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BEGIN:VEVENT
SUMMARY:Teresa Conde (University Of Stuttgart)
DTSTART;VALUE=DATE-TIME:20210106T150000Z
DTEND;VALUE=DATE-TIME:20210106T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/1
DESCRIPTION:Title: Qua
sihereditary algebras with exact Borel subalgebras\nby Teresa Conde (U
niversity Of Stuttgart) as part of The TRAC Seminar - Théorie de Représe
ntations et ses Applications et Connections\n\n\nAbstract\nExact Borel sub
algebras of quasihereditary algebras emulate the role of "classic" Borel s
ubalgebras of complex semisimple Lie algebras. Not every quasihereditary a
lgebra A has an exact Borel subalgebra. However\, a theorem by Koenig\, K
ülshammer and Ovsienko establishes that there always exists a quasiheredi
tary algebra Morita equivalent to A that has a (regular) exact Borel subal
gebra. Despite that\, an explicit characterisation of such "special" Morit
a representatives is not directly obtainable from Koenig\, Külshammer and
Ovsienko's work. In this talk\, I shall present a numerical criterion to
decide whether a quasihereditary algebra contains a regular exact Borel su
balgebra and I will provide a method to compute all Morita representatives
of A that have a regular exact Borel subalgebra. We shall also see that t
he Cartan matrix of a regular exact Borel subalgebra of a quasihereditary
algebra A only depends on the composition factors of the standard and cost
andard A-modules and on the dimension of the Hom-spaces between standard A
-modules. I will conclude the talk with a characterisation of the basic qu
asihereditary algebras that admit a regular exact Borel subalgebra.\n
LOCATION:https://researchseminars.org/talk/TRAC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Job Rock
DTSTART;VALUE=DATE-TIME:20210113T150000Z
DTEND;VALUE=DATE-TIME:20210113T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/2
DESCRIPTION:Title: Dec
omposition of Pointwise Finite-Dimensional Representations of the Circle\nby Job Rock as part of The TRAC Seminar - Théorie de Représentations
et ses Applications et Connections\n\n\nAbstract\nRepresentations of the
circle generalize representations of Ãn quivers. We will briefly motivate
the study of such representations and show how to decompose an arbitrary
pointwise finite-dimensional representation. We’ll also talk about isomo
rphism classes of indecomposable representations. This is joint work with
Eric J. Hanson.\n
LOCATION:https://researchseminars.org/talk/TRAC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Armenta
DTSTART;VALUE=DATE-TIME:20210120T150000Z
DTEND;VALUE=DATE-TIME:20210120T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
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 Applications et Co
nnections\n\n\nAbstract\nIn this talk I will present recent applications o
f representation theory to the study of neural networks in artificial inte
lligence. First\, a neural network can be taken as a representation-like o
bject to which we can apply isomorphisms of quiver representations that pr
eserve what a neural network computes. Second\, we can encode the decision
s and computations of a neural network on a single sample of data in terms
of a stable double-framed thin quiver representation\, and since the outp
ut of a neural network is independent of the representative in the isomorp
hism class\, it makes sense to consider these "data quiver representations
" in a moduli space of stable thin representations.\n
LOCATION:https://researchseminars.org/talk/TRAC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Hanson
DTSTART;VALUE=DATE-TIME:20210203T150000Z
DTEND;VALUE=DATE-TIME:20210203T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/4
DESCRIPTION:Title: Inf
initesimal semi-invariant pictures\nby Eric Hanson as part of The TRAC
Seminar - Théorie de Représentations et ses Applications et Connections
\n\n\nAbstract\nSemi-invariant pictures (or wall and chamber structures) a
rise naturally when considering stability conditions for finite dimensiona
l algebras. For algebras which are not tau-tilting finite\, these semi-inv
ariant pictures contain accumulation points. In this talk\, we describe a
new semi-invariant picture which captures the local structure near such an
accumulation point. For tame hereditary algebras\, we further show that t
his new semi-invariant picture can be described (both geometrically and vi
a tau-tilting theory) from those of certain Nakayama algebras. This is joi
nt work with Kiyoshi Igusa\, Moses Kim\, and Gordana Todorov.\n
LOCATION:https://researchseminars.org/talk/TRAC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland
DTSTART;VALUE=DATE-TIME:20210217T150000Z
DTEND;VALUE=DATE-TIME:20210217T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
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 Applications et
Connections\n\n\nAbstract\nA Postnikov diagram consists of a collection o
f strands in the disc\, with combinatorial restrictions on their crossings
. Such diagrams were used by Postnikov and others to study weakly separate
d collections in certain matroids called positroids. In this talk I will e
xplain how the diagram determines a cluster algebra structure on a suitabl
e subvariety of the Grassmannian\, and simultaneously provides a (Frobeniu
s) categorification of this cluster algebra.\n
LOCATION:https://researchseminars.org/talk/TRAC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon
DTSTART;VALUE=DATE-TIME:20210324T140000Z
DTEND;VALUE=DATE-TIME:20210324T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/6
DESCRIPTION:Title: The
g-vector fan of a tame algebra\nby Pierre-Guy Plamondon as part of Th
e TRAC Seminar - Théorie de Représentations et ses Applications et Conne
ctions\n\n\nAbstract\nThe g-vector fan of a finite-dimensional algebra enc
odes information about several of its properties\, including its tau-tilti
ng theory and its set of stability conditions. In this talk\, I will pres
ent 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 Yurikusa.
