BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Teresa Conde (University Of Stuttgart)
DTSTART:20210106T150000Z
DTEND:20210106T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/1
DESCRIPTION:Title: Quasihereditary algebras with exact Borel subalgebras\nby Teresa C
onde (University Of Stuttgart) as part of The TRAC Seminar - Théorie de R
eprésentations et ses Applications et Connections\n\n\nAbstract\nExact Bo
rel subalgebras of quasihereditary algebras emulate the role of "classic"
Borel subalgebras of complex semisimple Lie algebras. Not every quasihered
itary algebra A has an exact Borel subalgebra. However\, a theorem by Koen
ig\, Külshammer and Ovsienko establishes that there always exists a quasi
hereditary algebra Morita equivalent to A that has a (regular) exact Borel
subalgebra. Despite that\, an explicit characterisation of such "special"
Morita representatives is not directly obtainable from Koenig\, Külshamm
er and Ovsienko's work. In this talk\, I shall present a numerical criteri
on to decide whether a quasihereditary algebra contains a regular exact Bo
rel subalgebra and I will provide a method to compute all Morita represent
atives of A that have a regular exact Borel subalgebra. We shall also see
that the Cartan matrix of a regular exact Borel subalgebra of a quasihered
itary algebra A only depends on the composition factors of the standard an
d costandard A-modules and on the dimension of the Hom-spaces between stan
dard A-modules. I will conclude the talk with a characterisation of the ba
sic quasihereditary algebras that admit a regular exact Borel subalgebra.\
n
LOCATION:https://stable.researchseminars.org/talk/TRAC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Job Rock
DTSTART:20210113T150000Z
DTEND:20210113T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/2
DESCRIPTION:Title: Decomposition of Pointwise Finite-Dimensional Representations of the C
ircle\nby Job Rock as part of The TRAC Seminar - Théorie de Représen
tations et ses Applications et Connections\n\n\nAbstract\nRepresentations
of the circle generalize representations of Ãn quivers. We will briefly m
otivate the study of such representations and show how to decompose an arb
itrary pointwise finite-dimensional representation. We’ll also talk abou
t isomorphism classes of indecomposable representations. This is joint wor
k with Eric J. Hanson.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Armenta
DTSTART:20210120T150000Z
DTEND:20210120T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/3
DESCRIPTION:Title: The representation theory of neural networks\nby Marco Armenta as
part of The TRAC Seminar - Théorie de Représentations et ses Application
s et Connections\n\n\nAbstract\nIn this talk I will present recent applica
tions of representation theory to the study of neural networks in artifici
al intelligence. First\, a neural network can be taken as a representation
-like object to which we can apply isomorphisms of quiver representations
that preserve what a neural network computes. Second\, we can encode the d
ecisions and computations of a neural network on a single sample of data i
n terms of a stable double-framed thin quiver representation\, and since t
he output of a neural network is independent of the representative in the
isomorphism class\, it makes sense to consider these "data quiver represen
tations" in a moduli space of stable thin representations.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Hanson
DTSTART:20210203T150000Z
DTEND:20210203T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/4
DESCRIPTION:Title: Infinitesimal semi-invariant pictures\nby Eric Hanson as part of T
he TRAC Seminar - Théorie de Représentations et ses Applications et Conn
ections\n\n\nAbstract\nSemi-invariant pictures (or wall and chamber struct
ures) arise naturally when considering stability conditions for finite dim
ensional algebras. For algebras which are not tau-tilting finite\, these s
emi-invariant pictures contain accumulation points. In this talk\, we desc
ribe a new semi-invariant picture which captures the local structure near
such an accumulation point. For tame hereditary algebras\, we further show
that this new semi-invariant picture can be described (both geometrically
and via tau-tilting theory) from those of certain Nakayama algebras. This
is joint work with Kiyoshi Igusa\, Moses Kim\, and Gordana Todorov.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland
DTSTART:20210217T150000Z
DTEND:20210217T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/5
DESCRIPTION:Title: The cluster category of a Postnikov diagram\nby Matthew Pressland
as part of The TRAC Seminar - Théorie de Représentations et ses Applicat
ions et Connections\n\n\nAbstract\nA Postnikov diagram consists of a colle
ction of strands in the disc\, with combinatorial restrictions on their cr
ossings. Such diagrams were used by Postnikov and others to study weakly s
eparated collections in certain matroids called positroids. In this talk I
will explain how the diagram determines a cluster algebra structure on a
suitable subvariety of the Grassmannian\, and simultaneously provides a (F
robenius) categorification of this cluster algebra.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon
DTSTART:20210324T140000Z
DTEND:20210324T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/6
DESCRIPTION:Title: The g-vector fan of a tame algebra\nby Pierre-Guy Plamondon as par
t of The TRAC Seminar - Théorie de Représentations et ses Applications e
t Connections\n\n\nAbstract\nThe g-vector fan of a finite-dimensional alge
bra encodes information about several of its properties\, including its ta
u-tilting theory and its set of stability conditions. In this talk\, I wi
ll present known and conjectural properties of this fan\, focusing on the
case of a tame algebra. \n\nThis is based on a joint work with Toshiya Yu
rikusa.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilke Canakci
DTSTART:20210331T140000Z
DTEND:20210331T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/7
DESCRIPTION:Title: Infinite friezes\nby Ilke Canakci as part of The TRAC Seminar - Th
éorie de Représentations et ses Applications et Connections\n\n\nAbstrac
t\nFrieze patterns\, introduced by Coxeter\, are infinite arrays of number
s where neighbouring numbers satisfy a local arithmetic rule. Under a cert
ain finiteness assumption\, they are in one-to-one correspondence with tri
angulations of polygons [Conway–Coxeter] and they come from triangulatio
ns of annuli in an infinite setting [Baur–Parsons–Tschabold]. I will d
iscuss a relationship between pairs of infinite friezes associated with a
triangulation of the annulus and how one determines the other in an essent
ially unique way. We will also consider module categories associated with
triangulated annuli where infinite friezes may be recovered using a specia
lised CC-map. \n\nThis is joint work with Karin Baur\, Karin Jacobsen\, Ma
itreyee Kulkarni\, and Gordana Todorov.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand
DTSTART:20210317T140000Z
DTEND:20210317T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/8
DESCRIPTION:Title: Minimal ($\\tau$)-tilting Infinite Algebras\nby Kaveh Mousavand as
part of The TRAC Seminar - Théorie de Représentations et ses Applicatio
ns et Connections\n\n\nAbstract\nMotivated by a new conjecture on $\\tau$-
tilting infinite algebras\, we study minimal $\\tau$-tilting infinite alge
bras as a modern counterpart of minimal representation infinite algebras.
