fat-spherical) objects.
This has purely topological corollaries. One feature\, which I will proba
bly gloss over but is actually fundamental\, is that our categories have a
dependence on the characteristic of the ground field. This is joint work
with Ivan Smith (arXiv:2010.10114).\n\nThursday 29th October 2020\, 12:00
– 13:00 (GMT)\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXczUF
dJc282bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur (University of Leeds\, UK and University of Graz\, Aust
ria)
DTSTART:20201001T110000Z
DTEND:20201001T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/17
DESCRIPTION:Title: Structure of Grassmannian cluster categories\nby Karin Baur (Un
iversity of Leeds\, UK and University of Graz\, Austria) as part of Longit
udinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nTh
e category of Cohen Macaulay modules over a quotient of a preprojective al
gebra provides an additive categorification of Scott’s cluster algebra s
tructure of the coordinate ring of the Grassmannian of k-subspaces in n-sp
ace\, by work of Jensen\, King and Su. Under this correspondence\, rigid i
ndecomposable objects map to cluster variables. A special role is played b
y rank 1 indecomposables which correspond bijectively to Plücker coordina
tes. These are in fact all indecomposables in case k=2. In the other finit
e types (i.e. $(k\,n)\\in \\{(3\,6)\,(3\,7)\,(3\,8)\\}$)\, there are also
rank 2 and rank 3 rigid indecomposables. In general\, the Grassmannian cat
egories are not well understood. We provide characterisations for these lo
w rank modules in infinite types. This is joint work with Dusko Bogdanic
and Ana Garcia Elsener and with Bogdanic\, Garcia Elsener and Jianrong Li.
\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Lazarev (Lancaster University\, UK)
DTSTART:20201008T110000Z
DTEND:20201008T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/18
DESCRIPTION:Title: Koszul duality for dg-categories and infinity-categories\nby An
drey Lazarev (Lancaster University\, UK) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nDifferential grade
d (dg) Koszul duality is a certain adjunction between the category of dg a
lgebras and conilpotent dg coalgebras that becomes an equivalence on the l
evels of homotopy categories. More precisely\, this adjunction is a Quille
n equivalence of the corresponding closed model categories. Various versio
ns of this result exist and play important roles in rational homotopy theo
ry\, deformation theory\, representation theory and other related fields.
We extend it to a Quillen equivalence between dg categories (generalizing
dg algebras) and a class of dg coalgebras\, more general than conilpotent
ones. As applications we describe explicitly and conceptually Lurie’s dg
nerve functor as well as its adjoint and characterize derived categories
of (\\infty\,1)-categories as derived categories of comodules over simplic
ial chain coalgebras.(joint work with J. Holstein)\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Saccà (Collège de France and Columbia University\, USA)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/19
DESCRIPTION:Title: Hodge numbers of OG10 via Ngô strings\nby Giulia Saccà (Coll
ège de France and Columbia University\, USA) as part of Longitudinal Alge
bra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk o
n joint work with M. de Cataldo and A. Rapagnetta\, in which we compute th
e Hodge numbers of the 10-dimensional hyperkähler manifold known as OG10.
The main technique is the use of Ngô's support theorem\, applied to a na
tural Lagrangian fibration on a certain projective model of OG10\, togethe
r with the study of the geometry of the fibration itself.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Catanese (University of Bayreuth\, Germany)
DTSTART:20201015T110000Z
DTEND:20201015T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/20
DESCRIPTION:Title: Topologically trivial automorphisms of compact Kähler surfaces and
manifolds\nby Fabrizio Catanese (University of Bayreuth\, Germany) as
part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\
n\nAbstract\nThe abstract can be downloaded here: \nhttps://drive.google.c
om/file/d/1B6aZ-46iUgPic9YJyJ5lGnr2MsvP3lvl/view\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukinobu Toda (Kavli IPMU\, Tokyo\, Japan)
DTSTART:20201105T120000Z
DTEND:20201105T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/21
DESCRIPTION:Title: On d-critical birational geometry and categorical DT theories\n
by Yukinobu Toda (Kavli IPMU\, Tokyo\, Japan) as part of Longitudinal Alge
bra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk\
, I will explain an idea of analogue of birational geometry for \nJoyce's
d-critical loci\, and categorical Donaldson-Thomas theories \non Calabi-Y
au 3-folds. The motivations of this framework include \ncategorifications
of wall-crossing formulas of DT invariants and also \na d-critical analogu
e of D/K conjecture in birational geometry. \nThe main result is to realiz
e the above story for local surfaces. \nI will show the window theorem for
categorical DT theories on local surfaces\nand apply it to categorify wal
l-crossing invariance of genus zero GV invariants\, \nMNOP/PT corresponden
ce\, etc.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Greenlees (University of Warwick\, UK)
DTSTART:20201119T120000Z
DTEND:20201119T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/22
DESCRIPTION:Title: The singularity category of C^*(BG)\nby John Greenlees (Univers
ity of Warwick\, UK) as part of Longitudinal Algebra and Geometry Open ONl
ine Seminar (LAGOON)\n\n\nAbstract\n[joint work with G.Stevenson and D.Ben
son] For an ordinary commutative Noetherian ring R we would define the sin
gularity category to be the quotient of the (derived category of) finitely
generated modules modulo the (derived category of) fg projective modules
[``the bounded derived category modulo compact objects’’]. For a ring
spectrum like C^*(BG) (coefficients in a field of characteristic p) it is
easy to define the module category and the compact objects\, but finitely
generated objects need a new definition. The talk will describe the defin
ition and show that the singularity category is trivial exactly when G is
p-nilpotent. We will go on to describe the singularity category for groups
with cyclic Sylow p-subgroup.\n\nMeeting Link\nThursday 19th November 20
20\, 12:00 – 13:00 (GMT)\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFW
QXZnMXczUFdJc282bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\
n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (HMI Bonn\, Germany)
DTSTART:20201022T110000Z
DTEND:20201022T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/23
DESCRIPTION:Title: Caldero–Chapoton formulas for generalized cluster algebras from o
rbifolds\nby Lang Mou (HMI Bonn\, Germany) as part of Longitudinal Alg
ebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nTo a marked
bordered surface with orbifold points of order 3\, we associated a quiver
(with loops) with potential. We then connect the cluster structure of the
corresponding skew-symmetrizable matrix with the stability conditions and
the $\\tau$-tiliting theory of the Jacobian algebra. Finally we provide Ca
ldero–Chapoton type formulas for cluster monomials of the generalized cl
uster algebra of Chekhov and Shapiro associated to the surface. This is jo
int work with Labardini-Fragoso\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralph Kaufmann (Purdue University\, USA)
DTSTART:20201210T120000Z
DTEND:20201210T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/24
DESCRIPTION:Title: Categorical Interactions in Algebra\, Geometry and Representation T
heory\nby Ralph Kaufmann (Purdue University\, USA) as part of Longitud
inal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nTher
e are several fundamental interactions between combinatorics\, algebra and
geometry\, where the combinatorial structures give representations and su
itably interpreted encode cells for a geometric realization. A prime examp
le of this is Deligne's conjecture\, where the representation of certain g
raphs yields actions on the Hochschild complex and geometrically these gra
phs can be considered as graphs dual to a system of arcs on a surface. The
re is a way to encode the combinatorial structures into categorical ones\,
the so-called Feynman categories. The representations in this setting fun
ctors out of them. More generally they yield the representations can also
be algebras of certain types. In the functorial formalism one has restrict
ion\, reduction and Frobenius reciprocity. To make these geometric\, one c
an use a so-called W-construction. For trees and graphs\, this program lea
ds to the construction of moduli spaces of graphs and Riemann surfaces. Th
ese are versions of the commutative and associative geometries studied by
Kontsevich. Staying inside the algebraic world\, one can use functors to e
nrich Feynman categories. The enriched categories play the role of algebra
s and the representations are modules - all with possible higher operation
s. The enrichment is made by using a plus construction\, which has a conne
ction to bi-algebras and Hopf algebras based on the morphisms of a Feynman
category.\n\nMeeting Link\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFW
QXZnMXczUFdJc282bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\
n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Shinder (University of Sheffield\, UK)
DTSTART:20201126T120000Z
DTEND:20201126T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/25
DESCRIPTION:Title: Birationality centers\, rationality problems and Cremona groups
\nby Evgeny Shinder (University of Sheffield\, UK) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will i
ntroduce a framework to account for the ambiguity of stable birational typ
es of a sequence of centers for birational transformations. I will explain
in which settings the introduced invariants are nonvanishing\, and give a
pplications to the structure of Cremona groups over various fields. This i
s joint work in progress with Hsueh-Yung Lin and Susanna Zimmermann.\n\nMe
eting Link\nhttps://us02web.zoom.us/j/89958893469?pwd=aWFWQXZnMXczUFdJc282
bWx3bE5Idz09\nMeeting ID: 899 5889 3469\nPasscode: Lagoon\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amihay Hanany (Imperial College London\, UK)
DTSTART:20201112T120000Z
DTEND:20201112T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/26
DESCRIPTION:Title: Coulomb branch\nby Amihay Hanany (Imperial College London\, UK)
as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)
\n\n\nAbstract\nThe Coulomb branch is a symplectic singularity that appear
s in the physics study of gauge theories (more precisely in 3d N=4 supersy
mmetric gauge theories). A recent (2013) progress in understanding the Cou
lomb branch was when a combinatorial formula for this singularity was intr
oduced\, named the monopole formula. This raised excitement both in physic
s and in mathematics.It plays an important role in a collection of physica
l phenomena which were hard to solve previously\, and it gives a new const
ruction of geometric singularities that opens new directions of study in r
epresentation theory. This talk will focus on the monopole formula for a q
uiver and will discuss the different objects and features which arise from
the quiver.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Kaplan (University of Birmingham\, UK)
DTSTART:20210128T120000Z
DTEND:20210128T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/28
DESCRIPTION:Title: Multiplicative preprojective algebras in geometry and topology\
nby Dan Kaplan (University of Birmingham\, UK) as part of Longitudinal Alg
ebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn 2006\, Cr
awley-Boevey and Shaw defined the multiplicative preprojective algebra (MP
A) to study certain character varieties. More recently\, MPAs appeared in
work of Etgü--Lekili in the study of Fukaya categories of 4-manifolds. Ni
ce properties of the (additive) preprojective algebra are expected to hold
for MPAs\, but most proof techniques are not available. In joint work wit
h Travis Schedler\, we define the strong free product property\, following
older work of Anick. Using this property\, we prove MPAs are 2-Calabi--Ya
u algebras for quivers containing a cycle. Moreover\, using a result of Bo
cklandt--Galluzzi--Vaccarino\, we prove the formal local structure of mult
iplicative quiver varieties is isomorphic to that of a (usual) quiver vari
ety. In this talk\, I'll survey these ideas and illustrate them in small e
xamples.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bertrand Toën (CNRS\, Université de Toulouse\, France)
DTSTART:20210211T120000Z
DTEND:20210211T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/29
DESCRIPTION:Title: Foliations on schemes\nby Bertrand Toën (CNRS\, Université de
Toulouse\, France) as part of Longitudinal Algebra and Geometry Open ONli
ne Seminar (LAGOON)\n\n\nAbstract\nIn this talk I will present a notion of
foliations on\narbitrary schemes (possibly of positive or mixed character
istics)\, based on techniques\nfrom derived algebraic geometry. As an inst
ance of application I will explain\nhow Baum-Bott's existence of residues
for singular holomorphic\nfoliations can be extended to the positive chara
cteristic setting.\n\nhttps://us02web.zoom.us/j/87160036709\nMeeting ID: 8
71 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (University of Hamburg\, Germany)
DTSTART:20210204T120000Z
DTEND:20210204T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/30
DESCRIPTION:Title: A gluing construction for Ginzburg algebras of triangulated surface
s\nby Merlin Christ (University of Hamburg\, Germany) as part of Longi
tudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nG
inzburg algebras associated to triangulated surfaces are a class of 3-Cala
bi-Yau dg-algebras which categorify the cluster algebras of the underlying
marked surfaces. In this talk\, we will discuss a description of these Gi
nzburg algebras in terms of the global sections of a constructible cosheaf
of dg-categories (modelling a perverse Schober). This cosheaf description
shows that the Ginzburg algebras arise via the gluing of relative version
s of Ginzburg algebras associated to the faces of the triangulation along
their common edges. The definition of the cosheaf is inspired by a result
of Ivan Smith\, by which the finite derived category of such a Ginzburg al
gebra embeds into the Fukaya category of a Calabi-Yau 3-fold equipped with
a Lefschetz fibration to the surface.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (University of Milano\, Italy)
DTSTART:20210218T120000Z
DTEND:20210218T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/31
DESCRIPTION:Title: Uniqueness of enhancements for derived and geometric categories
\nby Paolo Stellari (University of Milano\, Italy) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this
talk we address several open questions and generalize the existing results
about the uniqueness of enhancements for triangulated categories which ar
ise as derived categories of abelian categories or from geometric contexts
. If time permits\, we will also discuss applications to the description o
f exact equivalences. This is joint work with A. Canonaco and A. Neeman.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chelsea Walton (Rice University\, USA)
DTSTART:20210701T140000Z
DTEND:20210701T150000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/32
DESCRIPTION:Title: Frobenius algebras galore\nby Chelsea Walton (Rice University\,
USA) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LA
GOON)\n\n\nAbstract\nIn this talk\, I’ll chat about wonderful algebraic
structures that were discovered in the early 1900’s: Frobenius algebras.