\n
LOCATION:https://researchseminars.org/talk/TRAC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilke Canakci
DTSTART;VALUE=DATE-TIME:20210331T140000Z
DTEND;VALUE=DATE-TIME:20210331T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/7
DESCRIPTION:Title: Inf
inite friezes\nby Ilke Canakci as part of The TRAC Seminar - Théorie
de Représentations et ses Applications et Connections\n\n\nAbstract\nFrie
ze patterns\, introduced by Coxeter\, are infinite arrays of numbers where
neighbouring numbers satisfy a local arithmetic rule. Under a certain fin
iteness assumption\, they are in one-to-one correspondence with triangulat
ions of polygons [Conway–Coxeter] and they come from triangulations of a
nnuli in an infinite setting [Baur–Parsons–Tschabold]. I will discuss
a relationship between pairs of infinite friezes associated with a triangu
lation of the annulus and how one determines the other in an essentially u
nique way. We will also consider module categories associated with triangu
lated annuli where infinite friezes may be recovered using a specialised C
C-map. \n\nThis is joint work with Karin Baur\, Karin Jacobsen\, Maitreyee
Kulkarni\, and Gordana Todorov.\n
LOCATION:https://researchseminars.org/talk/TRAC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand
DTSTART;VALUE=DATE-TIME:20210317T140000Z
DTEND;VALUE=DATE-TIME:20210317T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/8
DESCRIPTION:Title: Min
imal ($\\tau$)-tilting Infinite Algebras\nby Kaveh Mousavand as part o
f The TRAC Seminar - Théorie de Représentations et ses Applications et C
onnections\n\n\nAbstract\nMotivated by a new conjecture on $\\tau$-tilting
infinite algebras\, we study minimal $\\tau$-tilting infinite algebras as
a modern counterpart of minimal representation infinite algebras. This ta
lk begins by a discussion of some fundamental similarities and differences
between these two families of algebras. Then we relate our studies to the
classical tilting theory. In particular\, for each minimal $\\tau$-tiltin
g infinite algebra $A$\, we show that the mutation graph of tilting $A$-mo
dules 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 joint work
with Charles Paquette.\n
LOCATION:https://researchseminars.org/talk/TRAC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:CATS-21
DTSTART;VALUE=DATE-TIME:20210303T150000Z
DTEND;VALUE=DATE-TIME:20210303T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/9
DESCRIPTION:Title: Add
itive categories between algebra and functional analysis\nby CATS-21 a
s part of The TRAC Seminar - Théorie de Représentations et ses Applicati
ons et Connections\n\n\nAbstract\n1–5 March\, 2021 (fully online)\n\nOrg
anisers\nThomas Brüstle (Bishop's University and Université de Sherbrook
e)\n\nSouheila Hassoun (Université de Sherbrooke)\n\nAmit Shah (Universit
y of Leeds)\n\nSven-Ake Wegner (Universität Hamburg)\n\nContact\naddcats2
021@gmail.com\n\nRegistration is now open. \n\nAims & Scope:\n\nThe aim of
this conference is to exchange ideas and foster collaboration between res
earchers from representation theory and functional analysis working on cat
egorical aspects of the theory. Besides lectures on recent results\, there
will be four mini-courses of introductory character.\n\nMini-courses:\n\n
Lidia Angeleri Hügel (University of Verona): Silting and tilting theory\n
Bernhard Keller (Université de Paris): Derived categories of exact catego
ries\nYann Palu (Université de Picardie Jules Verne): Extriangulated cate
gories\nSven-Ake Wegner (Universität Hamburg): Non-abelian categories in
functional analysis\n
LOCATION:https://researchseminars.org/talk/TRAC/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sondre Kvamme
DTSTART;VALUE=DATE-TIME:20210310T150000Z
DTEND;VALUE=DATE-TIME:20210310T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/10
DESCRIPTION:Title: Ad
missibly finitely presented functors for exact categories\nby Sondre K
vamme as part of The TRAC Seminar - Théorie de Représentations et ses Ap
plications et Connections\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TRAC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Paquette (Royal Military College of Canada)
DTSTART;VALUE=DATE-TIME:20210224T150000Z
DTEND;VALUE=DATE-TIME:20210224T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/11
DESCRIPTION:Title: Cl
uster characters and completed discrete cluster categories of type A\n
by Charles Paquette (Royal Military College of Canada) as part of The TRAC
Seminar - Théorie de Représentations et ses Applications et Connections
\n\n\nAbstract\nAfter reviewing discrete cluster categories of type A and
their completions\, we will see how the properties of these categories (wh
ich 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 fin
itely presented representations. This is joint work with Emine Yildirim.\n
LOCATION:https://researchseminars.org/talk/TRAC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laertis Vaso
DTSTART;VALUE=DATE-TIME:20210210T150000Z
DTEND;VALUE=DATE-TIME:20210210T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/12
DESCRIPTION:Title: n-
cluster tilting modules for radical square zero algebras\nby Laertis V
aso as part of The TRAC Seminar - Théorie de Représentations et ses Appl
ications et Connections\n\n\nAbstract\nFor a quiver Q denote by J(Q) the i
deal of the path algebra KQ generated by the arrows.\n\nA central role in
Iyama's higher dimensional Auslander–Reiten theory is played by n-cluste
r tilting modules. However\, such modules are not so easy to find. In this
talk\, I will present a simple criterion that characterises all bound qui
ver algebras of the form $KQ/J(Q)^2$ that admit an n-cluster tilting modul
e for some n>1. This criterion is based only on the shape of Q.\n
LOCATION:https://researchseminars.org/talk/TRAC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magnus Botnan
DTSTART;VALUE=DATE-TIME:20210127T150000Z
DTEND;VALUE=DATE-TIME:20210127T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/13
DESCRIPTION:Title: Qu
iver Representations from Data\nby Magnus Botnan as part of The TRAC S
eminar - Théorie de Représentations et ses Applications et Connections\n
\n\nAbstract\nUnderstanding the representation theory of a wild quiver Q i
s an unfeasible task. But if one restricts one’s attention to representa
tions constructed from a fixed 'model'\, one may hope that only a small nu
mber of indecomposable representations can be ‘realized’. In this talk
\, I will discuss a few models for generating quiver representations from
‘data'\, computational experiments\, and relevant theorems emerging from
recent work with U. Bauer\, S. Oppermann\, and J. Steen.\n
LOCATION:https://researchseminars.org/talk/TRAC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yildirim
DTSTART;VALUE=DATE-TIME:20210407T140000Z
DTEND;VALUE=DATE-TIME:20210407T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/14