This talk begins by a discussion of some fundamental similarities and diff
erences between these two families of algebras. Then we relate our studies
to the classical tilting theory. In particular\, for each minimal $\\tau$
-tilting infinite algebra $A$\, we show that the mutation graph of tilting
$A$-modules is infinite and almost $n$-regular at each vertex\, where $n$
is the rank of Grothendieck group of $A$. \n\nThis is a report on my join
t work with Charles Paquette.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:CATS-21
DTSTART:20210303T150000Z
DTEND:20210303T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/9
DESCRIPTION:Title: Additive categories between algebra and functional analysis\nby CA
TS-21 as part of The TRAC Seminar - Théorie de Représentations et ses Ap
plications et Connections\n\n\nAbstract\n1–5 March\, 2021 (fully online)
\n\nOrganisers\nThomas Brüstle (Bishop's University and Université de Sh
erbrooke)\n\nSouheila Hassoun (Université de Sherbrooke)\n\nAmit Shah (Un
iversity of Leeds)\n\nSven-Ake Wegner (Universität Hamburg)\n\nContact\na
ddcats2021@gmail.com\n\nRegistration is now open. \n\nAims & Scope:\n\nThe
aim of this conference is to exchange ideas and foster collaboration betw
een researchers from representation theory and functional analysis working
on categorical aspects of the theory. Besides lectures on recent results\
, there will be four mini-courses of introductory character.\n\nMini-cours
es:\n\nLidia Angeleri Hügel (University of Verona): Silting and tilting t
heory\nBernhard Keller (Université de Paris): Derived categories of exact
categories\nYann Palu (Université de Picardie Jules Verne): Extriangulat
ed categories\nSven-Ake Wegner (Universität Hamburg): Non-abelian categor
ies in functional analysis\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sondre Kvamme
DTSTART:20210310T150000Z
DTEND:20210310T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/10
DESCRIPTION:Title: Admissibly finitely presented functors for exact categories\nby S
ondre Kvamme as part of The TRAC Seminar - Théorie de Représentations et
ses Applications et Connections\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Paquette (Royal Military College of Canada)
DTSTART:20210224T150000Z
DTEND:20210224T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/11
DESCRIPTION:Title: Cluster characters and completed discrete cluster categories of type
A\nby Charles Paquette (Royal Military College of Canada) as part of T
he TRAC Seminar - Théorie de Représentations et ses Applications et Conn
ections\n\n\nAbstract\nAfter reviewing discrete cluster categories of type
A and their completions\, we will see how the properties of these categor
ies (which do not have a Serre functor\, and hence not 2-Calabi-Yau) still
allow one to define a cluster character map on some infinite dimensional
but finitely presented representations. This is joint work with Emine Yild
irim.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laertis Vaso
DTSTART:20210210T150000Z
DTEND:20210210T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/12
DESCRIPTION:Title: n-cluster tilting modules for radical square zero algebras\nby La
ertis Vaso as part of The TRAC Seminar - Théorie de Représentations et s
es Applications et Connections\n\n\nAbstract\nFor a quiver Q denote by J(Q
) the ideal of the path algebra KQ generated by the arrows.\n\nA central r
ole in Iyama's higher dimensional Auslander–Reiten theory is played by n
-cluster tilting modules. However\, such modules are not so easy to find.
In this talk\, I will present a simple criterion that characterises all bo
und quiver algebras of the form $KQ/J(Q)^2$ that admit an n-cluster tiltin
g module for some n>1. This criterion is based only on the shape of Q.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magnus Botnan
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/13
DESCRIPTION:Title: Quiver Representations from Data\nby Magnus Botnan as part of The
TRAC Seminar - Théorie de Représentations et ses Applications et Connec
tions\n\n\nAbstract\nUnderstanding the representation theory of a wild qui
ver Q is an unfeasible task. But if one restricts one’s attention to rep
resentations constructed from a fixed 'model'\, one may hope that only a s
mall number of indecomposable representations can be ‘realized’. In th
is talk\, I will discuss a few models for generating quiver representation
s from ‘data'\, computational experiments\, and relevant theorems emergi
ng from recent work with U. Bauer\, S. Oppermann\, and J. Steen.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yildirim
DTSTART:20210407T140000Z
DTEND:20210407T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/14
DESCRIPTION:Title: Webs and Modules\nby Emine Yildirim as part of The TRAC Seminar -
Théorie de Représentations et ses Applications et Connections\n\n\nAbst
ract\nI will talk about an ongoing work with Ian Le (Australian National U
niversity). \n\nWe look at the categorification of cluster algebras in the
context of Jensen-King-Su and try to relate this representation theoretic
al approach to combinatorics of webs which are introduced by Kuperberg and
studied by Fomin-Pylyavskyy in their work on cluster structures of certai
n invariant rings.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke
DTSTART:20210414T140000Z
DTEND:20210414T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/15
DESCRIPTION:Title: Framed quiver moduli spaces\nby Markus Reineke as part of The TRA
C Seminar - Théorie de Représentations et ses Applications et Connection
s\n\n\nAbstract\nThe aim of this talk is to review the utility of studying
framed versions of moduli spaces of quiver representations. We first revi
ew the general construction of framed moduli spaces\, and discuss several
classes of examples (for example\, acyclic quivers and quiver Grassmannian