I will survey the 100+ year history of the development and uses of these
structures\, ending with very recent research results from joint work with
Harshit Yadav.\n\nMeeting Link\nThursday\, 15:00 - 16:00 (BST\, UK Time)
\nhttps://us02web.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF3dz
09 \nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Scheimbauer (TU München\, Germany)
DTSTART:20210225T120000Z
DTEND:20210225T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/33
DESCRIPTION:Title: Derived symplectic geometry and AKSZ topological field theories
\nby Claudia Scheimbauer (TU München\, Germany) as part of Longitudinal A
lgebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nDerived al
gebraic geometry and derived symplectic geometry in the sense of Pantev-To
en-Vaquié-Vezzosi allows for a reinterpretation/analog of the classical A
KSZ construction for certain $\\sigma$-models. After recalling this proced
ure I will explain how it can be extended to give a fully extended oriente
d TFT in the sense of Lurie with values in a higher category whose objects
are $n$-shifted symplectic derived stacks and (higher) morphisms are (hig
her) Lagrangian correspondences. It is given by taking mapping stacks with
a fixed target building and describes ``semi-classical TFTs". This is joi
nt work in progress with Damien Calaque and Rune Haugseng.\n\nMeeting Link
\nThursday 18 February\, 12:00 - 13:00 (GMT)\nhttps://us02web.zoom.us/j/8
7160036709\nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Letterio Gatto (Polytechnic University of Turin\, Italy)
DTSTART:20210318T120000Z
DTEND:20210318T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/34
DESCRIPTION:Title: HiDEAs to work with\nby Letterio Gatto (Polytechnic University
of Turin\, Italy) as part of Longitudinal Algebra and Geometry Open ONline
Seminar (LAGOON)\n\n\nAbstract\nHiDEA is the acronym of Higher Derivation
s on Exterior Algebra\, a project I am currently working on together with
many collaborators\, such as O. Behzad & A. Nasrollah Nejad (Iran)\, L. R
owen & I. Scherbak (Israel)\, A. Contiero\, P. Salehyan & R. Vidal Martins
(Brasil)\, S. Amukugu\, M. Mugochi & G. Marelli (Namibia). Originally int
roduced by Hasse & Schmidt (1937) to extend Taylor expansions of analytic
functions and Wronskians in in the realm of positive characteristic comm
utative algebra\, the notion of Higher Order derivations (Hasse-Schmidt de
rivation in the sequel) provides an extremely rich theory when applied to
the super--commutative situation supplied by exterior algebras of free mod
ules. The purpose of this talk is to advertise HiDEAs practise\, focusing
on its main tool\, the so-called integration by parts formula. The latter
shows how the theory is concerned with multilinear algebra (via an extens
ion of the Cayley-Hamilton theorem for possible infinite dimensional vecto
r spaces)\, with intersection theory of Grassmannians (Schubert Calculus v
ia Pieri's & Giambelli's formula)\, with Representation Theory and Mathema
tical Physics\, given the spontaneously arising of the vertex operators oc
curring in the boson-fermion correspondence from the so-called Schubert D
erivations. The talk aims to be general\, non specialistic and self--cont
ained\, requiring no more than basics in multilinear algebra (exterior alg
ebras)\, elementary calculus (Taylor expansions) and a little routine com
binatorics (formal power series\, partitions\, symmetric functions).\n\nht
tps://us02web.zoom.us/j/87160036709\nMeeting ID: 871 6003 6709\nPasscode:
LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Zvonareva (University of Stuttgart\, Germany)
DTSTART:20210311T120000Z
DTEND:20210311T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/35
DESCRIPTION:Title: Derived equivalence classification of Brauer graph algebras\nby
Alexandra Zvonareva (University of Stuttgart\, Germany) as part of Longit
udinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn
this talk\, I will explain the classification of Brauer graph algebras up
to derived equivalence. These algebras first appeared in representation t
heory of finite groups and can be defined for any suitably decorated graph
on an oriented surface. The classification relies on the connection betwe
en Brauer graph algebras and gentle algebras and the classification of the
mapping class group orbits of the homotopy classes of line fields on surf
aces. We consider A-infinity trivial extensions of partially wrapped Fukay
a categories associated to surfaces with boundary\, this construction natu
rally enlarges the class of Brauer graph algebras and provides a way to co
nstruct derived equivalences. This is based on joint work with Sebastian O
pper.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University Prague\, Czech Republic)
DTSTART:20210304T120000Z
DTEND:20210304T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/36
DESCRIPTION:Title: Spherical objects on cycles of projective lines and transitivity\nby Sebastian Opper (Charles University Prague\, Czech Republic) as part
of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAb
stract\nPolishchuk showed that spherical objects in the derived category o
f any cycle of projective lines yield solutions of the associative Yang-Ba
xter equation which raises the question whether one can classify spherical
objects. He further posed the question whether the group of derived auto
-equivalences of a cycle acts transitively on isomorphism classes of spher
ical objects. Partial solutions to both problems were given in works of Bu
rban-Kreussler and Lekili-Polishchuk. A theorem of Burban-Drozd establish
es a connection between the derived category of any cycle of projective li
nes with the derived category of a certain gentle algebra which can be mod
eled by a (toplogical) surface and which allows us to translate algebraic
information in the derived category such as objects into geometric informa
tion on the surface such as curves. I will explain how the result of Burba
n-Drozd can be used to find a similar model for the derived category of a
cycle. Afterwards we discuss how this can be exploited to classify spheric
al objects and establish transitivity. Further applications include a desc
ription of the group of derived auto-equivalences of a cycle and faithfuln
ess of a certain group action as defined by Sibilla.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valery Lunts (Indiana University\, USA)
DTSTART:20210415T140000Z
DTEND:20210415T150000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/37
DESCRIPTION:Title: Subcategories of derived categories on affine schemes and projectiv
e curves\nby Valery Lunts (Indiana University\, USA) as part of Longit
udinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI
will report on my joint recent work with Alexey Elagin (arXiv:2007.02134 \
, arXiv:2002.06416\, arXiv:1711.01492).\nThe famous theorem of Hopkins-Nee
man gives a simple geometric classification of thick subcategories of the
category Perf(X) for an affine noetherian scheme X. It is natural to ask i
f there is a similar classification of thick subcategories of D^b(cohX) (f
or an affine X). I will discuss some positive and some negative results in
this direction. In a different situation: surprisingly one is able to cla
ssify (up to equivalence) all thick subcategories of D^b(cohC) for a smoot
h projective curve.\n\nhttps://us02web.zoom.us/j/87160036709 \nMeeting ID
: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (University of Freiburg\, Germany)
DTSTART:20210422T110000Z
DTEND:20210422T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/38
DESCRIPTION:Title: Scattering amplitudes from derived categories and cluster categorie
s\nby Severin Barmeier (University of Freiburg\, Germany) as part of L
ongitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstrac
t\nScattering amplitudes are physical observables which play a central rol
e in interpreting scattering experiments at particle colliders. In recent
years a new perspective on scattering amplitudes has revealed a fascinatin
g link to various mathematical structures\, such as positive Grassmannians
and cluster algebras. In this talk I will explain this connection from th
e point of view of derived and cluster categories of type A quivers\, from
which the formulae for scattering amplitudes can be obtained from project
ives of hearts of intermediate t-structures. This talk is based on arXiv:2
101.02884 joint with Koushik Ray.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Okke van Garderen (University of Glasgow\, UK)
DTSTART:20210429T110000Z
DTEND:20210429T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/39
DESCRIPTION:Title: Stability\, duality\, and DT invariants for flopping curves\nby
Okke van Garderen (University of Glasgow\, UK) as part of Longitudinal Al
gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThreefold f
lops are birational surgeries on a contractible curve that connect minimal
models of threefolds\, and are therefore crucial to the minimal model pro
gram. To examine these flops one would like to compute their Donaldson-Tho
mas invariants\, which are virtual counts of semistable objects in the der
ived category. In this talk I will explain how to determine the semistable
objects supported on a flopping curve by showing that their K-theory clas
ses are dual to a hyperplane arrangement induced by tilting complexes. I w
ill also show how this duality can be categorified to give a full descript
ion of the (3-Calabi-Yau) deformation theory of these objects\, which has
various implications for the DT theory.\n\nhttps://us02web.zoom.us/j/87160
036709 \nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Ros Camacho (Cardiff University\, UK)
DTSTART:20210506T110000Z
DTEND:20210506T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/40
DESCRIPTION:Title: On the Landau-Ginzburg/conformal field theory correspondence\nb
y Ana Ros Camacho (Cardiff University\, UK) as part of Longitudinal Algebr
a and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe Landau-Ginz
burg/conformal field theory (LG/CFT) correspondence is a result from the t
heoretical physics literature dating back to the late 80s-early 90s\, whic
h in particular predicts a certain relation between categories of matrix f
actorizations and categories of representations of vertex operator algebra
s. Currently we lack a precise mathematical statement for this physics res
ult\, but fortunately we have some examples available that we will review
during this talk\, as well as some current work in progress towards more.