DESCRIPTION:Title: We
bs and Modules\nby Emine Yildirim as part of The TRAC Seminar - Théor
ie de Représentations et ses Applications et Connections\n\n\nAbstract\nI
will talk about an ongoing work with Ian Le (Australian National Universi
ty). \n\nWe look at the categorification of cluster algebras in the contex
t of Jensen-King-Su and try to relate this representation theoretical appr
oach to combinatorics of webs which are introduced by Kuperberg and studie
d by Fomin-Pylyavskyy in their work on cluster structures of certain invar
iant rings.\n
LOCATION:https://researchseminars.org/talk/TRAC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke
DTSTART;VALUE=DATE-TIME:20210414T140000Z
DTEND;VALUE=DATE-TIME:20210414T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/15
DESCRIPTION:Title: Fr
amed quiver moduli spaces\nby Markus Reineke as part of The TRAC Semin
ar - Théorie de Représentations et ses Applications et Connections\n\n\n
Abstract\nThe aim of this talk is to review the utility of studying framed
versions of moduli spaces of quiver representations. We first review the
general construction of framed moduli spaces\, and discuss several classes
of examples (for example\, acyclic quivers and quiver Grassmannians\, m-l
oop quivers and explicit normal forms). Turning to the topology of framed
quiver moduli spaces\, we state a formula for their Betti numbers\, and ex
hibit a coupled system of functional equations relating Euler characterist
ic of framed and unframed moduli spaces. Finally\, we study the geometry o
f the Hilbert-Chow map from framed to unframed moduli spaces\, and derive
a formula for the intersection Betti numbers of unframed moduli spaces fro
m this.\n
LOCATION:https://researchseminars.org/talk/TRAC/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz
DTSTART;VALUE=DATE-TIME:20210421T140000Z
DTEND;VALUE=DATE-TIME:20210421T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/16
DESCRIPTION:Title: Hi
gher SL(k)-friezes\nby Sira Gratz as part of The TRAC Seminar - Théor
ie de Représentations et ses Applications et Connections\n\n\nAbstract\nC
lassical frieze patterns are combinatorial structures which relate back to
Gauss’ Pentagramma Mirificum\, and have been extensively studied by Con
way and Coxeter in the 1970’s.\n\nA classical frieze pattern is an array
of numbers satisfying a local (2 × 2)- determinant rule. Conway and Coxe
ter gave a beautiful and natural classification of SL(2)-friezes via trian
gulations of polygons. One way to generalise the notion of a classical fri
eze pattern is to ask of such an array to satisfy a (k × k)-determinant r
ule instead\, for k at least 2\, leading to the notion of higher SL(k)-fri
ezes. While the task of classifying classical friezes yields a very satisf
ying 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 higher SL(k
)-frieze patterns. The links between frieze patterns and cluster combinato
rics encoded by triangulations of polygons in the k=2 case suggests a link
to Grassmannian varieties under the Plücker embedding and the cluster al
gebra structure on their homogeneous coordinate rings. We find a way to ex
ploit this relation for higher SL(k)-friezes and provide an easy way to ge
nerate SL(k)-friezes via Grassmannian combinatorics.\n\nThis talk is based
on joint work with Baur\, Faber\, Serhiyenko and Todorov.\n
LOCATION:https://researchseminars.org/talk/TRAC/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin M. Jacobsen
DTSTART;VALUE=DATE-TIME:20210512T140000Z
DTEND;VALUE=DATE-TIME:20210512T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
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 Représentations et s
es Applications et Connections\n\n\nAbstract\nIn higher homological algebr
a\, (d+2)-angulated categories are higher analogues of triangulated catego
ries. They primarily appear as d-cluster-tilting subcategories of triangul
ated categories closed under d-suspension. We give a complete classificati
on of such d-cluster-tilting subcategories of the derived category of a ge
ntle algebra by using the geometric model given by Opper-Plamondon-Schroll
. It turns out that\, up to derived equivalence\, they occur only in Dynki
n type A\; in other words we have a puzzling lack of d-cluster-tilting sub
categories associated to gentle algebras. \n\nThis is joint work with Joha
nne Haugland and Sibylle Schroll.\n
LOCATION:https://researchseminars.org/talk/TRAC/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Cortes Izurdiaga
DTSTART;VALUE=DATE-TIME:20210616T140000Z
DTEND;VALUE=DATE-TIME:20210616T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/18
DESCRIPTION:Title: Pa
rtial morphisms and injective hulls in exact categories\nby Manuel Cor
tes Izurdiaga as part of The TRAC Seminar - Théorie de Représentations e
t ses Applications et Connections\n\n\nAbstract\nIn the seminal paper wher
e Ziegler developed the model theory of modules\, he introduced\, using mo
del theoretical language\, the notion of partial morphism. Later\, Monari
Martinez characterized this notion in module theoretical terms. In the tal
k\, we will give a categorical characterization of partial morphisms in mo
dule categories\, which will allow us to extend them to any exact category
. Then\, we will see how all properties of partial morphisms in module cat
egories extend to exact categories\, and we will establish their relations
hip with cophantom morphisms and injective objects. Finally\, we will disc
uss how partial morphisms can be used to characterize injective hulls\, an
d we will give a condition that implies the existence of such hulls in an
exact category.\n
LOCATION:https://researchseminars.org/talk/TRAC/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:VirtARTA
DTSTART;VALUE=DATE-TIME:20210519T140000Z
DTEND;VALUE=DATE-TIME:20210519T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/19
DESCRIPTION:Title: Ad
vances in Representation Theory of Algebras\nby VirtARTA as part of Th
e TRAC Seminar - Théorie de Représentations et ses Applications et Conne
ctions\n\n\nAbstract\nA special edition of the conference "Advances in Rep
resentation Theory of Algebras" (ARTA) dedicated to the memory of Andrzej
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 a
nd one of the founders of the ARTA series. The conference will feature tal
ks on recent developments in the following topics:\n\nStructure of finite
dimensional algebras\n\nStructure of module categories\n\nAuslander--Reite
n components\n\nHomological methods in representation theory\n\nHomologica
l conjectures\n\nAlgebras of finite global dimension\n\nSelf-injective alg
ebras\n\nTame algebras\n\nCombinatorial aspects of representation theory\n
\nGeometry of algebras and modules\n\nHomological invariants of algebras a
nd modules\n\nTriangulated categories and tilting theory\n\nRelations of t
he above topics with Lie theory\, Singularity theory\, Cohen--Macaulay mod