s\, m-loop quivers and explicit normal forms). Turning to the topology of
framed quiver moduli spaces\, we state a formula for their Betti numbers\,
and exhibit a coupled system of functional equations relating Euler chara
cteristic of framed and unframed moduli spaces. Finally\, we study the geo
metry of the Hilbert-Chow map from framed to unframed moduli spaces\, and
derive a formula for the intersection Betti numbers of unframed moduli spa
ces from this.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz
DTSTART:20210421T140000Z
DTEND:20210421T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/16
DESCRIPTION:Title: Higher SL(k)-friezes\nby Sira Gratz as part of The TRAC Seminar -
Théorie de Représentations et ses Applications et Connections\n\n\nAbst
ract\nClassical frieze patterns are combinatorial structures which relate
back to Gauss’ Pentagramma Mirificum\, and have been extensively studied
by Conway and Coxeter in the 1970’s.\n\nA classical frieze pattern is a
n array of numbers satisfying a local (2 × 2)- determinant rule. Conway a
nd Coxeter gave a beautiful and natural classification of SL(2)-friezes vi
a triangulations of polygons. One way to generalise the notion of a classi
cal frieze pattern is to ask of such an array to satisfy a (k × k)-determ
inant rule instead\, for k at least 2\, leading to the notion of higher SL
(k)-friezes. While the task of classifying classical friezes yields a very
satisfying answer\, higher SL(k)-friezes are not that well understood to
date.\n\nIn this talk\, we’ll discuss how one might start to fathom high
er SL(k)-frieze patterns. The links between frieze patterns and cluster co
mbinatorics encoded by triangulations of polygons in the k=2 case suggests
a link to Grassmannian varieties under the Plücker embedding and the clu
ster algebra structure on their homogeneous coordinate rings. We find a wa
y to exploit this relation for higher SL(k)-friezes and provide an easy wa
y to generate SL(k)-friezes via Grassmannian combinatorics.\n\nThis talk i
s based on joint work with Baur\, Faber\, Serhiyenko and Todorov.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin M. Jacobsen
DTSTART:20210512T140000Z
DTEND:20210512T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/17
DESCRIPTION:Title: On the role of gentle algebras in Higher Homological algebra\nby
Karin M. Jacobsen as part of The TRAC Seminar - Théorie de Représentatio
ns et ses Applications et Connections\n\n\nAbstract\nIn higher homological
algebra\, (d+2)-angulated categories are higher analogues of triangulated
categories. They primarily appear as d-cluster-tilting subcategories of t
riangulated categories closed under d-suspension. We give a complete class
ification of such d-cluster-tilting subcategories of the derived category
of a gentle algebra by using the geometric model given by Opper-Plamondon-
Schroll. It turns out that\, up to derived equivalence\, they occur only i
n Dynkin type A\; in other words we have a puzzling lack of d-cluster-tilt
ing subcategories associated to gentle algebras. \n\nThis is joint work wi
th Johanne Haugland and Sibylle Schroll.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Cortes Izurdiaga
DTSTART:20210616T140000Z
DTEND:20210616T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/18
DESCRIPTION:Title: Partial morphisms and injective hulls in exact categories\nby Man
uel Cortes Izurdiaga as part of The TRAC Seminar - Théorie de Représenta
tions et ses Applications et Connections\n\n\nAbstract\nIn the seminal pap
er where Ziegler developed the model theory of modules\, he introduced\, u
sing model theoretical language\, the notion of partial morphism. Later\,
Monari Martinez characterized this notion in module theoretical terms. In
the talk\, we will give a categorical characterization of partial morphism
s in module categories\, which will allow us to extend them to any exact c
ategory. Then\, we will see how all properties of partial morphisms in mod
ule categories extend to exact categories\, and we will establish their re
lationship with cophantom morphisms and injective objects. Finally\, we wi
ll discuss how partial morphisms can be used to characterize injective hul
ls\, and we will give a condition that implies the existence of such hulls
in an exact category.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:VirtARTA
DTSTART:20210519T140000Z
DTEND:20210519T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/19
DESCRIPTION:Title: Advances in Representation Theory of Algebras\nby VirtARTA as par
t of The TRAC Seminar - Théorie de Représentations et ses Applications e
t Connections\n\n\nAbstract\nA special edition of the conference "Advances
in Representation Theory of Algebras" (ARTA) dedicated to the memory of A
ndrzej Skowroński will be held online from May 17 to May 28 of 2021. Our
friend and collaborator Andrzej Skowroński was one of the leaders in our
field and one of the founders of the ARTA series. The conference will feat
ure talks on recent developments in the following topics:\n\nStructure of
finite dimensional algebras\n\nStructure of module categories\n\nAuslander
--Reiten components\n\nHomological methods in representation theory\n\nHom
ological conjectures\n\nAlgebras of finite global dimension\n\nSelf-inject
ive algebras\n\nTame algebras\n\nCombinatorial aspects of representation t
heory\n\nGeometry of algebras and modules\n\nHomological invariants of alg
ebras and modules\n\nTriangulated categories and tilting theory\n\nRelatio
ns of the above topics with Lie theory\, Singularity theory\, Cohen--Macau
lay modules\, quantum groups and other algebraic structures.\n\nThe confer
ence will be held on Zoom. The Zoom link and passcode for talks will be sh
ared with all registered participants. \n\nThe in-person ARTA series will
resume as soon as the COVID-19 pandemic would allow us to do so. For more
updates and past editions of ARTA\, please visit here .\n\nRegistration: P