This is joint work with I. Runkel\, A. Davydov et al.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Szymik (NTNU Trondheim\, Norway)
DTSTART:20210603T110000Z
DTEND:20210603T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/41
DESCRIPTION:Title: A homological stroll into the algebraic theories of racks and quand
les\nby Markus Szymik (NTNU Trondheim\, Norway) as part of Longitudina
l Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nRacks a
nd quandles are rudimentary algebraic structures akin to groups and tied t
o symmetry. I will begin my presentation with an introduction to these con
cepts\, focussing on their ubiquity in geometry and topology. Current deve
lopments illustrate how an interplay between conceptual curiosity and comp
utational aspiration can substantially progress our understanding of such
structures. I will take a homological vantage point and weave a narrative
around some recent joint work with Tyler Lawson and Victoria Lebed.\n\nhtt
ps://us02web.zoom.us/j/87160036709 Meeting ID: 871 6003 6709 Passcode: LAG
OON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Booth (University ofd Antwerp\, Belgium)
DTSTART:20210513T110000Z
DTEND:20210513T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/42
DESCRIPTION:Title: Topological Hochschild cohomology for schemes\nby Matt Booth (U
niversity ofd Antwerp\, Belgium) as part of Longitudinal Algebra and Geome
try Open ONline Seminar (LAGOON)\n\n\nAbstract\nTopological Hochschild coh
omology is a sort of refinement of usual Hochschild cohomology that incorp
orates data from stable homotopy theory. Instead of working over a base ri
ng\, one works over the sphere spectrum\, which is a commutative ring in a
n appropriate sense. I'll give a quick introduction to spectral algebra an
d THH^*. Then I'll define the THH^* of a scheme in a `derived noncommutati
ve' way - i.e. using appropriate dg categories of sheaves - and explain so
me invariance results\, which in the non-topological setting are due to Lo
wen and Van den Bergh via Keller. I'll discuss some toy non-affine computa
tions\, and time permitting I'll talk about the relationship to deformatio
n theory\, especially in positive characteristic. This is joint work with
Dmitry Kaledin and Wendy Lowen.\n\nhttps://us02web.zoom.us/j/87160036709
\nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (University of Oxford\, UK)
DTSTART:20210610T110000Z
DTEND:20210610T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/43
DESCRIPTION:Title: New 3CY categories of topological surfaces\nby Fabian Haiden (U
niversity of Oxford\, UK) as part of Longitudinal Algebra and Geometry Ope
n ONline Seminar (LAGOON)\n\n\nAbstract\nTo a topological surface\, perhap
s with certain markings\, one can attach several different triangulated ca
tegories whose objects are\, roughly speaking\, curves on the surface. One
such example is the Fukaya category of the surface\, another is the 3-d C
alabi-Yau (3CY) category of an ideal triangulation. These have proven usef
ul\, among other things\, in the study of Bridgeland stability conditions
and the representation theory of finite-dimensional algebras. In the recen
t preprint arXiv:2104.06018 I introduce yet another class of triangulated
A-infinity categories of surfaces. The motivation for constructing them wa
s to extend the work of Bridgeland-Smith on stability conditions and quadr
atic differentials to the finite area case (e.g. holomorphic differentials
). They are closely related to the existing triangulated categories of sur
faces and clarify the relation between them. Their construction involves s
ome algebraic tricks\, such as twisted complexes and modules over curved A
-infinity categories\, which will be discussed in detail.\n\nhttps://us02w
eb.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF3dz09 \nMeeting ID
: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College Dublin\, Ireland)
DTSTART:20210520T110000Z
DTEND:20210520T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/44
DESCRIPTION:Title: DT invariants of some 3CY quotients\nby Sergey Mozgovoy (Trinit
y College Dublin\, Ireland) as part of Longitudinal Algebra and Geometry O
pen ONline Seminar (LAGOON)\n\n\nAbstract\nGiven a finite subgroup of SL3\
, the corresponding quotient singularity has a natural non-commutative cre
pant resolution\, the skew group algebra. By the result of Ginzburg\, this
crepant resolution is Morita equivalent to the Jacobian algebra of the Mc
Kay quiver equipped with a canonical potential. We will discuss refined DT
invariants of such Jacobian algebras for the cases of finite subgroups of
SL2 and SO3\, where the quotient singularity admits a small crepant resol
ution and the McKay quiver is symmetric.\n\nhttps://us02web.zoom.us/j/8716
0036709 \nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wu (Université Paris Diderot - Paris 7\, France)
DTSTART:20210624T110000Z
DTEND:20210624T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/46
DESCRIPTION:Title: Derived equivalences from mutations of ice quivers with potential\nby Yilin Wu (Université Paris Diderot - Paris 7\, France) as part of
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstra
ct\nIn 2009\, Keller and Yang categorified quiver mutation by interpretin
g it in terms of equivalences between derived categories. Their approach w
as based on Ginzburg’s Calabi--Yau algebras and on Derksen--Weyman--Zele
vinsky’s mutation of quivers with potential. Recently\, Matthew Presslan
d has generalized mutation of quivers with potential to that of ice quiver
s with potential. We will explain how his rule yields derived equivalences
between the associated relative Ginzburg algebras\, which are special cas
es of Yeung’s deformed relative Calabi–Yau completions arising in the
theory of relative Calabi--Yau structures due to Toën and Brav--Dyckerhof
f. We will illustrate our results on examples arising in the work of Baur-
-King--Marsh on dimer models and cluster categories of Grassmannians. If t
ime permits\, we will also sketch a categorification of mutation at frozen
vertices as it appears in recent work of Fraser--Sherman-Bennett on posit
roid cluster structures.\n\nMeeting Link\nThursday\, 12:00 - 13:00 (BST\,
UK Time)\nhttps://us02web.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzR
FdiYUF3dz09 \nMeeting ID: 871 6003 6709\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pauksztello (Lancaster University\, UK)
DTSTART:20210617T110000Z
DTEND:20210617T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/47
DESCRIPTION:Title: Functorially finite hearts\, simple-minded systems and negative clu
ster categories\nby David Pauksztello (Lancaster University\, UK) as p
art of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\
nAbstract\nSimple-minded systems (SMSs) were introduced by Koenig-Liu as a
n abstraction of nonprojective simple modules in stable module categories:
the idea was to use SMSs as a way to get around the lack of projective ge
nerators to help develop a Morita theory for stable module categories. Rec
ent developments have shown that SMSs in negative Calabi-Yau categories ad
mit mutation theories and combinatorics that are highly suggestive of clus
ter-tilting theory. In this talk\, we explain one such development: that n
egative Calabi-Yau orbit categories of bounded derived categories of acycl
ic quivers serve as categorical models of positive Fuss-Catalan combinator
ics and one can think of SMSs as negative cluster-tilting objects. Along
the way\, we will make use of the rather surprising observation that in a
triangulated category of finite homological dimension\, functorial finiten
ess of the heart of a t-structure is related to the property of the heart
having enough injectives and enough projectives. This is surprising becaus
e it says that some feature of how a heart behaves within an ambient trian
gulated category can be detected intrinsically in the heart. This talk is
based on joint work with Raquel Coelho Simoes and David Ploog.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Tamaroff (MPIMiS\, Leipzig\, Germany)
DTSTART:20211007T110000Z
DTEND:20211007T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/48
DESCRIPTION:Title: Minimal models for monomial algebras\nby Pedro Tamaroff (MPIMiS
\, Leipzig\, Germany) as part of Longitudinal Algebra and Geometry Open ON
line Seminar (LAGOON)\n\n\nAbstract\nWe will explain how to obtain the min
imal model of a monomial associative algebra A\, as in [1]. This multiplic
ative resolution has for generators the Anick chains of A\, and as a diffe
rential a combinatorial `cutting' operation that splits such chains into `
smaller' ones. Along with the formalism of Anick chains\, our results make
use of the algebraic discrete Morse theory of Jöllenbeck--Welker and Sk
öldberg\, and the general theory of A_infty-(co)algebras. We aim to also
mention certain open questions and conjectures that emerged from [1] and r
elated work [2] with Dotsenko and Gélinas\, and how one could begin eluci
dating similar results for other algebraic structures\, where it is known
the behaviour of the minimal model is already pathological. \n\n[1] Minima
l models for monomial algebras\, Homology\, Homotopy and Applications Volu
me 23 (2021) no. 1\, pp. 341 – 366. (arXiv:1804.01435)\n\n[2] Finite gen
eration for Hochschild cohomology of Gorenstein monomial algebras\, prepri
nt arXiv:1909.00487\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Tohoku University\, Japan)
DTSTART:20211014T110000Z
DTEND:20211014T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/49
DESCRIPTION:Title: Categorical dynamical systems arising from sign-stable mutation loo
ps\nby Shunsuke Kano (Tohoku University\, Japan) as part of Longitudin
al Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA pair
formed by a triangulated category and an autoequivalence is called a cate
gorical dynamical system. Its complexity is measured by the so-called cate
gorical entropy. In this talk\, I will present a computation of the catego
rical entropies of categorical dynamical systems obtained by lifting a sig
n-stable mutation loop of a quiver to an autoequivalence of the derived ca
tegory of the corresponding Ginzburg dg algebra. The notion of sign-stabil
ity is introduced as ananalogy of the pseudo-Anosov property of mapping cl
asses of surfaces. If time permits\, we will discuss the pseudo-Anosovness
of the autoequivalences constructed.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (USTC Hefei\, China)
DTSTART:20211021T110000Z
DTEND:20211021T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/50
DESCRIPTION:Title: The dg Leavitt path algebra\, singular Yonda category and singulari
ty category\nby Xiao-Wu Chen (USTC Hefei\, China) as part of Longitudi
nal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nWe pr
ove that\, for any finite dimensional algebra given by a quiver with relat
ions\, its dg singularity category is quasi-equivalent to the perfect dg d
erived category of the dg Leavitt path algebra of its radical quiver. This
result might be viewed as a deformation of the known description of the d
g singularity category of a radical-square-zero algebra in terms of a Leav
itt path algebra. The main ingredient is a new dg enhancement of the sing
ularity category\, namely the singular Yoneda dg category\, which is obtai
ned by a new strict dg localization inverting a natural transformation. Th
is is joint with Zhengfang Wang.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Neeman (Mathematical Sciences Institute\, ANU Canberra\, Aus
tralia)
DTSTART:20211028T110000Z
DTEND:20211028T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/51
DESCRIPTION:Title: Finite approximations as a tool for studying triangulated categorie
s\nby Amnon Neeman (Mathematical Sciences Institute\, ANU Canberra\, A
ustralia) as part of Longitudinal Algebra and Geometry Open ONline Seminar
(LAGOON)\n\n\nAbstract\nA metric on a category assigns lengths to morphis
ms\, with the triangle inequality holding. This notion goes back to a 1974
article by Lawvere. We'll begin with a quick review of some basic constru
ctions\, like forming the Cauchy completion of a category with respect to
a metric.And then will begin a string of surprising new results. It turns
out that\, in a triangulated category with a metric\, there is a reasonabl
e notion of Fourier series\, and an approximable triangulated category can
be thought of as a category where many objects are the limits of their Fo
urier expansions. And then come two types of theorems: (1) theorems provid
ing examples\, meaning showing that some category you might naturally want
to look at is approximable\, and (2) general structure theorems about app
roximable triangulated categories. And what makes it all interesting is (3
) applications. These turn out to include the proof of a conjecture by Bon
dal and Van den Bergh\, a major generalization of a theorem of Rouquier's\
, and a short\, sweet proof of Serre's GAGA theorem.\n\nhttps://icms-org-u
k.zoom.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09\n\nMeeting ID