ules\, quantum groups and other algebraic structures.\n\nThe conference wi
ll be held on Zoom. The Zoom link and passcode for talks will be shared wi
th 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: Please c
omplete the registration here. \n\nLocal Organizers: Ibrahim Assem\, Thoma
s Brüstle\, Charles Paquette\, Sonia Trepode\, Tianyuan Xu\, Emine Yildir
im.\n\nScientific Committee: Ibrahim Assem\, Piotr Dowbor\, Charles Paquet
te\, José Antonio de la Peña\, Sonia Trepode.\n\nContact: For inquiries\
, please contact any member of the organizing committee or write to VirtAR
TA.2021@gmail.com.\n
LOCATION:https://researchseminars.org/talk/TRAC/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny August
DTSTART;VALUE=DATE-TIME:20210428T140000Z
DTEND;VALUE=DATE-TIME:20210428T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/20
DESCRIPTION:Title: Gr
assmannian categories of infinite rank\nby Jenny August as part of The
TRAC Seminar - Théorie de Représentations et ses Applications et Connec
tions\n\n\nAbstract\nIn this talk\, I'll describe our work towards providi
ng an infinite rank version of the Grassmannian cluster categories introdu
ced by Jensen\, King and Su. We show that there is a structure preserving
bijection between Plücker coordinates and the generically free modules of
rank 1 in our Grassmannian category of infinite rank. In the k=2 case\, t
his allows us to model our category\, and its cluster combinatorics\, usin
g triangulations of an infinity-gon. This is joint work with Man-Wai Cheun
g\, Eleonore Faber\, Sira Gratz and Sibylle Schroll.\n
LOCATION:https://researchseminars.org/talk/TRAC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Martsinkovsky
DTSTART;VALUE=DATE-TIME:20210505T140000Z
DTEND;VALUE=DATE-TIME:20210505T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/21
DESCRIPTION:Title: Ho
mological Aspects of (Co)Torsion Functors over Artin Algebras\nby Alex
ander Martsinkovsky as part of The TRAC Seminar - Théorie de Représentat
ions et ses Applications et Connections\n\n\nAbstract\nIn this talk I will
completely determine the derived functors (both left and right) of both t
orsion and cotorsion functors defined on the module category of an arbitra
ry artin algebra. The obtained results hold even in greater generality. 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://researchseminars.org/talk/TRAC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:VirtARTA
DTSTART;VALUE=DATE-TIME:20210526T140000Z
DTEND;VALUE=DATE-TIME:20210526T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/22
DESCRIPTION:Title: Ad
vances in Representation Theory of Algebras\nby VirtARTA as part of Th
e TRAC Seminar - Théorie de Représentations et ses Applications et Conne
ctions\n\n\nAbstract\nA special edition of the conference "Advances in Rep
resentation Theory of Algebras" (ARTA) dedicated to the memory of Andrzej
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 a
nd one of the founders of the ARTA series. The conference will feature tal
ks on recent developments in the following topics:\n\nStructure of finite
dimensional algebras\n\nStructure of module categories\n\nAuslander--Reite
n components\n\nHomological methods in representation theory\n\nHomologica
l conjectures\n\nAlgebras of finite global dimension\n\nSelf-injective alg
ebras\n\nTame algebras\n\nCombinatorial aspects of representation theory\n
\nGeometry of algebras and modules\n\nHomological invariants of algebras a
nd modules\n\nTriangulated categories and tilting theory\n\nRelations of t
he above topics with Lie theory\, Singularity theory\, Cohen--Macaulay mod
ules\, quantum groups and other algebraic structures.\n\nThe conference wi
ll be held on Zoom. The Zoom link and passcode for talks will be shared wi
th 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: Please c
omplete the registration here. \n\nLocal Organizers: Ibrahim Assem\, Thoma
s Brüstle\, Charles Paquette\, Sonia Trepode\, Tianyuan Xu\, Emine Yildir
im.\n\nScientific Committee: Ibrahim Assem\, Piotr Dowbor\, Charles Paquet
te\, José Antonio de la Peña\, Sonia Trepode.\n\nContact: For inquiries\
, please contact any member of the organizing committee or write to VirtAR
TA.2021@gmail.com.\n
LOCATION:https://researchseminars.org/talk/TRAC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Zvonareva
DTSTART;VALUE=DATE-TIME:20210609T140000Z
DTEND;VALUE=DATE-TIME:20210609T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/23
DESCRIPTION:Title: HR
S tilting for co-t-structures and cotorsion pairs\nby Alexandra Zvonar
eva as part of The TRAC Seminar - Théorie de Représentations et ses Appl
ications 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) and a co
mplete cotorsion pair in its extended co-heart C=Σ^2A∩B. This construct
ion is similar to the Happel-Reiten-Smalo tilt of a t-structure with respe
ct to a torsion pair in its heart and it induces a bijection between inter
mediate co-t-structures and complete cotorsion pairs. For a finite dimensi
onal algebra this introduces a new component to the numerous existing bije
ctions studied in tau-tilting theory and in silting theory\, that is the b
ijections between intermediate algebraic t-structures\, functorially finit
e torsion pairs\, two-term silting complexes\, and so on. \n\nBased on joi
nt work with David Pauksztello.\n
LOCATION:https://researchseminars.org/talk/TRAC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:SSAC
DTSTART;VALUE=DATE-TIME:20210623T140000Z
DTEND;VALUE=DATE-TIME:20210623T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/24
DESCRIPTION:Title: Su
mmer School of Algebraic Combinatorics\nby SSAC as part of The TRAC Se
minar - Théorie de Représentations et ses Applications et Connections\n\
n\nAbstract\nOrganizers/ Organisatrices:\n\nVéronique Bazier-Matte\, Souh
eila Hassoun et Nancy Wallace\n\nCourses and lecturers - Cours et professe
ures \n\nCluster Categories and Related Topics by Pr. Gordana Todorov\n\nI
ntroduction to Cluster Algebras and Combinatorics of Friezes by Pr. Khryst
yna Serhiyenko\n\nSchubert calculus and symmetric functions by Pr. Maria G
illespie\n\nTamari Lattices and Posets by Pr. Emily Barnard\n\nThe aim of
this school is to advance the participants knowledge and enthusiasm toward
s algebraic combinatorics. Through high-level presentations\, the students
will learn multiple combinatorial aspects linked to representation theory
. Every day\, a postdoctoral researcher will introduce a research topic ti
ed to the introductory classes.\nSchubert calculus\, symmetric functions\,
cluster algebra\, Tamari lattices\, frieze combinatorics and cluster cate
gories are not only ways to study representation theory\, but have many li
nks between them. On one hand\, cluster algebras\, introduced by Sergey Fo
min and Andrei Zelevinsky\, can be studied using the combinatorics of frie