lease complete the registration here. \n\nLocal Organizers: Ibrahim Assem\
, Thomas Brüstle\, Charles Paquette\, Sonia Trepode\, Tianyuan Xu\, Emine
Yildirim.\n\nScientific Committee: Ibrahim Assem\, Piotr Dowbor\, Charles
Paquette\, José Antonio de la Peña\, Sonia Trepode.\n\nContact: For inq
uiries\, please contact any member of the organizing committee or write to
VirtARTA.2021@gmail.com.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny August
DTSTART:20210428T140000Z
DTEND:20210428T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/20
DESCRIPTION:Title: Grassmannian categories of infinite rank\nby Jenny August as part
of The TRAC Seminar - Théorie de Représentations et ses Applications et
Connections\n\n\nAbstract\nIn this talk\, I'll describe our work towards
providing an infinite rank version of the Grassmannian cluster categories
introduced by Jensen\, King and Su. We show that there is a structure pres
erving bijection between Plücker coordinates and the generically free mod
ules of rank 1 in our Grassmannian category of infinite rank. In the k=2 c
ase\, this allows us to model our category\, and its cluster combinatorics
\, using triangulations of an infinity-gon. This is joint work with Man-Wa
i Cheung\, Eleonore Faber\, Sira Gratz and Sibylle Schroll.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Martsinkovsky
DTSTART:20210505T140000Z
DTEND:20210505T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/21
DESCRIPTION:Title: Homological Aspects of (Co)Torsion Functors over Artin Algebras\n
by Alexander Martsinkovsky as part of The TRAC Seminar - Théorie de Repr
ésentations et ses Applications et Connections\n\n\nAbstract\nIn this tal
k I will completely determine the derived functors (both left and right) o
f both torsion and cotorsion functors defined on the module category of an
arbitrary artin algebra. The obtained results hold even in greater genera
lity. No prior knowledge of (co)torsion or functor categories is assumed.\
n\n The talk is based on joint work with Jeremy Russell.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:VirtARTA
DTSTART:20210526T140000Z
DTEND:20210526T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/22
DESCRIPTION:Title: Advances in Representation Theory of Algebras\nby VirtARTA as par
t of The TRAC Seminar - Théorie de Représentations et ses Applications e
t Connections\n\n\nAbstract\nA special edition of the conference "Advances
in Representation Theory of Algebras" (ARTA) dedicated to the memory of A
ndrzej Skowroński will be held online from May 17 to May 28 of 2021. Our
friend and collaborator Andrzej Skowroński was one of the leaders in our
field and one of the founders of the ARTA series. The conference will feat
ure talks on recent developments in the following topics:\n\nStructure of
finite dimensional algebras\n\nStructure of module categories\n\nAuslander
--Reiten components\n\nHomological methods in representation theory\n\nHom
ological conjectures\n\nAlgebras of finite global dimension\n\nSelf-inject
ive algebras\n\nTame algebras\n\nCombinatorial aspects of representation t
heory\n\nGeometry of algebras and modules\n\nHomological invariants of alg
ebras and modules\n\nTriangulated categories and tilting theory\n\nRelatio
ns of the above topics with Lie theory\, Singularity theory\, Cohen--Macau
lay modules\, quantum groups and other algebraic structures.\n\nThe confer
ence will be held on Zoom. The Zoom link and passcode for talks will be sh
ared with all registered participants. \n\nThe in-person ARTA series will
resume as soon as the COVID-19 pandemic would allow us to do so. For more
updates and past editions of ARTA\, please visit here .\n\nRegistration: P
lease complete the registration here. \n\nLocal Organizers: Ibrahim Assem\
, Thomas Brüstle\, Charles Paquette\, Sonia Trepode\, Tianyuan Xu\, Emine
Yildirim.\n\nScientific Committee: Ibrahim Assem\, Piotr Dowbor\, Charles
Paquette\, José Antonio de la Peña\, Sonia Trepode.\n\nContact: For inq
uiries\, please contact any member of the organizing committee or write to
VirtARTA.2021@gmail.com.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Zvonareva
DTSTART:20210609T140000Z
DTEND:20210609T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/23
DESCRIPTION:Title: HRS tilting for co-t-structures and cotorsion pairs\nby Alexandra
Zvonareva as part of The TRAC Seminar - Théorie de Représentations et s
es Applications et Connections\n\n\nAbstract\nIn this talk I will explain
how to construct a new co-t-structure from a given co-t-structure (A\,B) a
nd a complete cotorsion pair in its extended co-heart C=Σ^2A∩B. This co
nstruction is similar to the Happel-Reiten-Smalo tilt of a t-structure wit
h respect to a torsion pair in its heart and it induces a bijection betwee
n intermediate co-t-structures and complete cotorsion pairs. For a finite
dimensional algebra this introduces a new component to the numerous existi
ng bijections studied in tau-tilting theory and in silting theory\, that i
s the bijections between intermediate algebraic t-structures\, functoriall
y finite torsion pairs\, two-term silting complexes\, and so on. \n\nBased
on joint work with David Pauksztello.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:SSAC
DTSTART:20210623T140000Z
DTEND:20210623T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/24
DESCRIPTION:Title: Summer School of Algebraic Combinatorics\nby SSAC as part of The
TRAC Seminar - Théorie de Représentations et ses Applications et Connect
ions\n\n\nAbstract\nOrganizers/ Organisatrices:\n\nVéronique Bazier-Matte
\, Souheila Hassoun et Nancy Wallace\n\nCourses and lecturers - Cours et p
rofesseures \n\nCluster Categories and Related Topics by Pr. Gordana Todor
ov\n\nIntroduction to Cluster Algebras and Combinatorics of Friezes by Pr.
Khrystyna Serhiyenko\n\nSchubert calculus and symmetric functions by Pr.