: 816 0176 7022\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Université Sorbonne-Paris Nord\, France)
DTSTART:20211111T120000Z
DTEND:20211111T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/52
DESCRIPTION:Title: Deformation theory of Cohomological Field Theories\nby Bruno Va
llette (Université Sorbonne-Paris Nord\, France) as part of Longitudinal
Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIn this t
alk\, I will develop the deformation theory of Cohomological Field Theorie
s (CohFTs)\, that is algebras over the moduli spaces of stable curves with
marked points. This will lead to two new natural extensions of the notion
of a CohFT: homotopical (necessary to structure chain-level Gromov--Witte
n invariants) and quantum (with examples found in the works of Buryak--Ros
si on integrable systems). I will introduce a new version of Kontsevich's
graph complex\, enriched with tautological classes\, and I will use it to
study a new universal deformation group which acts naturally on the moduli
spaces of quantum homotopy CohFTs. This group is shown to contain both t
he prounipotent Grothendieck--Teichmüller group and the Givental group. (
Joint work with Vladimir Dotsenko\, Sergey Shadrin\, Arkady Vaintrob avail
able at arxiv.org/abs/2006.01649.)\n\nZoom link:\nhttps://icms-org-uk.zoom
.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09\nMeeting ID: 816 01
76 7022\nPasscode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (University of Hamburg\, Germany)
DTSTART:20211118T120000Z
DTEND:20211118T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/53
DESCRIPTION:Title: Perverse sheaves and schobers on Riemann surfaces\nby Tobias Dy
ckerhoff (University of Hamburg\, Germany) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nReporting on joi
nt work with M. Kapranov\, V. Schechtman\, and Y. Soibelman\, I will expla
in how to describe the derived constructible category of a stratified Riem
ann surface as representations of the so-called paracyclic category of the
surface. This allows for geometric depictions of the various t-structures
of interest (including the perverse one) and their interplay with Verdier
duality. We will then discuss how this leads to an approach to categorifi
ed perverse sheaves (perverse schobers) and provide some examples.\n\nZoom
link: https://icms-org-uk.zoom.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwT
lNiVmZodz09 Meeting ID: 816 0176 7022 Passcode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (University of Connecticut\, USA)
DTSTART:20211104T120000Z
DTEND:20211104T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/54
DESCRIPTION:Title: Triangulations of the Möbius strip and its connections with quasi-
cluster algebras\nby Véronique Bazier-Matte (University of Connecticu
t\, USA) as part of Longitudinal Algebra and Geometry Open ONline Seminar
(LAGOON)\n\n\nAbstract\nIn 2015\, Dupont and Palesi defined quasi-cluster
algebras\, which are cluster algebras arising from surfaces\, orientable o
r not. They proved that the only quasi-cluster algebras with a finite numb
er of clusters are the ones arising from the Möbius strip. In this talk\,
we will define quasi-cluster algebras\, list some of their properties and
count the number of clusters in a quasi-cluster algebra arising from a M
öbius strip\, i.e. the number of triangulations of the Möbius strip.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcy Robertson (University of Melbourne\, Australia)
DTSTART:20211125T120000Z
DTEND:20211125T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/55
DESCRIPTION:Title: A topological characterization of the Kashiwara-Vergne groups\n
by Marcy Robertson (University of Melbourne\, Australia) as part of Longit
udinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nSo
lutions to the Kashiwara--Vergne equations in noncommutative geometry are
a "higher dimensional" version of Drinfeld associators. In this talk we bu
ild on work of Bar-Natan and Dancso and identify solutions of the Kashiwar
a--Vergne equations with isomorphisms of (completed) wheeled props of "wel
ded tangled foams" -- a class of knotted surfaces in $\\mathbb{R}^4$. As a
consequence\, we identify the symmetry groups of the Kashiwara-Vergne equ
ations with automorphisms of our (completed) wheeled props. This talk is
aimed at a general audience and I will not assume familiarity with the Kas
hiwara-Vergne equations\, Drinfeld associators or wheeled props. Includes
joint work with Z. Dancso and I. Halacheva.\n\nZoom link: https://icms-org
-uk.zoom.us/j/81601767022?pwd=dDZwV1dEeW1STUZkOTUwTlNiVmZodz09 Meeting ID:
816 0176 7022 Passcode: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Brightbill (UC Santa Barbara\, USA)
DTSTART:20211209T160000Z
DTEND:20211209T170000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/56
DESCRIPTION:Title: Higher simple-minded systems in negative Calabi-Yau categories.
\nby Jeremy Brightbill (UC Santa Barbara\, USA) as part of Longitudinal Al
gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nHigher simp
le-minded systems are collections of objects in a negative Calabi-Yau cate
gory whose behavior mimics that of simple modules. Under certain hypothes
es the collection of all simple-minded systems admits a theory of mutation
s. In this talk\, we shall discuss how to construct many examples of nega
tive Calabi-Yau categories using the so-called "dg-stable category". For a
concrete example\, we consider the dg-stable category of a negatively-gra
ded Brauer tree algebra. Using a combinatorial model\, we classify the si
mple-minded systems of this category and describe its mutation theory.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Canonaco (University of Pavia\, Italy)
DTSTART:20220203T120000Z
DTEND:20220203T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/57
DESCRIPTION:Title: Dg enhancements of triangulated categories and their uniqueness
\nby Alberto Canonaco (University of Pavia\, Italy) as part of Longitudina
l Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIt is w
ell known that often some intrinsic defects of triangulated categories can
be avoided by enhancing them to suitable higher categorical structures\,
like (pretriangulated) dg categories. However\, despite significant progre
ss made in recent years\, the relation between the triangulated and the dg
level is not yet completely clear\, and some foundational questions have
received only partial answers so far. After presenting the general picture
\, I will report on a joint work (partly in progress) with Neeman and Stel
lari about uniqueness of dg enhancements.\n\nMeeting Link\nhttps://icms-or
g-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting
ID: 829 0135 6928\nPasscode: LAGOON22\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Sheridan (University of Edinburgh\, UK)
DTSTART:20220310T120000Z
DTEND:20220310T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/58
DESCRIPTION:Title: The Gamma and SYZ conjectures\nby Nick Sheridan (University of
Edinburgh\, UK) as part of Longitudinal Algebra and Geometry Open ONline S
eminar (LAGOON)\n\n\nAbstract\nI will give some background on the Gamma Co
njecture\, which says that mirror symmetry does *not* respect integral cyc
les: rather\, the integral cycles on a complex manifold correspond to inte
gral cycles on the symplectic mirror\, multiplied by a certain transcenden
tal characteristic class called the Gamma class. In the second part of the
talk I will explain a new geometric approach to the Gamma Conjecture\, wh
ich is based on the SYZ viewpoint on mirror symmetry. We find that the app
earance of zeta(k) in the asymptotics of period integrals arises from the
codimension-k singular locus of the SYZ fibration. This is based on joint
work with Abouzaid\, Ganatra\, and Iritani.\n\nMeeting Link\nhttps://icms-
org-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeetin
g ID: 829 0135 6928\nPasscode: LAGOON22\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Pressland (University of Glasgow\, UK)
DTSTART:20220210T120000Z
DTEND:20220210T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/59
DESCRIPTION:Title: Grassmannian twists categorified\nby Matt Pressland (University
of Glasgow\, UK) as part of Longitudinal Algebra and Geometry Open ONline
Seminar (LAGOON)\n\n\nAbstract\nThe Grassmannian of k-dimensional subspac
es of an n-dimensional space carries a birational automorphism called the
twist (or sometimes the Donaldson–Thomas transformation)\, defined by Be
renstein–Fomin–Zelevinsky and Marsh–Scott. This automorphism respect
s the cluster algebra structure on the coordinate ring\, being a quasi-clu
ster automorphism in the sense of Fraser. By work of Muller–Speyer\, sim
ilar results hold for positroid strata in the Grassmannian. The cluster al
gebras in this picture have been categorified\, by Jensen–King–Su in t
he case of the full Grassmannian\, and by myself for more general (connect
ed) positroid varieties. In this talk I will report on joint work with İl
ke Çanakçı and Alastair King\, in which we describe the twist in terms
of these categorifications. The key ingredient is provided by perfect matc
hing modules\, certain combinatorially defined representations for a quive
r 'with faces'\, and I will also explain this construction.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College Dublin\, Ireland)
DTSTART:20220217T120000Z
DTEND:20220217T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/60
DESCRIPTION:Title: Wall-crossing structures arising from surfaces\nby Sergey Mozgo
voy (Trinity College Dublin\, Ireland) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nFamilies of Bridgela
nd stability conditions induce families of stability data (DT invariants)\
, wall-crossing structures and scattering diagrams on the motivic Hall alg
ebra. These structures can be transferred to the quantum torus if the stab
ility conditions of the family have global dimension at most 2. I will dis
cuss geometric stability conditions on a surface with nef anticanonical bu
ndle. These stability conditions have global dimension 2\, hence induce a
family of stability data. I will also discuss the relationship of this fam
ily to the family of stability data associated to a quiver with potential\
, with an emphasis on the projective plane.\n\nhttps://icms-org-uk.zoom.us
/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting ID: 829 0135
6928\nPasscode: LAGOON22\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow\, UK)
DTSTART:20220224T120000Z
DTEND:20220224T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/61
DESCRIPTION:Title: When Aisles Meet\nby Sira Gratz (University of Glasgow\, UK) as
part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\
n\nAbstract\nDiscrete cluster categories of type A are an exciting playing
field on which to learn about infinite rank cluster combinatorics: On the
one hand\, they combinatorially behave\, in many ways\, in a familiar fin
ite type A way. On the other hand\, they exhibit new phenomena for which f
inite type A is “too small”. One such phenomenon is the existence of t
-structures. In this talk\, we describe the classification of t-structures
in discrete cluster categories of type A via decorated non-crossing parti
tions and explain how they form a lattice under inclusion of aisles – an
unusual occurrence for t-structures in a triangulated category. This clas
sification of t-structures can inform our understanding of posets of t-str
uctures more generally and help to tackle completions of triangulated cate
gories from a combinatorial perspective. This talk is based on joint work
with Alexandra Zvonareva\, and with Thorsten Holm and Peter Jørgensen.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleonore Faber (University of Leeds\, UK)
DTSTART:20220303T120000Z
DTEND:20220303T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/62
DESCRIPTION:Title: Matrix factorizations of some discriminants\nby Eleonore Faber
(University of Leeds\, UK) as part of Longitudinal Algebra and Geometry Op
en ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk\, we consider discr
iminants of complex reflection groups. We identify certain matrix factoriz
ations\, whose corresponding Cohen-Macaulay modules give a noncommutative
resolution of the discriminant. We will in particular consider the family
of pseudo-reflection groups G(r\,p\,n)\, for which one can explicitly dete
rmine these matrix factorizations that are indexed by partitions\, using h
igher Specht polynomials (work in progress with Colin Ingalls\, Simon May\
, and Marco Talarico).\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Safronov (University of Edinburgh\, UK)
DTSTART:20220407T110000Z
DTEND:20220407T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/64
DESCRIPTION:Title: Euler structures and noncommutative volume forms\nby Pavel Safr
onov (University of Edinburgh\, UK) as part of Longitudinal Algebra and Ge
ometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nCalabi-Yau structures o
n dg categories provide a noncommutative analog of symplectic structures.