zes\, on the other hand\, they can be studied algebraically using cluster
categories. Moreover\, they have a correspondence with double Bruhat cells
. In the case of Flag varieties and grassmanians\, the decomposition into
Bruhat cells gives way to decomposition into Schubert cells. These can be
obtained using Schubert calculus. Schubbert polynomials are a generalizati
on of Schur functions\, which are symmetric functions. Using sub-word comp
lexes\, Schubert varieties are tied to the study of Tamari Lattices. These
lattices correspond to exchange graphs of some cluster algebra.\nFinally\
, our goal is to promote the visibility and accomplishment of women in mat
hematics. Even though the school is open to people of all genders\, only w
omen were invited to give lectures and talks. It seems important to us to
give the occasion to students to interact accomplished women in mathematic
s\, since they are underrepresented among teachers in mathematics in unive
rsities.\n
LOCATION:https://researchseminars.org/talk/TRAC/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte
DTSTART;VALUE=DATE-TIME:20210630T140000Z
DTEND;VALUE=DATE-TIME:20210630T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/25
DESCRIPTION:Title: Qu
ivers associated with non-orientable surfaces\nby Véronique Bazier-Ma
tte as part of The TRAC Seminar - Théorie de Représentations et ses Appl
ications et Connections\n\n\nAbstract\nIn 2015\, F Dupont and G Palesi def
ined quasi-cluster algebras from triangulations of non-orientable surfaces
. We now associate quivers to these triangulations and define a mutation r
ule to encode flips of arcs in non-orientable surfaces. We will show some
properties of these quivers and their mutation rule\; in particular\, we w
ill demonstrate that they generalize the classical definitions of quiver a
nd mutation. \n\nJoint work with Linda He\, Ruiyang Huang\, Hanyi Luo and
Kayla Wright.\n
LOCATION:https://researchseminars.org/talk/TRAC/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The FDSeminar organizers
DTSTART;VALUE=DATE-TIME:20210630T150000Z
DTEND;VALUE=DATE-TIME:20210630T151500Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/26
DESCRIPTION:Title: Pa
nel discussion: online meetings - past and future?\nby The FDSeminar o
rganizers as part of The TRAC Seminar - Théorie de Représentations et se
s Applications et Connections\n\n\nAbstract\nThis online podium discussion
marks the last TRAC Seminar before our summer break. We like to end the s
eries with a discussion about online events\, and the future of meetings i
n the field of representation theory in general. We plan to discuss how th
e panel members see in retrospective what changes the pandemic has brought
to our field\, which changes might stay\, what was their experience\, and
what are future plans.\n\nPanel members in this first section are the FDS
eminar organizers:\n\nEleonore Faber\, Gustavo Jasso\, Ryan Kinser\, Julia
n Külshammer\, Rosanna Laking\, Alexandra Zvonareva\n
LOCATION:https://researchseminars.org/talk/TRAC/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The OCAS organizers
DTSTART;VALUE=DATE-TIME:20210630T151500Z
DTEND;VALUE=DATE-TIME:20210630T153000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/27
DESCRIPTION:Title: Pa
nel discussion: online meetings - past and future?\nby The OCAS organi
zers as part of The TRAC Seminar - Théorie de Représentations et ses App
lications et Connections\n\n\nAbstract\nThis online podium discussion mark
s 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 pan
el members see in retrospective what changes the pandemic has brought to o
ur field\, which changes might stay\, what was their experience\, and what
are future plans.\n\nPanel members in this first section are the OCAS org
anizers: \n\nAnna Felikson\, Misha Gekhtman\, Pierre-Guy Plamondon\, Ralf
Schiffler\, Khrystyna Serhiyenko\n
LOCATION:https://researchseminars.org/talk/TRAC/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angeleri-Hügel\, Keller\, Martsinkovsky
DTSTART;VALUE=DATE-TIME:20210630T153000Z
DTEND;VALUE=DATE-TIME:20210630T155500Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/28
DESCRIPTION:Title: Pa
nel discussion: online meetings - past and future?\nby Angeleri-Hügel
\, Keller\, Martsinkovsky as part of The TRAC Seminar - Théorie de Repré
sentations et ses Applications et Connections\n\n\nAbstract\nThis online p
odium discussion marks the last TRAC Seminar before our summer break. We l
ike to end the series with a discussion about online events\, and the futu
re of meetings in the field of representation theory in general. We plan t
o discuss how the panel members see in retrospective what changes the pand
emic has brought to our field\, which changes might stay\, what was their
experience\, and what are future plans.\n\nPanel members in this last sect
ion are Senior Experts in the field of representation theory: \n\nLidia An
geleri-Hügel\, Bernhard Keller\, and Alex Martsinkovsky.\n
LOCATION:https://researchseminars.org/talk/TRAC/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur
DTSTART;VALUE=DATE-TIME:20210602T140000Z
DTEND;VALUE=DATE-TIME:20210602T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/29
DESCRIPTION:Title: Fr
ieze patterns and cluster theory\nby Karin Baur as part of The TRAC Se
minar - Théorie de Représentations et ses Applications et Connections\n\
n\nAbstract\nCluster categories and cluster algebras can be described via
triangulations of surfaces or via Postnikov diagrams. In type A\, such tri
angulations lead to frieze patterns or SL_2-friezes in the sense of Conway
and Coxeter. We explain how infinite frieze patterns arise and how Grassm
annians give rise to SL_k-friezes.\n
LOCATION:https://researchseminars.org/talk/TRAC/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hipolito Treffinger (Université de Paris)
DTSTART;VALUE=DATE-TIME:20220118T150000Z
DTEND;VALUE=DATE-TIME:20220118T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/30
DESCRIPTION:Title: St
ratifying systems\, τ-tilting theory and g-vectors\nby Hipolito Treff
inger (Université de Paris) as part of The TRAC Seminar - Théorie de Rep
résentations et ses Applications et Connections\n\n\nAbstract\nIn this ta
lk we will talk about the relationship between the stratifying systems def
ined 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 talk exp
laining how the properties of the mutation process on tau-tilting pairs en
ables us to build at least one stratifying from every τ-rigid module. \n\
n\n\nIn the second part of the talk we will change gears slightly and spea
k about Cartan matrices as an invariant for stratifying systems\, as it wa
s recently proposed by Marcos\, Mendoza and Sáenz. In particular we will
speak how the Cartan matrix for a stratifying systems induced by a τ-rigi
d module can be computed using the g-vectors of the said τ-rigid module.