Maria Gillespie\n\nTamari Lattices and Posets by Pr. Emily Barnard\n\nThe
aim of this school is to advance the participants knowledge and enthusiasm
towards algebraic combinatorics. Through high-level presentations\, the s
tudents will learn multiple combinatorial aspects linked to representation
theory. Every day\, a postdoctoral researcher will introduce a research t
opic tied to the introductory classes.\nSchubert calculus\, symmetric func
tions\, cluster algebra\, Tamari lattices\, frieze combinatorics and clust
er categories are not only ways to study representation theory\, but have
many links between them. On one hand\, cluster algebras\, introduced by Se
rgey Fomin and Andrei Zelevinsky\, can be studied using the combinatorics
of friezes\, on the other hand\, they can be studied algebraically using c
luster categories. Moreover\, they have a correspondence with double Bruha
t cells. In the case of Flag varieties and grassmanians\, the decompositio
n into Bruhat cells gives way to decomposition into Schubert cells. These
can be obtained using Schubert calculus. Schubbert polynomials are a gener
alization of Schur functions\, which are symmetric functions. Using sub-wo
rd complexes\, Schubert varieties are tied to the study of Tamari Lattices
. These lattices correspond to exchange graphs of some cluster algebra.\nF
inally\, our goal is to promote the visibility and accomplishment of women
in mathematics. Even though the school is open to people of all genders\,
only women were invited to give lectures and talks. It seems important to
us to give the occasion to students to interact accomplished women in mat
hematics\, since they are underrepresented among teachers in mathematics i
n universities.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte
DTSTART:20210630T140000Z
DTEND:20210630T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/25
DESCRIPTION:Title: Quivers associated with non-orientable surfaces\nby Véronique Ba
zier-Matte as part of The TRAC Seminar - Théorie de Représentations et s
es Applications et Connections\n\n\nAbstract\nIn 2015\, F Dupont and G Pal
esi defined quasi-cluster algebras from triangulations of non-orientable s
urfaces. We now associate quivers to these triangulations and define a mut
ation rule to encode flips of arcs in non-orientable surfaces. We will sho
w some properties of these quivers and their mutation rule\; in particular
\, we will demonstrate that they generalize the classical definitions of q
uiver and mutation. \n\nJoint work with Linda He\, Ruiyang Huang\, Hanyi L
uo and Kayla Wright.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The FDSeminar organizers
DTSTART:20210630T150000Z
DTEND:20210630T151500Z
DTSTAMP:20260404T111005Z
UID:TRAC/26
DESCRIPTION:Title: Panel discussion: online meetings - past and future?\nby The FDSe
minar organizers as part of The TRAC Seminar - Théorie de Représentation
s et ses Applications et Connections\n\n\nAbstract\nThis online podium dis
cussion marks the last TRAC Seminar before our summer break. We like to en
d the series with a discussion about online events\, and the future of mee
tings in the field of representation theory in general. We plan to discuss
how the panel members see in retrospective what changes the pandemic has
brought to our field\, which changes might stay\, what was their experienc
e\, and what are future plans.\n\nPanel members in this first section are
the FDSeminar organizers:\n\nEleonore Faber\, Gustavo Jasso\, Ryan Kinser\
, Julian Külshammer\, Rosanna Laking\, Alexandra Zvonareva\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The OCAS organizers
DTSTART:20210630T151500Z
DTEND:20210630T153000Z
DTSTAMP:20260404T111005Z
UID:TRAC/27
DESCRIPTION:Title: Panel discussion: online meetings - past and future?\nby The OCAS
organizers as part of The TRAC Seminar - Théorie de Représentations et
ses Applications et Connections\n\n\nAbstract\nThis online podium discussi
on marks the last TRAC Seminar before our summer break. We like to end the
series with a discussion about online events\, and the future of meetings
in the field of representation theory in general. We plan to discuss how
the panel members see in retrospective what changes the pandemic has broug
ht to our field\, which changes might stay\, what was their experience\, a
nd what are future plans.\n\nPanel members in this first section are the O
CAS organizers: \n\nAnna Felikson\, Misha Gekhtman\, Pierre-Guy Plamondon\
, Ralf Schiffler\, Khrystyna Serhiyenko\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angeleri-Hügel\, Keller\, Martsinkovsky
DTSTART:20210630T153000Z
DTEND:20210630T155500Z
DTSTAMP:20260404T111005Z
UID:TRAC/28
DESCRIPTION:Title: Panel discussion: online meetings - past and future?\nby Angeleri
-Hügel\, Keller\, Martsinkovsky as part of The TRAC Seminar - Théorie de
Représentations et ses Applications et Connections\n\n\nAbstract\nThis o
nline podium discussion marks the last TRAC Seminar before our summer brea
k. We like to end the series with a discussion about online events\, and t
he future of meetings in the field of representation theory in general. We
plan to discuss how the panel members see in retrospective what changes t
he pandemic has brought to our field\, which changes might stay\, what was
their experience\, and what are future plans.\n\nPanel members in this la
st section are Senior Experts in the field of representation theory: \n\nL
idia Angeleri-Hügel\, Bernhard Keller\, and Alex Martsinkovsky.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur
DTSTART:20210602T140000Z
DTEND:20210602T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/29
DESCRIPTION:Title: Frieze patterns and cluster theory\nby Karin Baur as part of The
TRAC Seminar - Théorie de Représentations et ses Applications et Connect
ions\n\n\nAbstract\nCluster categories and cluster algebras can be describ
ed via triangulations of surfaces or via Postnikov diagrams. In type A\, s
uch triangulations lead to frieze patterns or SL_2-friezes in the sense of
Conway and Coxeter. We explain how infinite frieze patterns arise and how
Grassmannians give rise to SL_k-friezes.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hipolito Treffinger (Université de Paris)
DTSTART:20220118T150000Z
DTEND:20220118T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/30
DESCRIPTION:Title: Stratifying systems\, τ-tilting theory and g-vectors\nby Hipolit
o Treffinger (Université de Paris) as part of The TRAC Seminar - Théorie
de Représentations et ses Applications et Connections\n\n\nAbstract\nIn
this talk we will talk about the relationship between the stratifying syst
ems defined by Erdmann and Sáenz and the τ-tilting theory introduced by
Adachi Iyama and Reiten. In the first part of the talk we will start the t
alk explaining how the properties of the mutation process on tau-tilting p
airs enables us to build at least one stratifying from every τ-rigid modu