In this talk I will introduce a noncommutative analog of volume forms call
ed noncommutative Euler structures. I will give some examples of these and
relate noncommutative Euler structures to string topology-type operations
. An application of these ideas is the proof that the Goresky--Hingston st
ring coproduct on the homology of free loop space is not homotopy invarian
t. If I have time\, I will also discuss how Euler structures give rise to
volume forms on derived mapping stacks. This is a report on work in progre
ss joint with Florian Naef.\n\nZOOM Meeting Link\nhttps://icms-org-uk.zoom
.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nPassword: LAGOON2
2\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Labardini-Fragoso (UNAM Mexico City\, Mexico)
DTSTART:20220317T120000Z
DTEND:20220317T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/65
DESCRIPTION:Title: Gentle algebras arising from surfaces with orbifold points\nby
Daniel Labardini-Fragoso (UNAM Mexico City\, Mexico) as part of Longitudin
al Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nSome y
ears ago\, Diego Velasco and I associated a gentle algebra to each triangu
lation of a polygon with one orbifold point of order three\, and showed th
at the \\tau-tilting combinatorics of this gentle algebra coincides with t
he combinatorics of flips of triangulations. Moreover\, we showed that whe
never one mutates support \\tau-tilting pairs\, the corresponding Caldero-
Chapoton functions obey a generalized cluster exchange formula\, which mea
ns that the Caldero-Chapoton algebra is isomorphic to a generalized cluste
r algebra of Chekhov-Shapiro. Generalizing the aforementioned work\, in on
going collaboration Lang Mou and I associate a gentle algebra to each tria
ngulation of any unpunctured surface with orbifold points of order three.
We are able to define generalized reflection functors and DWZ-like mutatio
ns of representations. This is somewhat surprising\, since the quivers we
consider are allowed to have loops\, and the matrix-mutation classes of th
eir skew-symmetrizable matrices may fail to have acyclic representatives.\
n\nMeeting Link\nhttps://icms-org-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M
0MUFScEVLMEtyaU56dz09 \nMeeting ID: 829 0135 6928\nPasscode: LAGOON22\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (Mathematical Sciences Institute\, ANU Canberra\, Au
stralia)
DTSTART:20220331T110000Z
DTEND:20220331T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/66
DESCRIPTION:Title: The sphere of spherical objects\nby Asilata Bapat (Mathematical
Sciences Institute\, ANU Canberra\, Australia) as part of Longitudinal Al
gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nConsider th
e 2-Calabi--Yau triangulated category arising from the zigzag algebra of t
he An quiver. The braid group acts on this category by twists in spherical
objects. Given a Bridgeland stability condition\, we describe how to real
ise the spherical objects as a dense subset of a piecewise-linear manifold
. This manifold is canonically associated to the category\, and the braid
group acts on it piecewise-linearly. We also describe how the manifold tra
nsforms under wall-crossings of the stability condition. The talk is based
on joint work with Anand Deopurkar and Anthony M. Licata.\n\nZOOM Meeting
Link\nhttps://icms-org-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLM
EtyaU56dz09 \nPassword: LAGOON22\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Muro (Universidad de Sevilla\, Spain)
DTSTART:20220324T120000Z
DTEND:20220324T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/67
DESCRIPTION:Title: Enhanced n-angulated categories\nby Fernando Muro (Universidad
de Sevilla\, Spain) as part of Longitudinal Algebra and Geometry Open ONli
ne Seminar (LAGOON)\n\n\nAbstract\nThese categories were introduced by Gei
ss\, Keller\, and Oppermann in order to encode the behaviour of n-cluster
tilting subcategories of triangulated categories. In this talk I will defi
ne differential graded enhancements for these categories\, analogous to th
ose of Bondal and Kapranov for triangulated categories. I will present an
existence and uniqueness theorem for n-angulated enhancements which holds\
, for instance\, for the additivization of an n-cluster tilting object. As
a corollary\, I will deduce that a triangulated category with a (higher)
cluster tilting object has a unique triangulated enhancement. This is join
t work with Gustavo Jasso(Lund).\n\nMeeting Link\nhttps://icms-org-uk.zoom
.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 \nMeeting ID: 829 0
135 6928\nPasscode: LAGOON22\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chrysostomos Psaroudakis (Aristotle University of Thessaloniki\, G
reece)
DTSTART:20220505T110000Z
DTEND:20220505T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/68
DESCRIPTION:Title: Homological invariants of the arrow removal operation\nby Chrys
ostomos Psaroudakis (Aristotle University of Thessaloniki\, Greece) as par
t of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nA
bstract\nSeveral homological conjectures in representation theory are rela
ted with specific problems concerning the homological behaviour and the st
ructure theory of finite dimensional algebras. In joint work with Edward G
reen and Oyvind Solberg we developed new reduction techniques (vertex remo
val operation and arrow removal operation) on quotients of path algebras f
or testing the finiteness of the finitistic dimension. In this talk\, we w
ill review these operations and we will focus on the arrow removal operati
on. In particular\, we will show that Gorensteinness\, singularity categor
ies and the finite generation condition Fg for the Hochschild cohomology a
re invariants under the arrow removal operation for a finite dimensional a
lgebra. This is joint work with Karin Erdmann and Oyvind Solberg.\n\nMeeti
ng Link\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNa
lRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (University of Cologne\, Germany)
DTSTART:20220512T110000Z
DTEND:20220512T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/69
DESCRIPTION:Title: Deformations of categories of coherent sheaves via quivers with rel
ations\nby Severin Barmeier (University of Cologne\, Germany) as part
of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbs
tract\nIn this talk I will explain how to use the deformation theory of pa
th algebras of quivers with relations to give a concrete and complete desc
ription of the deformation theory of the Abelian category coh(X) of cohere
nt sheaves on any separated Noetherian scheme X. Deformations of coh(X) ar
e a generous source of interesting examples of noncommutative schemes aris
ing as an amalgamation of classical deformations of X\, quantizations of P
oisson structures on X and twists of the structure sheaf. Lowen and Van de
n Bergh showed that the deformation theory of coh(X) is equivalent to the
deformation theory of a certain associative algebra\, namely the "diagram
algebra" associated to the restriction of the structure sheaf to any affin
e open cover. When X is Noetherian\, this associative algebra and its defo
rmations can be described concretely via a finite quiver with relations. T
his talk is based on arXiv:2107.07490 and arXiv:2002.10001 both joint with
Zhengfang Wang.\n\nMeeting Link\nhttps://uni-koeln.zoom.us/j/91875528987?
pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPasswor
d: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Imma Gálvez Carrillo (UPC Barcelona\, Spain)
DTSTART:20220519T110000Z
DTEND:20220519T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/70
DESCRIPTION:Title: Combinatorial bialgebras and decomposition spaces\nby Imma Gál
vez Carrillo (UPC Barcelona\, Spain) as part of Longitudinal Algebra and G
eometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nDecomposition spaces (
introduced independently by Dyckerhoff and Kapranov under the name 2-Segal
spaces) are simplicial spaces with a certain exactness property that mode
ls coassociativity in the same way that usual Segal spaces capture associa
tive composition. I will talk about joint work with Joachim Kock and Andre
w Tonks on the application of decomposition spaces in "categorified" or "o
bjective" algebra. As motivating examples\, I will discuss decomposition
spaces for many classical combinatorial Hopf algebras\, such as those of s
ymmetric functions.\n\nMeeting Link uni-koeln.zoom.us/j/91875528987?pwd=Tj
NZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987 Password: LAGO
ON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengyuan Huang (University of Birmingham\, UK)
DTSTART:20220526T110000Z
DTEND:20220526T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/72
DESCRIPTION:Title: The HKR isomorphism and Hochschild cohomology\nby Shengyuan Hua
ng (University of Birmingham\, UK) as part of Longitudinal Algebra and Geo
metry Open ONline Seminar (LAGOON)\n\n\nAbstract\nFor a smooth scheme X\,
the HKR isomorphism identifies the Hochschild cohomology of X with the coh
omology of polyvector fields as vector spaces. This isomorphism is known a
s the classical HKR isomorphism for the diagonal embedding: X in X\\timesX
. We discuss the generalization of the HKR isomorphism to arbitrary closed
embeddings and the corresponding functoriality property. Then we recall t
he generalization of the HKR isomorphism to orbifolds. We apply all the re
sults above to study the product structure of orbifold Hochschild cohomolo
gy.\n\nMeeting Link\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNd
VJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022
\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jongmyeong Kim (IBS Center for Geometry and Physics\, South Korea)
DTSTART:20220623T110000Z
DTEND:20220623T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/73
DESCRIPTION:Title: Categorical entropy\, (co-)t-structures and ST-triples\nby Jong
myeong Kim (IBS Center for Geometry and Physics\, South Korea) as part of
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstra
ct\nIn this talk\, we study a dynamical property of an exact endofunctor F
of a triangulated category D using the notion of categorical entropy intr
oduced by Dimitrov–Haiden–Katzarkov–Kontsevich. In particular\, we c
onsider the following question: Given full triangulated subcategories A an
d B of D such that F restricts to A and B\, how the categorical entropies
of the restricted functors are related? To answer this question\, we will
introduce new entropy-type invariants using bounded (co-)t-structures and
see their basic properties. We then apply these results to answer our ques
tion for the case where our A and B form an ST-triple in which case A has
a bounded t-structure and B has a bounded co-t-structure which are\, in so
me sense\, dual to each other.\n\nMeeting Link\nhttps://uni-koeln.zoom.us/
j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552
8987\nPassword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Laboratoire de Mathématiques de Versailles\, Fran
ce)
DTSTART:20220707T110000Z
DTEND:20220707T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/74
DESCRIPTION:Title: Cluster structures on braid varieties\nby Mikhail Gorsky (Labor
atoire de Mathématiques de Versailles\, France) as part of Longitudinal A
lgebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA braid va
riety is a certain affine algebraic variety associated with a \nsimply-con
nected simple algebraic group G and a positive braid of the \ncorrespondin
g type. These varieties generalise open Richardson varieties \nand appear
in the context of symplectic topology and in the study of \nlink invariant
s such as HOMFLY-PT polynomials and Khovanov-Rozansky \nhomology.\nIn this
talk\, I will give a proof of the existence of cluster \nA-structures and
cluster Poisson structures on any braid variety. I will \nsketch an expli
cit construction of cluster seeds involving the \ndiagrammatic calculus of
weaves and a tropicalization of Lustig's \ncoordinates. These cluster alg
ebras are local acyclic and equal their \nupper cluster algebras. The main
result also proves the conjecture of B. \nLeclerc on the existence of clu
ster algebra structures on the coordinate \nrings of open Richardson varie
ties in simply laced types. The talk is \nbased on joint work with Roger C
asals\, Eugene Gorsky\, Ian Le\, Linhui \nShen\, and José Simental.\n\nMe
eting Link\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2
xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andy Tonks (Universidad de Málaga\, Spain)
DTSTART:20220630T110000Z
DTEND:20220630T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/75
DESCRIPTION:Title: On some generalisations of Baues-Wirsching cohomology\nby Andy
Tonks (Universidad de Málaga\, Spain) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will discuss the (
co)homology of categories of Baues-Wirsching\, and how it is related to se
veral other (co)homologies\, new and old: of decomposition spaces\, of 2-c
ategories (and higher) and of simplicial sets. Joint work and work in prog
ress with I Gálvez-Carrillo\, F Neumann and S Paoli.\n\nMeeting Link\nhtt
ps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\
n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolò Sibilla (SISSA\, Italy)
DTSTART:20221013T110000Z
DTEND:20221013T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/76
DESCRIPTION:Title: Fukaya category of surfaces and pants decomposition'\nby Nicol
ò Sibilla (SISSA\, Italy) as part of Longitudinal Algebra and Geometry Op
en ONline Seminar (LAGOON)\n\n\nAbstract\nIn this talk I will explain some
results joint with James Pascaleff on the Fukaya category of Riemann surf
aces. I will explain a local-to-global principle which allows us to reduce
the calculation of the Fukaya category of surfaces of genus g greater tha
n one to the case of the pair-of-pants\, and which holds both in the punct
ured and in the compact case. The starting point are the sheaf-theoretic m
ethods which are available in the exact setting\, and which I will review
at the beginning of the talk. This result has several interesting conseque
nces for HMS and geometrization of objects in the Fukaya category. I will
conclude the talk hinting at more recent developments\, related to work of
Max Jeffs on the Fukaya category of singular surfaces\, and conjectures o
f Lekili-Ueda. The talk is based on ArXiv 1604.06448\, 2103.03366 and 2208
.03896.\n\nMeeting Link\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjN
ZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGO
ON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Di Dedda (King's College London\, UK)
DTSTART:20221020T110000Z
DTEND:20221020T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/77
DESCRIPTION:Title: A symplectic interpretation of Auslander correspondence\nby Ila
ria Di Dedda (King's College London\, UK) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nAuslander corresp
ondence establishes a bijection between the class of algebras of finite re
presentation type and the class of Auslander algebras\, with both families
considered up to Morita equivalence. This allows one to study the represe
ntation theory of the former via the homological properties of the latter.