\n\n\n\nThis is a report on joint work with Octavio Mendoza and Corina Sá
enz. \n\nhttps://arxiv.org/abs/1904.11903\n\nhttps://arxiv.org/abs/2111.11
376\n
LOCATION:https://researchseminars.org/talk/TRAC/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Scoccola (Northeastern University)
DTSTART;VALUE=DATE-TIME:20220125T150000Z
DTEND;VALUE=DATE-TIME:20220125T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/31
DESCRIPTION:Title: St
ability of homological invariants of multiparameter persistence modules\nby Luis Scoccola (Northeastern University) as part of The TRAC Seminar
- Théorie de Représentations et ses Applications et Connections\n\n\nAbs
tract\nUnlike one-parameter persistence modules\, for which we have the ba
rcode\, persistence modules with two or more parameters do not admit a com
plete discrete invariant\, and thus incomplete invariants must be used to
study the structure of such modules in practice. The Hilbert function and
the multigraded Betti numbers are among the simplest such incomplete invar
iants. Although these two invariants are already being used in application
s\, it is a priori unclear whether they satisfy a stability result analogo
us to the stability of the one-parameter barcode. Stability results are es
sential for the interpretability and consistency of practical methods. I w
ill present joint work with Steve Oudot in which we prove stability result
s for multigraded Betti numbers and for the Hilbert function. I will also
discuss ongoing work in which we prove the stability of finer invariants c
oming from different exact structures on a category of multiparameter pers
istence modules.\n
LOCATION:https://researchseminars.org/talk/TRAC/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Shah (Aarhus University)
DTSTART;VALUE=DATE-TIME:20220201T150000Z
DTEND;VALUE=DATE-TIME:20220201T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/32
DESCRIPTION:Title: A
characterisation of n-exangulated functors\nby Amit Shah (Aarhus Unive
rsity) as part of The TRAC Seminar - Théorie de Représentations et ses A
pplications et Connections\n\n\nAbstract\nExamples of structure-preserving
functors between extriangulated categories\, so-called extriangulated fun
ctors\, include the canonical functor from an abelian category to its deri
ved category\, and the quotient functor from a Frobenius exact category to
its stable category. The first\, for example\, is structure-preserving in
the sense that short exact sequences are sent to distinguished triangles
in a functorial way. In higher homological algebra\, we also see examples
of structure-preserving functors\, but not covered by the current terminol
ogy. E.g. n-cluster tilting subcategories sitting inside an ambient abelia
n category. In an attempt\, with R. Bennett-Tennenhaus\, J. Haugland 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 extriangulated (or\,
more generally\, n-exangulated) functors. The aim of my talk is to explai
n this.\n
LOCATION:https://researchseminars.org/talk/TRAC/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Dequêne (UQAM)
DTSTART;VALUE=DATE-TIME:20220208T150000Z
DTEND;VALUE=DATE-TIME:20220208T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/33
DESCRIPTION:Title: Jo
rdan recoverability of some categories of modules over gentle algebras
\nby Benjamin Dequêne (UQAM) as part of The TRAC Seminar - Théorie de Re
présentations et ses Applications et Connections\n\n\nAbstract\nGentle al
gebras form a class of finite dimensional algebras introduced by Assem and
Skowroński in the 80’s. Indecomposable modules over such an algebra ad
mit a combinatorial description in terms of strings and bands\, which are
walks in the associated gentle quiver (satisfying some further conditions)
\, thanks to the work of Butler and Ringel. A subcategory C of modules is
said to be Jordan recoverable if a module X in C can be recovered from the
Jordan forms\, at each vertex\, of a generic nilpotent endomorphism. This
data is encoded by a tuple of integer partitions. \n\nAfter we have intro
duced some definitions and set the context\, the main aim of the talk is t
o explain the notion of Jordan recoverability through various examples\, a
nd to highlight a combinatorial characterization of when that property hol
ds for some special subcategories of modules. This result is extending the
work of Garver\, Patrias and Thomas in Dynkin types. If time allows\, we
may discuss some open questions related to this result and\, in particular
\, exhibit new ideas to characterize all the subcategories of modules that
are Jordan recoverable in the A_n case.\n\nThis is a part of my Ph.D. wor
k supervised by Hugh Thomas.\n
LOCATION:https://researchseminars.org/talk/TRAC/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Weigandt (MIT)
DTSTART;VALUE=DATE-TIME:20220215T150000Z
DTEND;VALUE=DATE-TIME:20220215T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/34
DESCRIPTION:Title: Th
e Castelnuovo-Mumford Regularity of Matrix Schubert Varieties\nby Anna
Weigandt (MIT) as part of The TRAC Seminar - Théorie de Représentations
et ses Applications et Connections\n\n\nAbstract\nThe Castelnuovo-Mumford
regularity of a graded module provides a measure of how complicated its m
inimal free resolution is. In work with Rajchgot\, Ren\, Robichaux\, and
St. Dizier\, we noted that the regularity of Matrix Schubert Varieties can
be easily obtained by knowing the degree of the corresponding Grothendiec
k polynomial. Furthermore\, we gave explicit\, combinatorial formulas for
the degrees of symmetric Grothendieck polynomials. In this talk\, I will
present a combinatorial degree formula for arbitrary Grothendieck polynom
ials. This is joint work with Oliver Pechenik and David Speyer.\n
LOCATION:https://researchseminars.org/talk/TRAC/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Hogancamp (Northeastern University)
DTSTART;VALUE=DATE-TIME:20220222T150000Z
DTEND;VALUE=DATE-TIME:20220222T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/35
DESCRIPTION:Title: Id
empotent (co)algebras and generalizations of Hochschild cohomology\nby
Matt Hogancamp (Northeastern University) as part of The TRAC Seminar - Th
éorie de Représentations et ses Applications et Connections\n\n\nAbstrac
t\nIn this talk I will discuss the notion of an idempotent (co)algebra (or
perhaps more descriptively\, idempotent *dg* (co)algebra). The two-sided
bar complex of an algebra gives an especially important class of examples
\, but there is a plethora of other examples appearing throughout mathemat
ics. I will describe how the endomorphism algebra of an idempotent (co)al
gebra naturally admits the structure of a Gerstenhaber algebra\, generaliz
ing a well known structure on Hochschild cohomology.\n
LOCATION:https://researchseminars.org/talk/TRAC/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Crooks (Northeastern University)
DTSTART;VALUE=DATE-TIME:20220301T150000Z
DTEND;VALUE=DATE-TIME:20220301T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/36
DESCRIPTION:Title: Sh
ift-of-argument algebras in geometry and representation theory\nby Pet
er Crooks (Northeastern University) as part of The TRAC Seminar - Théorie
de Représentations et ses Applications et Connections\n\n\nAbstract\nInt
egrable systems first came to prominence as a geometric abstraction of str