le. \n\n\n\nIn the second part of the talk we will change gears slightly a
nd speak about Cartan matrices as an invariant for stratifying systems\, a
s it was recently proposed by Marcos\, Mendoza and Sáenz. In particular w
e will speak how the Cartan matrix for a stratifying systems induced by a
τ-rigid module can be computed using the g-vectors of the said τ-rigid m
odule. \n\n\n\nThis is a report on joint work with Octavio Mendoza and Cor
ina Sáenz. \n\nhttps://arxiv.org/abs/1904.11903\n\nhttps://arxiv.org/abs/
2111.11376\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Scoccola (Northeastern University)
DTSTART:20220125T150000Z
DTEND:20220125T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/31
DESCRIPTION:Title: Stability of homological invariants of multiparameter persistence mod
ules\nby Luis Scoccola (Northeastern University) as part of The TRAC S
eminar - Théorie de Représentations et ses Applications et Connections\n
\n\nAbstract\nUnlike one-parameter persistence modules\, for which we have
the barcode\, persistence modules with two or more parameters do not admi
t a complete discrete invariant\, and thus incomplete invariants must be u
sed to study the structure of such modules in practice. The Hilbert functi
on and the multigraded Betti numbers are among the simplest such incomplet
e invariants. Although these two invariants are already being used in appl
ications\, it is a priori unclear whether they satisfy a stability result
analogous to the stability of the one-parameter barcode. Stability results
are essential for the interpretability and consistency of practical metho
ds. I will present joint work with Steve Oudot in which we prove stability
results for multigraded Betti numbers and for the Hilbert function. I wil
l also discuss ongoing work in which we prove the stability of finer invar
iants coming from different exact structures on a category of multiparamet
er persistence modules.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Shah (Aarhus University)
DTSTART:20220201T150000Z
DTEND:20220201T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/32
DESCRIPTION:Title: A characterisation of n-exangulated functors\nby Amit Shah (Aarhu
s University) as part of The TRAC Seminar - Théorie de Représentations e
t ses Applications et Connections\n\n\nAbstract\nExamples of structure-pre
serving functors between extriangulated categories\, so-called extriangula
ted functors\, include the canonical functor from an abelian category to i
ts derived category\, and the quotient functor from a Frobenius exact cate
gory to its stable category. The first\, for example\, is structure-preser
ving in the sense that short exact sequences are sent to distinguished tri
angles in a functorial way. In higher homological algebra\, we also see ex
amples of structure-preserving functors\, but not covered by the current t
erminology. E.g. n-cluster tilting subcategories sitting inside an ambient
abelian category. In an attempt\, with R. Bennett-Tennenhaus\, J. Hauglan
d and M. H. Sandøy\, to place these kinds of more general situations in a
formal framework\, we have been led to a new perspective on extriangulate
d (or\, more generally\, n-exangulated) functors. The aim of my talk is to
explain this.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Dequêne (UQAM)
DTSTART:20220208T150000Z
DTEND:20220208T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/33
DESCRIPTION:Title: Jordan recoverability of some categories of modules over gentle algeb
ras\nby Benjamin Dequêne (UQAM) as part of The TRAC Seminar - Théori
e de Représentations et ses Applications et Connections\n\n\nAbstract\nGe
ntle algebras form a class of finite dimensional algebras introduced by As
sem and Skowroński in the 80’s. Indecomposable modules over such an alg
ebra admit a combinatorial description in terms of strings and bands\, whi
ch are walks in the associated gentle quiver (satisfying some further cond
itions)\, thanks to the work of Butler and Ringel. A subcategory C of modu
les is said to be Jordan recoverable if a module X in C can be recovered f
rom the Jordan forms\, at each vertex\, of a generic nilpotent endomorphis
m. This data is encoded by a tuple of integer partitions. \n\nAfter we hav
e introduced some definitions and set the context\, the main aim of the ta
lk is to explain the notion of Jordan recoverability through various examp
les\, and to highlight a combinatorial characterization of when that prope
rty holds for some special subcategories of modules. This result is extend
ing the work of Garver\, Patrias and Thomas in Dynkin types. If time allow
s\, we may discuss some open questions related to this result and\, in par
ticular\, exhibit new ideas to characterize all the subcategories of modul
es that are Jordan recoverable in the A_n case.\n\nThis is a part of my Ph
.D. work supervised by Hugh Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Weigandt (MIT)
DTSTART:20220215T150000Z
DTEND:20220215T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/34
DESCRIPTION:Title: The Castelnuovo-Mumford Regularity of Matrix Schubert Varieties\n
by Anna Weigandt (MIT) as part of The TRAC Seminar - Théorie de Représen
tations et ses Applications et Connections\n\n\nAbstract\nThe Castelnuovo-
Mumford regularity of a graded module provides a measure of how complicate
d its minimal free resolution is. In work with Rajchgot\, Ren\, Robichaux
\, and St. Dizier\, we noted that the regularity of Matrix Schubert Variet
ies can be easily obtained by knowing the degree of the corresponding Grot
hendieck polynomial. Furthermore\, we gave explicit\, combinatorial formu
las for the degrees of symmetric Grothendieck polynomials. In this talk\,
I will present a combinatorial degree formula for arbitrary Grothendieck
polynomials. This is joint work with Oliver Pechenik and David Speyer.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Hogancamp (Northeastern University)
DTSTART:20220222T150000Z
DTEND:20220222T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/35
DESCRIPTION:Title: Idempotent (co)algebras and generalizations of Hochschild cohomology<
/a>\nby Matt Hogancamp (Northeastern University) as part of The TRAC Semin
ar - Théorie de Représentations et ses Applications et Connections\n\n\n
Abstract\nIn this talk I will discuss the notion of an idempotent (co)alge
bra (or perhaps more descriptively\, idempotent *dg* (co)algebra). The tw
o-sided bar complex of an algebra gives an especially important class of e
xamples\, but there is a plethora of other examples appearing throughout m
athematics. I will describe how the endomorphism algebra of an idempotent
(co)algebra naturally admits the structure of a Gerstenhaber algebra\, ge
neralizing a well known structure on Hochschild cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Crooks (Northeastern University)
DTSTART:20220301T150000Z
DTEND:20220301T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/36