The aim of this talk is to give a symplectic interpretation to this corre
spondence when the algebra of finite representation type is the path algeb
ra of the quiver of Dynkin type A_n. This result relies on a realisation o
f Auslander algebras of type A as Fukaya-Seidel categories of a family of
Lefschetz fibrations.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV
1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON
2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anya Nordskova (UHasselt\, Belgium)
DTSTART:20221117T120000Z
DTEND:20221117T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/78
DESCRIPTION:Title: Derived Picard groups of representation-finite symmetric algebras\nby Anya Nordskova (UHasselt\, Belgium) as part of Longitudinal Algebra
and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk abou
t my work on computing the derived Picard groups of a particular class of
symmetric representation-finite algebras of type D. We obtain an explicit
description of these groups via generators and relations. In particular\,
we prove that these groups are generated by spherical twists along a colle
ction of 0-spherical objects\, the shift and\, roughly speaking\, outer au
tomorphisms of the algebras. One of the key ingredients in the proof is th
e faithfulness of braid group actions by spherical twists along ADE config
urations of 0-spherical objects. Another part of the strategy is based on
the fact that symmetric representation-finite algebras are tilting-connect
ed. To apply this result we in particular develop a combinatorial-geometri
c model for silting mutations in type D\, generalising the classical conce
pts of Brauer trees and Kauer moves. I will also discuss possible directio
ns in which the result might be extended to a more general categorical con
text.\n\nMeeting Link\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV
1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON
2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Brav (Higher School of Economics\, Moscow\, Russia)
DTSTART:20221124T120000Z
DTEND:20221124T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/79
DESCRIPTION:Title: Poisson brackets and the string Lie algebra of a Calabi-Yau categor
y\nby Chris Brav (Higher School of Economics\, Moscow\, Russia) as par
t of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nA
bstract\nGoldman defined a symplectic structure on the moduli space of loc
al systems on a closed oriented surface\, constructed a collection of natu
ral Hamiltonians on the moduli space by taking trace of monodromy around l
oops on the surface\, and computed Poisson brackets among these Hamiltonia
ns in terms of what is now called the Goldman bracket on free homotopy cla
sses of loops. Chas and Sullivan generalized the Goldman bracket to a stri
ng bracket on the degree-shifted equivariant homology of the free loop spa
ce of a closed oriented manifold of any dimension\, but the compatibility
with the corresponding shifted-symplectic geometry on the moduli space of
local systems remained mostly conjectural. We generalize these results of
Goldman and of Chas-Sullivan to higher dimensional ’non-commutative’ c
losed oriented manifolds in the form of smooth Calabi-Yau categories. Our
main results are the description of a chain-level ’string Lie bracket’
on cyclic chains of a smooth Calabi-Yau category and the intertwining of
this string Lie bracket on cyclic chains with the shifted Poisson bracket
on functions on the moduli space of objects in the category.\n\nMeeting Li
nk\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRu
QWk3dz09\n\nMeeting ID: 918 7552 8987 Password: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Hoskins (Radboud University Nijmegen\, Netherlands)
DTSTART:20221110T120000Z
DTEND:20221110T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/80
DESCRIPTION:Title: Motivic mirror symmetry for Higgs bundles\nby Victoria Hoskins
(Radboud University Nijmegen\, Netherlands) as part of Longitudinal Algebr
a and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nModuli spaces o
f Higgs bundles for Langlands dual groups are conjecturally related by a f
orm of mirror symmetry. For SL_n and PGL_n\, Hausel and Thaddeus conjectur
ed a topological mirror symmetry given by an equality of (twisted orbifold
) Hodge numbers\, which was proven by Groechenig--Wyss--Ziegler and also M
aulik--Shen. We lift this to an isomorphism of Voevodsky motives\, and thu
s in particular an equality of (twisted orbifold) rational Chow groups. Ou
r method is based on Maulik and Shen's approach to the Hausel--Thaddeus co
njecture\, as well as showing certain motives are abelian\, in order to us
e conservativity of the Betti realisation on abelian motives. This is join
t work with Simon Pepin Lehalleur.\n\nMeeting Link\nhttps://uni-koeln.zoom
.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918
7552 8987\nPassword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Barbieri (University of Padova\, Italy)
DTSTART:20221201T120000Z
DTEND:20221201T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/81
DESCRIPTION:Title: Categories associated with weighted marked surfaces and their stabi
lity manifold\nby Anna Barbieri (University of Padova\, Italy) as part
of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAb
stract\nIn a paper in 2015\, Bridgeland and Smith identified some moduli s
paces of meormorphic quadratic differentials with simple zeroes on a Riema
nn surface with some spaces of stability conditions on certain categories.
This identification passes through associating a quiver with potential an
d a Ginzburg category to a triangulation of a marked bordered surface defi
ned by a quadratic differential. I will review this correspondence and dis
cuss how the picture changes when quadratic differentials with zeroes of a
rbitrary order are considered. This involves the study of Verdier quotient
s of Ginzburg categories and their t-structures. The talk is based on a jo
int work with M.Moeller\, Y.Qiu\, and J.So.\n\nMeeting Link\n\nuni-koeln.z
oom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 9
18 7552 8987 Password: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanwool Bae (Seoul National University\, South Korea)
DTSTART:20221103T120000Z
DTEND:20221103T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/82
DESCRIPTION:Title: Cluster categories from Fukaya categories\nby Hanwool Bae (Seou
l National University\, South Korea) as part of Longitudinal Algebra and G
eometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe wrapped Fukaya cat
egory of the plumbing X of the cotangent bundles of spheres along a tree T
is shown to be quasi-equivalent to the dg category of dg modules over the
Ginzburg dg algebra associated to a quiver Q whose underlying graph is T.
In this talk\, I will first discuss that the quotient of the wrapped Fuk
aya category W of X by its compact Fukaya category F is equivalent to the
Amiot–Guo–Keller cluster category associated to Q\, and a certain gene
rator L of W becomes a cluster-tilting object of W/F. Then using the minim
al model of the Ginzburg dg algebra computed by Hermes\, in the case the t
ree T is given by a Dynkin diagram of type A\,D or E\, I will explain how
to show that the endomorphism algebra of L in the quotient category W/F is
isomorphic to the path algebra of a certain quiver with relations. This t
alk is based on a joint work with Wonbo Jeong and Jongmyeong Kim.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (Université Paris Cité\, France)
DTSTART:20221027T110000Z
DTEND:20221027T120000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/83
DESCRIPTION:Title: On exact dg categories\nby Xiaofa Chen (Université Paris Cité
\, France) as part of Longitudinal Algebra and Geometry Open ONline Semina
r (LAGOON)\n\n\nAbstract\nIn this talk\, we propose a framework of dg enha
ncements\, which we call exact dg categories\, for a certain class of extr
iangulated categories\, which we call algebraic. The motivation comes from
typical examples like Yilin Wu’s Higgs categories and Haibo Jin’s cat
egories of dg Cohen-Macaulay modules. We will present several results conc
erning the dg nerve\, the dg derived category\, tensor products and functo
r dg categories with exact target. We will conclude by computing the latti
ce of all exact structures on dg categories satisfying certain strong fini
teness conditions.\n\nMeeting Link\n\nhttps://uni-koeln.zoom.us/j/91875528
987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09\n\nMeeting ID: 918 7552 8987\nPas
sword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasper van de Kreeke (KDV Amsterdam\, Netherlands)
DTSTART:20221215T120000Z
DTEND:20221215T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/84
DESCRIPTION:Title: Deformation theory of gentle algebras\nby Jasper van de Kreeke
(KDV Amsterdam\, Netherlands) as part of Longitudinal Algebra and Geometry
Open ONline Seminar (LAGOON)\n\n\nAbstract\nGentle algebras are discrete
models for Fukaya categories of punctured surfaces. How to deform them? We
will start with one specific deformation\, motivated by Seidel's relative
Fukaya categories. We will classify the entire deformation theory of gent
le algebras and prove that their Hochschild DGLA is formal. We will commen
t on deformed mirror symmetry and related work of Barmeier-Schroll-Wang. O
n a technical level\, this talk teaches us A∞-deformations\, L∞-algebr
as\, Kadeishvili constructions and Koszul duality. This work is part of my
PhD thesis supervised by Raf Bocklandt.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (University of Stuttgart\, Germany)
DTSTART:20221208T120000Z
DTEND:20221208T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/85
DESCRIPTION:Title: A-infinity deformations of extended Khovanov arc algebras and Strop
pel's conjecture\nby Zhengfang Wang (University of Stuttgart\, Germany
) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON
)\n\n\nAbstract\nExtended Khovanov arc algebras K_m^n are introduced by St
roppel when studying parabolic category O. They naturally appear in differ
ent subjects (including representation theory and symplectic geometry) and
have many nice algebraic properties\, for example they are Koszul and qua
si-hereditary. In this talk\, we will first give the diagrammatic descript
ion of K_m^n due to Brundan-Stroppel. Then\, by writing K_m^n as the path
algebra of a quiver with relations\, we show that the Koszul dual of K_m^n
admits a natural reduction system satisfying diamond condition\, by relat
ing the number of the associated "irreducible paths" to the Kazhdan-Luszti
g polynomials. We also explain how to apply this reduction system to study
Stroppel's conjecture. As a result\, we show that K_m^n is not intrinsica
lly formal for m\, n>1. This is joint work with S. Barmeier.\n\nMeeting Li
nk\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRu
QWk3dz09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON2022\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naoki Koseki (University of Liverpool\, UK)
DTSTART:20230927T120000Z
DTEND:20230927T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/86
DESCRIPTION:Title: Symmetric products of dg categories and semi-orthogonal decompositi
ons\nby Naoki Koseki (University of Liverpool\, UK) as part of Longitu
dinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe
notion of symmetric products of a dg category was introduced by Ganter an
d Kapranov. I will explain how a semi-orthogonal decomposition (SOD) of an
original dg category induces an SOD on the symmetric products. This is a
generalization of the direct sum decomposition of the symmetric product of
a direct sum of two vector spaces.\nThe main application is the construct
ion of various interesting SODs on the derived categories of the Hilbert s
chemes of points on surfaces.\n\nThe Zoomlink is as follows:\nhttps://uni-
koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\nMeeting
ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (Tsinghua University\, China)
DTSTART:20231025T120000Z
DTEND:20231025T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/87
DESCRIPTION:Title: On cluster braid groups\nby Yu Qiu (Tsinghua University\, China
) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON
)\n\n\nAbstract\nWe introduce cluster braid groups\, with motivations comi
ng from the study of stability conditions and quadratic differentials. In
the Coxeter–Dynkin case\, they are naturally isomorphic to the correspon
ding braid groups (1407.5986 and 2310.02871). In the surface case\, they a
re naturally isomorphic to braid twist groups (1407.0806\, 1703.10053 and
1805.00030).\n\nThe Zoom link is as follows:\n \nhttps://uni-koeln.zoom.us
/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 755
2 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Pertusi (University of Milano\, Italy)
DTSTART:20231129T130000Z
DTEND:20231129T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/88
DESCRIPTION:Title: Non-commutative abelian surfaces and generalized Kummer varieties\nby Laura Pertusi (University of Milano\, Italy) as part of Longitudina
l Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA hyper
kaehler manifold is a compact complex simply connected Kaehler manifold wh
ose space of holomorphic two-forms is generated by a symplectic form\, uni
que up to scalar multiplication. Together with complex tori and irreducibl
e Calabi--Yau manifolds\, they are building blocks for compact Kaehler man
ifolds with trivial first Chern class. In dimension two hyperkaehler manif
olds are K3 surfaces\, while finding examples in higher dimensions is a ch