ucture in classical mechanics. Despite these origins\, integrable systems
have been found to interact meaningfully with pure mathematics. Modern exa
mples 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 mathemat
ics. They exhibit the kind of Lie-theoretic symmetry that allows difficult
geometric problems to be posed and solved entirely in algebraic terms. Th
e algebraic incarnations of Mishchenko-Fomenko systems are the so-called s
hift-of-argument algebras\, which enjoy connections to geometry and repres
entation 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 Iv
a Halacheva and Valerio Toledano Laredo.\n
LOCATION:https://researchseminars.org/talk/TRAC/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Fedele (Università di Verona)
DTSTART;VALUE=DATE-TIME:20220308T150000Z
DTEND;VALUE=DATE-TIME:20220308T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/37
DESCRIPTION:Title: Un
iversal localizations of d-homological pairs\nby Francesca Fedele (Uni
versità di Verona) as part of The TRAC Seminar - Théorie de Représentat
ions et ses Applications et Connections\n\n\nAbstract\nLet k be an algebra
ically closed field and A a finite dimensional k-algebra. The universal lo
calization of A with respect to a set of morphisms between finitely genera
ted projective A-modules always exists. Moreover\, when A is hereditary\,
Krause and Stovicek proved that the universal localizations of A are in bi
jection with various natural structures.\nIn this talk\, based on joint wo
rk with Peter Jorgensen\, I will introduce the higher analogue of universa
l localizations\, that is universal localizations of d-homological pairs w
ith respect to certain wide subcategories\, and show a (partial) generalis
ation of Krause and Stovicek result in the higher setup.\n
LOCATION:https://researchseminars.org/talk/TRAC/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Garcia Elsener (University of Glasgow)
DTSTART;VALUE=DATE-TIME:20220315T140000Z
DTEND;VALUE=DATE-TIME:20220315T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/38
DESCRIPTION:Title: Mo
nomial 2-Calabi Yau tilted algebras are Jacobian\nby Ana Garcia Elsene
r (University of Glasgow) as part of The TRAC Seminar - Théorie de Repré
sentations et ses Applications et Connections\n\n\nAbstract\nA celebrated
result by Keller and Reiten says that 2-Calabi–Yau tilted algebras are G
orenstein and stably 3-Calabi–Yau\, in particular Jacobian algebras over
an algebraically closed field satisfy this. Jacobian algebras are 2-Calab
i-Yau tilted as proven by Amiot. These results originated several conjectu
res in the opposite direction: Are all 2-Calabi-Yau tilted algebras Jacobi
an? (Amiot 2011 - Kalck Yang 2020). We show that the converse holds in the
monomial case: a 1-Gorenstein monomial algebra that is stably 3-Calabi–
Yau has to be 2-Calabi–Yau tilted\, moreover it has to be Jacobian. This
result can be explained fully in a 50 mins seminar\, so I aim to do that.
\n
LOCATION:https://researchseminars.org/talk/TRAC/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Bennett-Tennenhaus (Bielefeld University)
DTSTART;VALUE=DATE-TIME:20220322T140000Z
DTEND;VALUE=DATE-TIME:20220322T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/39
DESCRIPTION:Title: Se
milinear clannish algebras\nby Raphael Bennett-Tennenhaus (Bielefeld U
niversity) as part of The TRAC Seminar - Théorie de Représentations et s
es Applications et Connections\n\n\nAbstract\nAbstract: Indecomposable mod
ules over string algebras were classified by Butler and Ringel\, and take
exactly one of two forms: string modules\, defined by walks in the quiver\
; or band modules\, given by cyclic walks together with a representation o
f the Laurent polynomial ring. Clannish algebras\, introduced by Crawley-
Boevey\, are a generalisation of string algebras – where one specifies a
set of special loops\, each bounded by some quadratic polynomial. An anal
ogue of Butler and Ringel’s result was given where the class of string (
or band) modules splits into so-called asymmetric and symmetric subclasses
. Said symmetry is given by reflecting the walk about a special loop\, and
symmetric strings and bands are parameterised using appropriate replaceme
nts for the Laurent polynomial ring.\n\nBoth string algebras and clannish
algebras were defined over a field\, and the quadratics bounding special l
oops were assumed to have distinct roots in this field. This talk will be
about ongoing joint work with Bill Crawley-Boevey\, where we generalise th
e classification for clannish algebras. For the rings we consider we repla
ce this field with a division ring equipped with a set of automorphisms\,
indexed by arrows of the quiver\, and we allow irreducible quadratics to b
ound the special loops. The resulting notion of a semilinear clannish alge
bra recovers a generalisation of string algebras considered by Ringel\, wh
ere one allows the map associated to an arrow to be semilinear with respec
t to its automorphism.\n
LOCATION:https://researchseminars.org/talk/TRAC/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josh Wen
DTSTART;VALUE=DATE-TIME:20220412T140000Z
DTEND;VALUE=DATE-TIME:20220412T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/40
DESCRIPTION:Title: An
invitation to wreath Macdonald polynomials\nby Josh Wen as part of Th
e TRAC Seminar - Théorie de Représentations et ses Applications et Conne
ctions\n\n\nAbstract\nMacdonald polynomials are distinguished symmetric fu
nctions that have played important or useful roles in a wide range of fiel
ds: combinatorics\, enumerative geometry\, integrable systems\, probabilit
y\, knot theory\, etc. Defined by Haiman\, wreath Macdonald polynomials ar
e generalizations of Macdonald polynomials wherein the symmetric groups ar
e replaced with their wreath products with a fixed cyclic group Z/rZ. I wi
ll discuss work in progress where\, using the quantum toroidal algebra of
rank r\, one can derive analogues of some standard parts of Macdonald theo
ry: orthogonality\, evaluation formulas\, and difference operators. This i
s joint work with Daniel Orr and Mark Shimozono.\n
LOCATION:https://researchseminars.org/talk/TRAC/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART;VALUE=DATE-TIME:20220329T140000Z
DTEND;VALUE=DATE-TIME:20220329T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/41
DESCRIPTION:Title: Cr
ystals and cacti in representation theory\nby Iva Halacheva (Northeast
ern University) as part of The TRAC Seminar - Théorie de Représentations
et ses Applications et Connections\n\n\nAbstract\nOne approach to studyin
g the representation theory of Lie algebras and their associated quantum g
roups is through combinatorial shadows known as crystals. While the origin
al representations carry an action of the braid group\, their crystals car
ry an action of a closely related group known as the cactus group. I will
describe how we can realize this combinatorial action both geometrically\,
as a monodromy action coming from a family of ‘’shift of argument’
’ algebras\, as well as categorically through the structure of certain e
quivalences on triangulated categories known as Rickard complexes. Parts o
f this talk are based on joint work with Joel Kamnitzer\, Leonid Rybnikov\
, and Alex Weekes\, as well as Tony Licata\, Ivan Losev\, and Oded Yacobi.