DESCRIPTION:Title: Shift-of-argument algebras in geometry and representation theory\
nby Peter Crooks (Northeastern University) as part of The TRAC Seminar - T
héorie de Représentations et ses Applications et Connections\n\n\nAbstra
ct\nIntegrable systems first came to prominence as a geometric abstraction
of structure in classical mechanics. Despite these origins\, integrable s
ystems have been found to interact meaningfully with pure mathematics. Mod
ern examples include the role such systems play in the Langlands program\,
mirror symmetry\, and quantum cohomology. On the other hand\, Mishchenko-
Fomenko systems represent another paradigm of integrable systems in pure m
athematics. They exhibit the kind of Lie-theoretic symmetry that allows di
fficult geometric problems to be posed and solved entirely in algebraic te
rms. The algebraic incarnations of Mishchenko-Fomenko systems are the so-c
alled shift-of-argument algebras\, which enjoy connections to geometry and
representation theory.\n\n\n\nI will give a non-technical overview of the
themes mentioned above. Some emphasis will be placed on work in progress
with Iva Halacheva and Valerio Toledano Laredo.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Fedele (Università di Verona)
DTSTART:20220308T150000Z
DTEND:20220308T160000Z
DTSTAMP:20260404T111005Z
UID:TRAC/37
DESCRIPTION:Title: Universal localizations of d-homological pairs\nby Francesca Fede
le (Università di Verona) as part of The TRAC Seminar - Théorie de Repr
ésentations et ses Applications et Connections\n\n\nAbstract\nLet k be an
algebraically closed field and A a finite dimensional k-algebra. The univ
ersal localization of A with respect to a set of morphisms between finitel
y generated projective A-modules always exists. Moreover\, when A is hered
itary\, Krause and Stovicek proved that the universal localizations of A a
re in bijection with various natural structures.\nIn this talk\, based on
joint work with Peter Jorgensen\, I will introduce the higher analogue of
universal localizations\, that is universal localizations of d-homological
pairs with respect to certain wide subcategories\, and show a (partial) g
eneralisation of Krause and Stovicek result in the higher setup.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Garcia Elsener (University of Glasgow)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/38
DESCRIPTION:Title: Monomial 2-Calabi Yau tilted algebras are Jacobian\nby Ana Garcia
Elsener (University of Glasgow) as part of The TRAC Seminar - Théorie de
Représentations et ses Applications et Connections\n\n\nAbstract\nA cele
brated result by Keller and Reiten says that 2-Calabi–Yau tilted algebra
s are Gorenstein and stably 3-Calabi–Yau\, in particular Jacobian algebr
as over an algebraically closed field satisfy this. Jacobian algebras are
2-Calabi-Yau tilted as proven by Amiot. These results originated several c
onjectures in the opposite direction: Are all 2-Calabi-Yau tilted algebras
Jacobian? (Amiot 2011 - Kalck Yang 2020). We show that the converse holds
in the monomial case: a 1-Gorenstein monomial algebra that is stably 3-Ca
labi–Yau has to be 2-Calabi–Yau tilted\, moreover it has to be Jacobia
n. This result can be explained fully in a 50 mins seminar\, so I aim to d
o that.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Bennett-Tennenhaus (Bielefeld University)
DTSTART:20220322T140000Z
DTEND:20220322T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/39
DESCRIPTION:Title: Semilinear clannish algebras\nby Raphael Bennett-Tennenhaus (Biel
efeld University) as part of The TRAC Seminar - Théorie de Représentatio
ns et ses Applications et Connections\n\n\nAbstract\nAbstract: Indecomposa
ble modules over string algebras were classified by Butler and Ringel\, an
d take exactly one of two forms: string modules\, defined by walks in the
quiver\; or band modules\, given by cyclic walks together with a represent
ation of the Laurent polynomial ring. Clannish algebras\, introduced by C
rawley-Boevey\, are a generalisation of string algebras – where one spec
ifies a set of special loops\, each bounded by some quadratic polynomial.
An analogue of Butler and Ringel’s result was given where the class of s
tring (or band) modules splits into so-called asymmetric and symmetric sub
classes. Said symmetry is given by reflecting the walk about a special loo
p\, and symmetric strings and bands are parameterised using appropriate re
placements for the Laurent polynomial ring.\n\nBoth string algebras and cl
annish algebras were defined over a field\, and the quadratics bounding sp
ecial loops were assumed to have distinct roots in this field. This talk w
ill be about ongoing joint work with Bill Crawley-Boevey\, where we genera
lise the classification for clannish algebras. For the rings we consider w
e replace this field with a division ring equipped with a set of automorph
isms\, indexed by arrows of the quiver\, and we allow irreducible quadrati
cs to bound the special loops. The resulting notion of a semilinear clanni
sh algebra recovers a generalisation of string algebras considered by Ring
el\, where one allows the map associated to an arrow to be semilinear with
respect to its automorphism.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josh Wen
DTSTART:20220412T140000Z
DTEND:20220412T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/40
DESCRIPTION:Title: An invitation to wreath Macdonald polynomials\nby Josh Wen as par
t of The TRAC Seminar - Théorie de Représentations et ses Applications e
t Connections\n\n\nAbstract\nMacdonald polynomials are distinguished symme
tric functions that have played important or useful roles in a wide range
of fields: combinatorics\, enumerative geometry\, integrable systems\, pro
bability\, knot theory\, etc. Defined by Haiman\, wreath Macdonald polynom
ials are generalizations of Macdonald polynomials wherein the symmetric gr
oups are replaced with their wreath products with a fixed cyclic group Z/r
Z. I will discuss work in progress where\, using the quantum toroidal alge
bra of rank r\, one can derive analogues of some standard parts of Macdona
ld theory: orthogonality\, evaluation formulas\, and difference operators.
This is joint work with Daniel Orr and Mark Shimozono.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART:20220329T140000Z
DTEND:20220329T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/41
DESCRIPTION:Title: Crystals and cacti in representation theory\nby Iva Halacheva (No
rtheastern University) as part of The TRAC Seminar - Théorie de Représen
tations et ses Applications et Connections\n\n\nAbstract\nOne approach to
studying the representation theory of Lie algebras and their associated qu
antum groups is through combinatorial shadows known as crystals. While the
original representations carry an action of the braid group\, their cryst
als carry an action of a closely related group known as the cactus group.