allenging problem. In this talk we will construct new families of hyperkah
ler manifolds of generalized Kummer type via moduli spaces of stable objec
ts in a noncommutative deformation of the bounded derived category of an a
belian surface. This work in progress is joint with Arend Bayer\, Alex Per
ry and Xiaolei Zhao.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdj
NrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\
n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaiung Jun (State University of New York\, USA)
DTSTART:20231220T130000Z
DTEND:20231220T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/89
DESCRIPTION:Title: Quiver representations over ${\\mathbb F}_1$\nby Jaiung Jun (St
ate University of New York\, USA) as part of Longitudinal Algebra and Geom
etry Open ONline Seminar (LAGOON)\n\n\nAbstract\nA quiver is a directed gr
aph\, and a representation of a quiver assigns a vector space to each vert
ex and a linear map to each arrow. Quiver representations over ${\\mathbb
F}_1$\, "the field with one element"\, can be considered as a combinatoria
l model of quiver representations over a field\, where vector spaces and l
inear maps are replaced by ${\\mathbb F}_1$-vector spaces and ${\\mathbb F
}_1$-linear maps. I will introduce several aspects of quiver representatio
ns over ${\\mathbb F}_1$\, and its potential applications. This is joint w
ork with Jaehoon Kim and Alex Sistko.\n\nhttps://uni-koeln.zoom.us/j/91875
528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987 P
assword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucy Yang (Columbia University\, New York\, USA)
DTSTART:20240131T130000Z
DTEND:20240131T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/90
DESCRIPTION:Title: Categorical dynamics on stable module categories\nby Lucy Yang
(Columbia University\, New York\, USA) as part of Longitudinal Algebra and
Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nGiven a mathematical
object X and an endomorphism f of X\, entropy assigns to this pair a numb
er h(f) measuring the dynamical complexity of f. Initially defined for mea
sure spaces and topological spaces\, it has also been generalized by Dimit
rov--Haiden--Katzarkov--Kontsevich to measure the complexity of endomorphi
sms of stable ∞-categories. I will discuss a result showing that the cat
egorical polynomial entropy of a twist functor on stable module categories
of certain algebras A of cohomology operations over a field k reflects th
e complexity of A: it is at least one less than the Krull dimension of H*(
A\;k)\, generalizing results of Fan--Fu--Ouchi. We will then discuss work
in progress to bring this dynamicalperspective to homotopy theory.\n\nhtt
ps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\
n\nMeeting ID: 918 7552 8987 Password: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadia Romero (Universidad de Guanajuato\, Mexico)
DTSTART:20240228T130000Z
DTEND:20240228T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/91
DESCRIPTION:Title: Hochschild cohomology for functors on linear symmetric monoidal cat
egories\nby Nadia Romero (Universidad de Guanajuato\, Mexico) as part
of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbs
tract\nLet X be an essentially small symmetric monoidal category enriched
in R-Mod\, with R a commutative ring with identity. Under these conditions
\, the category F\, of R-linear functors from X to R-Mod\, becomes an abel
ian symmetric monoidal category\, also enriched in R-Mod. The fact that F
is monoidal and abelian at the same time allows for a nice theory of modul
es over the monoids in F\, in particular it allows for a nice and easy def
inition of an internal hom functor. In this talk\, we will see how this in
ternal hom is the key to define a Hochschild cohomology theory in F.\n\nht
tps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09
\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuele Pavia (SISSA\, Italy)
DTSTART:20240327T130000Z
DTEND:20240327T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/92
DESCRIPTION:Title: Sheaves of categories over topological and coaffine stacks\nby
Emmanuele Pavia (SISSA\, Italy) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\nStarting from any sufficien
tly nice topological space X\, one can produce two different (derived) sta
cks defined over a field k of characteristic 0: the Betti stack X_B\, whic
h bears information on the underlying homotopy type of X\, and the coaffin
e stack cSpec(C*(X\; k)) on the commutative algebra C*(X\; k) of k-valued
singular cochains on X\, which behaves as the affinization of the Betti st
ack X_B. In this talk\, I shall apply the technical machinery of sheaves o
f (∞-)categories on derived stacks as developed in Gaitsgory’s work to
the case of Betti stacks and their associated coaffine stacks. We shall s
ee how sheaves of categories on X_B are intimately related to categorified
local systems over the original space X and to homotopy-coherent actions
of topological groups on k-linear ∞-categories. At the very end\, I shal
l briefly describe how sheaves of categories on X_B and on cSpec(C*(X\; k)
) interact\, and how such interaction can be interpreted as an instance of
higher Koszul duality. This talk is based on upcoming joint work with J.
Pascaleff and N. Sibilla.See abstract under 'Paper link' below.\n\nLive st
ream: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREho
RE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pieter Belmans (University of Luxembourg\, Luxembourg)
DTSTART:20240424T120000Z
DTEND:20240424T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/93
DESCRIPTION:Title: Hochschild cohomology of Hilbert schemes of points\nby Pieter B
elmans (University of Luxembourg\, Luxembourg) as part of Longitudinal Alg
ebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will prese
nt a formula describing the Hochschild cohomology of symmetric quotient st
acks\, computing the Hochschild–Kostant–Rosenberg decomposition of thi
s orbifold. Through the Bridgeland–King–Reid–Haiman equivalence this
allows the computation of Hochschild cohomology of Hilbert schemes of poi
nts on surfaces. These computations explain how this invariant behaves dif
ferently from say Betti or Hodge numbers\, which have been studied intensi
vely in the past 30 years\, and it allows for new deformation-theoretic re
sults. This is joint work with Lie Fu and Andreas Krug.\n\nThe Zoom link i
s\n \nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREho
RE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Favero (University of Minnesota\, USA)
DTSTART:20240529T120000Z
DTEND:20240529T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/94
DESCRIPTION:Title: Homotopy path algebras and resolutions\nby Davide Favero (Unive
rsity of Minnesota\, USA) as part of Longitudinal Algebra and Geometry Ope
n ONline Seminar (LAGOON)\n\n\nAbstract\nA homotopy path algebra is like a
directed version of the group ring on a fundamental group. One can imagi
ne a directed graph (quiver) embedded in a topological space and consider
the path algebra up to homotopy. Alternatively\, one can think of homotop
y classes of directed paths in a stratified topological space. I will int
roduce homotopy path algebras and describe their connections to mirror sym
metry and resolutions of coherent sheaves on toric varieties.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Institut de Mathématiques de Jussieu\, France)
DTSTART:20240626T120000Z
DTEND:20240626T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/95
DESCRIPTION:Title: Relative graded Brauer graph algebras and stability conditions\
nby Merlin Christ (Institut de Mathématiques de Jussieu\, France) as part
of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAb
stract\nWe consider a class of dg-algebras which generalize Brauer graph a
lgebras\, called relative graded Brauer graph algebras. Their Koszul dual
dg-algebras are given by finite group quotients of relative Ginzburg algeb
ras associated with n-angulated surfaces. By constructing a partial geomet
ric model of the derived category\, we fully describe the finite heart til
ting theory. This leads to a description of the space of Bridgeland stabil
ity conditions in terms of quadratic differentials. Based on joint work wi
th Y. Qiu and F. Haiden.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US
8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAG
OON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alekos Robotis (Cornell University\, USA)
DTSTART:20241030T130000Z
DTEND:20241030T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/96
DESCRIPTION:Title: Partial compactification of the stability manifold by categorical d
ecompositions\nby Alekos Robotis (Cornell University\, USA) as part of
Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstr
act\nI will discuss new geometric-categorical structures on triangulated c
ategories that give a partial compactification of spaces of stability cond
itions. This is based on joint work with Daniel Halpern-Leistner.\n\nhttps
://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\
nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Schnitzer (University of Pavia\, Italy)
DTSTART:20241127T130000Z
DTEND:20241127T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/97
DESCRIPTION:Title: Global homotopies for differential Hochschild cohomologies\nby
Jonas Schnitzer (University of Pavia\, Italy) as part of Longitudinal Alge
bra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nIt is well kn
own that the Hochschild–Kostant–Rosenberg map from multivector fields
to differential Hochschild cochains is a quasi-isomorphism. Nevertheless\,
it is sometimes desirable to not only know the cohomology itself\, but al
so find reasonable formulas for primitives of exact cochains. In my talk I
will explain how to construct a quasi-inverse of the Hochschild–Kostant
–Rosenberg map and a homotopy to turn all the maps into a deformation re
tract. The difference to already existing attempts is that our constructio
n is performed globally and enjoys nice properties regarding symmetries.
Moreover\, the idea of this construction allows for generalizations in var
ious directions. This is a joint work with Marvin Dippell\, Chiara Esposit
o and Stefan Waldmann.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8w
djNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOO
N\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Burban (University of Paderborn\, Germany)
DTSTART:20241218T130000Z
DTEND:20241218T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/98
DESCRIPTION:Title: Exceptional hereditary non-commutative curves and real curve orbifo
lds\nby Igor Burban (University of Paderborn\, Germany) as part of Lon
gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\
nAn exceptional hereditary non-commutative curve over an algebraically clo
sed field is a weighted projective line of Geigle and Lenzing. However\, o
ver arbitrary fields\, the theory of exceptional curves is significantly r
icher. In my talk I am going to explain the definition\, examples and key
properties of these classes of non-commutative curves\, including their in
variants and relation to squid algebras and canonical algebras.\n\nhttps:/
/uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nM
eeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Barbieri (University of Verona\, Italy)
DTSTART:20250129T130000Z
DTEND:20250129T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/99
DESCRIPTION:Title: A compactification of the stability space for the Aₙ-quiver\n
by Anna Barbieri (University of Verona\, Italy) as part of Longitudinal Al
gebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe space o
f Bridgeland stability conditions is a non-compact complex manifold attach
ed to a triangulated category D\, parametrizing some t-structures of the c
ategory. In this talk I will propose a notion of multi-scale stability con
ditions that gives a smooth compactification of an appropriate quotient of
the stability manifold of the Ginzburg category of type Aₙ and a partia
l compactification for other Ginzburg categories attached to quivers with
potential from triangulated marked Riemann surfaces. Based on a joint work
with M. Möller and J. So.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd
=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987 Password: L
AGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Holstein (University of Hamburg\, Germany)
DTSTART:20250226T130000Z
DTEND:20250226T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/100
DESCRIPTION:Title: Curvature\, Koszul duality and Calabi–Yau structures\nby Jul
ian Holstein (University of Hamburg\, Germany) as part of Longitudinal Alg
ebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI will talk
about two aspects of Koszul duality. Firstly\, Koszul duality for dg categ
ories provides a way of modelling dg categories as certain curved coalgebr
as. This is a linearization of the correspondence of simplicial categories
as simplicial sets (quasi-categories) and curved coalgebras have better f
ormal properties than dg categories. Secondly\, Koszul duality exchanges t
wo self-dualities: smooth and proper Calabi–Yau structures. This is a ge
neralization and conceptual explanation of the following phenomenon: For a
topological space X with the homotopy type of a finite complex having an
oriented Poincaré duality structure (with local coefficients) is equivale
nt to having a smooth Calabi–Yau structure on the dg algebra of chains o
n the based loop space of X. A similar phenomenon occurs for Lie algebras.