\n
LOCATION:https://researchseminars.org/talk/TRAC/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Amiens)
DTSTART;VALUE=DATE-TIME:20220419T140000Z
DTEND;VALUE=DATE-TIME:20220419T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/42
DESCRIPTION:Title: Ma
ximal green sequences\, second Bruhat orders\, and second Cambrian maps\nby Mikhail Gorsky (Amiens) as part of The TRAC Seminar - Théorie de Re
présentations et ses Applications et Connections\n\n\nAbstract\nThis is a
report on joint work in progress with Nicholas Williams.\n\nMaximal 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. Recently\,
lattices of torsion classes have been a subject of intensive research. Dem
onet-Iyama-Reading-Reiten-Thomas proved that for a quiver Q of Dynkin type
ADE\, the lattice of torsion classes of its path algebra realizes the Cam
brian lattice\, while the lattice tors Π for the preprojective algebra is
isomorphic to the weak Bruhat order on the corresponding Weyl group. The
Cambrian map\, introduced by Reading in combinatorial terms\, can thus be
interpreted as a morphism of lattices of torsion classes.\n\nHigher versio
ns of Bruhat and Cambrian orders in type A first appeared in late 80s in w
orks of Manin-Shekhtman and Kapranov-Voevodsky\, respectively. Kapranov an
d Voevodsky also defined a family of maps from higher Bruhat orders to hig
her Tamari-Stasheff orders (the latter are the higher versions of Cambrian
orders in type A). More recently\, second Bruhat orders showed up in work
s by Elias on (monoidal) categories of Soergel bimodules. I will explain h
ow to realize a version of the second Bruhat order for a quiver Q as an or
der on equivalence classes of maximal green sequences for the correspondin
g preprojective algebra and the second Cambrian order as a similar order f
or the path algebra of Q. The second Cambrian map can then be interpreted
as the "second level" of the Demonet-Iyama-Reading-Reiten-Thomas map. In t
ype A this provides\, in a sense\, an additive categorification of the cor
responding Kapranov-Voevodsky map\, which allows for a representation-theo
retic interpretation of its fibers. If time permits\, I will also explain
how one can interpret second Cambrian orders in terms of polytopes and tor
ic varieties associated with certain subword complexes.\n
LOCATION:https://researchseminars.org/talk/TRAC/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Cliff (Université de Sherbrooke)
DTSTART;VALUE=DATE-TIME:20220503T140000Z
DTEND;VALUE=DATE-TIME:20220503T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/43
DESCRIPTION:Title: Mo
duli spaces of principal 2-group bundles and a categorification of the Fre
ed-Quinn line bundle\nby Emily Cliff (Université de Sherbrooke) as pa
rt of The TRAC Seminar - Théorie de Représentations et ses Applications
et Connections\n\n\nAbstract\nA 2-group is a higher categorical analogue o
f a group\, while a smooth 2-group is a higher categorical analogue of a L
ie group. An important example is the string 2-group in the sense of Schom
mer-Pries. We study the notion of principal bundles for smooth 2-groups\,
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 surfac
e\, 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 s
pace of Chern-Simons theory for the underlying finite group. We can also u
se our results to better understand the notion of geometric string structu
res (as previously studied by Waldorf and Stolz-Teichner).\n\nThe talk wil
l not assume background knowledge on 2-groups or Chern-Simons theory. It i
s based on joint work with Dan Berwick-Evans\, Laura Murray\, Apurva Nakad
e\, and Emma Phillips.\n
LOCATION:https://researchseminars.org/talk/TRAC/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Coelho Guardado Simoes (Lancaster University)
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DTEND;VALUE=DATE-TIME:20220517T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/44
DESCRIPTION:Title: Fr
om gentle to string algebras: a geometric model\nby Raquel Coelho Guar
dado Simoes (Lancaster University) as part of The TRAC Seminar - Théorie
de Représentations et ses Applications et Connections\n\n\nAbstract\nGeom
etric models associated to triangulations of Riemann surfaces arose in the
context of cluster algebras and have since been used as an important tool
to study representation theory of algebras and provide connections with a
lgebraic geometry and symplectic geometry.\n\nSignificant applications of
geometric models include a description of extensions and a classification
of support tau-tilting modules over gentle algebras. Gentle algebras are a
particular subclass of string algebras\, which are of tame representation
type\, meaning it is often possible to get a global understanding of thei
r representation theory.\n\nIn this talk I will describe the module catego
ry of a gentle algebra via partial triangulations of unpunctured surfaces\
, explain how to extend this model to a geometric model of the module cate
gory of any string algebra and use this model to obtain a classification o
f support tau-tilting modules. This is based on joint work in progress wit
h Karin Baur.\n
LOCATION:https://researchseminars.org/talk/TRAC/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (Cambridge)
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DTEND;VALUE=DATE-TIME:20220426T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T204815Z
UID:TRAC/46
DESCRIPTION:Title: Lo
cally free Caldero-Chapoton functions for rank 2 cluster algebras\nby
Lang Mou (Cambridge) as part of The TRAC Seminar - Théorie de Représenta
tions et ses Applications et Connections\n\n\nAbstract\nAssociated to any
acyclic skew-symmetrizable matrix B and a symmetrizer\, Geiss\, Leclerc an
d Schröer have defined a finite-dimensional algebra H over any field. Man
y geometric constructions for acyclic quivers carry over to this situation
by using complex numbers. They show that in finite types\, the non-initia
l cluster variables (of the cluster algebra associated to B) are exactly t
he locally free Caldero—Chapoton functions of indecomposable locally fre
e rigid H-modules and conjecture it to be true in general. We verify this
conjecture in rank 2 by showing that the locally free F-polynomials of cer
tain modules under reflection functors satisfy the same recursion of the F
-polynomials of cluster variables. This is joint work with Daniel Labardin
i-Fragoso.\n
LOCATION:https://researchseminars.org/talk/TRAC/46/
END:VEVENT
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