I will describe how we can realize this combinatorial action both geometri
cally\, as a monodromy action coming from a family of ‘’shift of argum
ent’’ algebras\, as well as categorically through the structure of cer
tain equivalences on triangulated categories known as Rickard complexes. P
arts of this talk are based on joint work with Joel Kamnitzer\, Leonid Ryb
nikov\, and Alex Weekes\, as well as Tony Licata\, Ivan Losev\, and Oded Y
acobi.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Amiens)
DTSTART:20220419T140000Z
DTEND:20220419T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/42
DESCRIPTION:Title: Maximal green sequences\, second Bruhat orders\, and second Cambrian
maps\nby Mikhail Gorsky (Amiens) as part of The TRAC Seminar - Théori
e de Représentations et ses Applications et Connections\n\n\nAbstract\nTh
is is a report on joint work in progress with Nicholas Williams.\n\nMaxima
l green sequences were introduced by Keller in the studies of connections
between cluster algebras and quantum dilogarithm identities. In a broader
sense\, such sequences are given by maximal chains in lattices of torsion
classes tors A in module categories of finite-dimensional algebras A. Rece
ntly\, lattices of torsion classes have been a subject of intensive resear
ch. Demonet-Iyama-Reading-Reiten-Thomas proved that for a quiver Q of Dynk
in type ADE\, the lattice of torsion classes of its path algebra realizes
the Cambrian lattice\, while the lattice tors Π for the preprojective alg
ebra is isomorphic to the weak Bruhat order on the corresponding Weyl grou
p. The Cambrian map\, introduced by Reading in combinatorial terms\, can t
hus be interpreted as a morphism of lattices of torsion classes.\n\nHigher
versions of Bruhat and Cambrian orders in type A first appeared in late 8
0s in works of Manin-Shekhtman and Kapranov-Voevodsky\, respectively. Kapr
anov and Voevodsky also defined a family of maps from higher Bruhat orders
to higher Tamari-Stasheff orders (the latter are the higher versions of C
ambrian orders in type A). More recently\, second Bruhat orders showed up
in works by Elias on (monoidal) categories of Soergel bimodules. I will ex
plain how to realize a version of the second Bruhat order for a quiver Q a
s an order on equivalence classes of maximal green sequences for the corre
sponding preprojective algebra and the second Cambrian order as a similar
order for the path algebra of Q. The second Cambrian map can then be inter
preted as the "second level" of the Demonet-Iyama-Reading-Reiten-Thomas ma
p. In type A this provides\, in a sense\, an additive categorification of
the corresponding Kapranov-Voevodsky map\, which allows for a representati
on-theoretic interpretation of its fibers. If time permits\, I will also e
xplain how one can interpret second Cambrian orders in terms of polytopes
and toric varieties associated with certain subword complexes.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Cliff (Université de Sherbrooke)
DTSTART:20220503T140000Z
DTEND:20220503T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/43
DESCRIPTION:Title: Moduli spaces of principal 2-group bundles and a categorification of
the Freed-Quinn line bundle\nby Emily Cliff (Université de Sherbrooke
) as part of The TRAC Seminar - Théorie de Représentations et ses Applic
ations et Connections\n\n\nAbstract\nA 2-group is a higher categorical ana
logue of a group\, while a smooth 2-group is a higher categorical analogue
of a Lie group. An important example is the string 2-group in the sense o
f Schommer-Pries. We study the notion of principal bundles for smooth 2-gr
oups\, and investigate the moduli "space" of such objects. In particular\,
in the case of flat principal bundles for a finite 2-group over a Riemann
surface\, we prove that the moduli space gives a categorification of the
Freed--Quinn line bundle. This line bundle has as its global sections the
state space of Chern-Simons theory for the underlying finite group. We can
also use our results to better understand the notion of geometric string
structures (as previously studied by Waldorf and Stolz-Teichner).\n\nThe t
alk will not assume background knowledge on 2-groups or Chern-Simons theor
y. It is based on joint work with Dan Berwick-Evans\, Laura Murray\, Apurv
a Nakade\, and Emma Phillips.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Coelho Guardado Simoes (Lancaster University)
DTSTART:20220517T140000Z
DTEND:20220517T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/44
DESCRIPTION:Title: From gentle to string algebras: a geometric model\nby Raquel Coel
ho Guardado Simoes (Lancaster University) as part of The TRAC Seminar - Th
éorie de Représentations et ses Applications et Connections\n\n\nAbstrac
t\nGeometric models associated to triangulations of Riemann surfaces arose
in the context of cluster algebras and have since been used as an importa
nt tool to study representation theory of algebras and provide connections
with algebraic geometry and symplectic geometry.\n\nSignificant applicati
ons of geometric models include a description of extensions and a classifi
cation of support tau-tilting modules over gentle algebras. Gentle algebra
s are a particular subclass of string algebras\, which are of tame represe
ntation type\, meaning it is often possible to get a global understanding
of their representation theory.\n\nIn this talk I will describe the module
category of a gentle algebra via partial triangulations of unpunctured su
rfaces\, explain how to extend this model to a geometric model of the modu
le category of any string algebra and use this model to obtain a classific
ation of support tau-tilting modules. This is based on joint work in progr
ess with Karin Baur.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (Cambridge)
DTSTART:20220426T140000Z
DTEND:20220426T150000Z
DTSTAMP:20260404T111005Z
UID:TRAC/46
DESCRIPTION:Title: Locally free Caldero-Chapoton functions for rank 2 cluster algebras\nby Lang Mou (Cambridge) as part of The TRAC Seminar - Théorie de Repr
ésentations et ses Applications et Connections\n\n\nAbstract\nAssociated
to any acyclic skew-symmetrizable matrix B and a symmetrizer\, Geiss\, Lec
lerc and Schröer have defined a finite-dimensional algebra H over any fie
ld. Many geometric constructions for acyclic quivers carry over to this si
tuation by using complex numbers. They show that in finite types\, the non
-initial cluster variables (of the cluster algebra associated to B) are ex
actly the locally free Caldero—Chapoton functions of indecomposable loca
lly free rigid H-modules and conjecture it to be true in general. We verif
y this conjecture in rank 2 by showing that the locally free F-polynomials
of certain modules under reflection functors satisfy the same recursion o
f the F-polynomials of cluster variables. This is joint work with Daniel L
abardini-Fragoso.\n
LOCATION:https://stable.researchseminars.org/talk/TRAC/46/
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