This is joint work with Andrey Lazarev and with Manuel Rivera\, respectiv
ely.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzRE
hoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow\, UK)
DTSTART:20250430T120000Z
DTEND:20250430T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/101
DESCRIPTION:Title: The classification of 3-fold flops via Jacobi algebras\nby Mic
hael Wemyss (University of Glasgow\, UK) as part of Longitudinal Algebra a
nd Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe talk will give
an overview of the analytic classification of smooth\, simple\, 3-fold fl
ops. There are three main aspects: (1) reducing the problem to the classi
fication of certain noncommutative finite dimensional algebras\, (2) a ful
l understanding of those algebras\, then lastly (3) building the associate
d geometry for each algebra in that class. There are various bonus coroll
aries. The talk will be algebraic\, and so will focus mostly on (1) and (
2)\, where new techniques in A∞ algebras and in noncommutative standard
bases will be explained. Perhaps the main point is that a new invariant o
f Jacobi algebras on the two-loop quiver called the "algebraic length" wil
l be introduced\, and I will speculate on how general this construction re
ally is. Part (1) is joint with Joe Karmazyn and Emma Lepri\, the rest is
joint with Gavin Brown.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Schedler (Imperial College London\, UK)
DTSTART:20250625T120000Z
DTEND:20250625T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/103
DESCRIPTION:Title: Creating quantum projective spaces by deforming q-symmetric algebr
as\nby Travis Schedler (Imperial College London\, UK) as part of Longi
tudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\nI
will explain how to construct new "quantum projective spaces"\, in the fo
rm of Koszul\, Calabi–Yau algebras with the Hilbert series of a polynomi
al ring. To do so we deform the relations of toric ones — q-symmetric al
gebras — using a diagrammatic calculus. Such deformations are unobstruct
ed under suitable nondegeneracy conditions\, which also guarantee that the
algebras are Kontsevich's canonical quantizations of corresponding quadr
atic Poisson structures. This produces the first broad class of quadratic
Poisson structures for which his quantization can be computed and shown to
converge\, as he conjectured in 2001. On the other hand\, we also give ex
amples of purely noncommutative deformations\, which cannot be obtained by
quantizing Poisson structures. This is joint work with Mykola Matviichuk
and Brent Pym.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5
dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Williams (University of Cambridge\, UK)
DTSTART:20250528T120000Z
DTEND:20250528T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/104
DESCRIPTION:Title: Steenrod operations via higher Bruhat orders\nby Nick Williams
(University of Cambridge\, UK) as part of Longitudinal Algebra and Geomet
ry Open ONline Seminar (LAGOON)\n\n\nAbstract\nThe cohomology of a topolog
ical space has a ring structure via the cup product. The cup product is de
fined at the level of cochains\, where it is not commutative\, but it beco
mes commutative at the cohomology level. At the cochain level\, the lack o
f commutativity is resolved homotopically by an infinite tower of higher p
roducts\, known as the Steenrod cup-i products. This additional structure
provides more refined information which can be used to tell apart non-homo
topy-equivalent spaces. In this talk\, I will explain recent work with Gui
llaume Laplante-Anfossi\, where we show how conceptual proofs of the key p
roperties of Steenrod's cup-i products can be given using the higher Bruha
t orders of Manin and Schechtman.\n\nhttps://uni-koeln.zoom.us/j/918755289
87?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPass
word: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Pridham (Hodge Institute\, University of Endinburgh\, UK)
DTSTART:20250924T120000Z
DTEND:20250924T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/105
DESCRIPTION:Title: Derived deformation functors\, Koszul duality\, and Maurer-Cartan
spaces\nby Jon Pridham (Hodge Institute\, University of Endinburgh\, U
K) as part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOO
N)\n\n\nAbstract\nFor Koszul dual pairs (L\, C) of differential graded ope
rads (the motivating case being Lie and commutative)\, I will give an over
view of the equivalence between dg L-algebras up to quasi-isomorphism and
functors on Artinian dg C-algebras satisfying some exactness conditions. T
he latter tend to arise as derived versions of natural deformation functor
s.\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREho
RE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (Aarhus University\, Denmark)
DTSTART:20251105T130000Z
DTEND:20251105T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/106
DESCRIPTION:Title: An equivalence of graded hypersurface singularities of infinite ty
pe A and D\nby Sira Gratz (Aarhus University\, Denmark) as part of Lon
gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\
nThe one-dimensional hypersurface singularities of countably infinite Cohe
n–Macaulay type are precisely those of infinite type A and D. They are t
he infinite analogues of simple plane curve singularities\, which have fin
ite Cohen–Macaulay type and are classified by the finite ADE diagrams. F
rom a cluster theoretic perspective\, it is natural to study these\, and r
elated\, singularities with a specific grading. This was pioneered in work
by Jensen\, King and Su for the finite rank case. We explain how to trans
late this idea to the infinite rank case\, and conclude with a surprising
observation: Under this grading\, we find a stable equivalence of graded C
ohen–Macaulay modules for the hypersurface singularities of infinite typ
es A and D. This talk is based on two WINART projects\, the first joint wi
th August\, Cheung\, Faber and Schroll and the second joint with Cummings\
, Kirkman\, Letz\, Rock and Špenko.\n\nhttps://uni-koeln.zoom.us/j/918755
28987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nP
assword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University\, UK)
DTSTART:20251210T130000Z
DTEND:20251210T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/107
DESCRIPTION:Title: Unbounded twisted complexes\nby Timothy Logvinenko (Cardiff Un
iversity\, UK) as part of Longitudinal Algebra and Geometry Open ONline Se
minar (LAGOON)\n\n\nAbstract\nThe notion of a (bounded) twisted complex of
objects in a DG category was introduced by Bondal and Kapranov as a tool
to study and construct DG enhancements of triangulated categories. It can
be viewed as a lift to the DG enhancement of a bounded complex of objects
in the underlying triangulated category. But what if one needs to work wit
h unbounded complexes of objects?\nIn this talk\, I will first give an int
roduction summarising the original theory of bounded twisted complexes. Th
en I will explain the difficulties involved in making it work with unbound
ed complexes\, and how they are dealt with in the resulting theory of unbo
unded twisted complexes due to Rina Anno and I. Finally\, I will talk abou
t some applications\, such as A-infinity structures in monoidal DG categor
ies and homotopy idempotents.\n\nTalk postponed to Wednesday December 10!\
n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1
PUT09\n\nMeeting ID: 918 7552 8987 Password: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro Sánchez (Universidad de Murcia\, Spain)
DTSTART:20260128T130000Z
DTEND:20260128T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/108
DESCRIPTION:Title: Abstract representation theory of quivers and spectral Picard grou
ps\nby Álvaro Sánchez (Universidad de Murcia\, Spain) as part of Lon
gitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n\nAbstract\
nWhile the (derived) representation theory of quivers over a field is by n
ow well-understood\, much less is known when moving to coefficients in the
integers or an arbitrary commutative ring. In this talk\, we take a rathe
r radical but well-founded approach: it has recently been observed that ce
rtain well-known symmetries of categories of representations (tilting resu
lts) are actually mere consequences of the stability of the coefficients i
nvolved\, and so they exist in a much broader generality\, often for the c
orresponding representations in any stable homotopy theory — this includ
es arbitrary rings\, schemes\, dg algebras\, or ring spectra. For a finite
acyclic quiver Q\, we present here a method for producing universal autoe
quivalences of representations C^Q in any stable ∞-category C\, which ar
e the elements of the spectral Picard group of Q. This is based on an abst
ract equivalence of C^Q with a certain mesh ∞-category of representation
s of the Auslander–Reiten quiver Γ_Q. Then our universal equivalences a
rise from symmetries of Γ_Q\, and thus yield abstract versions of key fun
ctors in classical representation theory — e.g. the Auslander-Reiten tra
nslation\, the Serre functor\, etc. Moreover\, for representations of tree
s this allows us to realize the whole derived Picard group over a field as
a factor of the spectral Picard group.\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Bozec (Université Angers\, France)
DTSTART:20260225T130000Z
DTEND:20260225T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/109
DESCRIPTION:Title: TFTs via DAG\nby Tristan Bozec (Université Angers\, France) a
s part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n
\n\nAbstract\nOne very nice feature of derived algebraic geometry\, and sp
ecifically shifted symplectic geometry\, is how convenient it is to tackle
topological field theories. We will first review the recent history of th
is approach\, through the fundamental use of mapping stacks and the Betti
shape. We will illustrate our review with many very concrete examples and
noncommutative applications\, before explaining how the (recently proved)
Moore--Tachikawa conjecture lead us to considering the Dolbeault shape in
view of defining a new TFT associated to Higgs fields. This reports an ong
oing collaboration with Damien Calaque\, Julien Grivaux and Hugo Pourcelot
.\n\nThe Zoom link is\n\nhttps://uni-koeln.zoom.us/j/91875528987?pwd=US8wd
jNrWjl5dXNQSVRzREhoRE1PUT09\n\nMeeting ID: 918 7552 8987\nPassword: LAGOON
\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (University of Science and Technology of China\, Hefe
i\, China)
DTSTART:20260325T130000Z
DTEND:20260325T140000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/110
DESCRIPTION:Title: Frobenius quotients\, inflation categories and weighted projective
lines\nby Xiao-Wu Chen (University of Science and Technology of China
\, Hefei\, China) as part of Longitudinal Algebra and Geometry Open ONline
Seminar (LAGOON)\n\n\nAbstract\nBy the work of Kussin\, Lenzing and Mel
tzer\, the category of vector bundles on a certain weighted projective li
ne is closely related to the graded submodule problem\, studied by Ringel-
Schmidmeier. However\, the connection is quite mysterious. We construct an
explicit functor\, which yields Kussin-Lenzing-Meltzer’s stable equival
ence. Inspired by Demonet-Iyama's work\, we introduce a general notion of
Frobenius quotients. We use multifold matrix factorizations in the proof.
This is joint with Qiang Dong and Shiquan Ruan.\n\nThe Zoom link is\n\nhtt
ps://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09\
n\nMeeting ID: 918 7552 8987\nPassword: LAGOON\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires\, Argentina)
DTSTART:20260429T120000Z
DTEND:20260429T130000Z
DTSTAMP:20260404T094834Z
UID:LAGOON/111
DESCRIPTION:by Andrea Solotar (University of Buenos Aires\, Argentina) as
part of Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/LAGOON/111/
END:VEVENT
END:VCALENDAR