BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Matthew Pressland (University of Leeds)
DTSTART:20200521T130000Z
DTEND:20200521T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/1
DESCRIPTION:Title: Calabi–Yau properties of Postnikov diagrams\nby Matthew Pressland
(University of Leeds) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pauksztello (Lancaster University)
DTSTART:20200528T130000Z
DTEND:20200528T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/2
DESCRIPTION:Title: Simple-mindedness: negativity and positivity\nby David Pauksztello
(Lancaster University) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Labardini-Fragoso (UNAM)
DTSTART:20200604T130000Z
DTEND:20200604T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/3
DESCRIPTION:Title: Schemes of modules over gentle algebras and laminations of surfaces
\nby Daniel Labardini-Fragoso (UNAM) as part of FD Seminar\n\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/fd-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Nagoya University)
DTSTART:20200618T130000Z
DTEND:20200618T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/4
DESCRIPTION:Title: Simple objects in torsion-free classes over preprojective algebras of D
ynkin type\nby Haruhisa Enomoto (Nagoya University) as part of FD Semi
nar\n\n\nAbstract\nIn this talk\, I propose to study exact-categorical str
uctures of torsion(-free) classes of module categories. For functorially f
inite torsion-free class\, indecomposable projective and injective objects
are easily described by \\tau^-τ \n−\n -tilting modules\, and in parti
cular\, the numbers of them coincide. However\, there can be more simple o
bjects in torsion-free class\, which I propose to study. I explain that th
e number of simple objects controls the validity of the Jordan–Hölder t
ype theorem in a torsion-free class.\n\nThen I’ll talk about simple obje
cts in a torsion-free class over the preprojective algebra (and path algeb
ra) of Dynkin type\, which is also important in Lie theory due to Geiss–
Leclerc–Schröer’s categorification of the cluster structure. By Mizun
o’s result\, we can associate an element ww of the Weyl group to each to
rsion-free class \\mathcal{F}F. By (extended) Gabriel’s theorem\, \\math
cal{F}F roughly corresponds to the inversion set of ww\, the set of positi
ve roots which are sent to negative by w^{-1}w \n−1\n . Then I show that
simple objects in \\mathcal{F}F are in bijection with Bruhat inversions o
f ww\, which are related to the Bruhat order of the Weyl group.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis-Philippe Thibault (NTNU)
DTSTART:20200611T130000Z
DTEND:20200611T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/5
DESCRIPTION:by Louis-Philippe Thibault (NTNU) as part of FD Seminar\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Schiffler (University of Connecticut)
DTSTART:20200625T130000Z
DTEND:20200625T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/6
DESCRIPTION:Title: A geometric model for the syzygies over certain 2-Calabi--Yau tilted al
gebras\nby Ralf Schiffler (University of Connecticut) as part of FD Se
minar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Amiot (Université Joseph Fourier)
DTSTART:20200702T130000Z
DTEND:20200702T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/7
DESCRIPTION:Title: Derived equivalences for skew-gentle algebras\nby Claire Amiot (Uni
versité Joseph Fourier) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur (University of Leeds)
DTSTART:20200716T130000Z
DTEND:20200716T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/8
DESCRIPTION:Title: Postnikov diagrams and orbifolds\nby Karin Baur (University of Leed
s) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Špela Špenko (Université libre de Bruxelles)
DTSTART:20200730T130000Z
DTEND:20200730T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/9
DESCRIPTION:Title: GKZ systems and perverse schobers\nby Špela Špenko (Université l
ibre de Bruxelles) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (Universidad de Buenos Aires)
DTSTART:20200709T130000Z
DTEND:20200709T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/10
DESCRIPTION:Title: Bounded extension algebras and Han's conjecture\nby Andrea Solotar
(Universidad de Buenos Aires) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cris Negron (University of North Carolina)
DTSTART:20200723T130000Z
DTEND:20200723T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/11
DESCRIPTION:Title: Finite generation of cohomology for Drinfeld doubles of finite group s
chemes\nby Cris Negron (University of North Carolina) as part of FD Se
minar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Université de Paris)
DTSTART:20200903T130000Z
DTEND:20200903T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/12
DESCRIPTION:Title: Relative Calabi-Yau completions and higher preprojective algebras\
nby Bernhard Keller (Université de Paris) as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shijie Zhu (The University of Iowa)
DTSTART:20200910T140000Z
DTEND:20200910T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/13
DESCRIPTION:Title: Hopf algebras of discrete representation type\nby Shijie Zhu (The
University of Iowa) as part of FD Seminar\n\n\nAbstract\nHopf algebra is a
n important topic in geometric representation theory. A basic algebra is o
f finite representation type if there are only finitely many non-isomorphi
c indecomposable representations. Basic Hopf algebras of finite representa
tion type have been classified by Liu and Li in 2004. As algebras\, they a
re just copies of Nakayama algebras. A pointed coalgebra is of discrete re
presentation type\, if there are only finitely many non-isomorphic indecom
posable representations for each dimension vector. In this talk\, I am goi
ng to give a classification of pointed Hopf algebras of discrete represent
ation type. The main tool we are using is called “covering maps” of (f
inite dimensional) coalgebras which comes from separable extensions of the
dual algebras. This is a joint work with Miodrag Iovanov\, Emre Sen\, and
Alexander Sistko.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny August (Max Plank Institut für Mathematik (MPIM))
DTSTART:20200917T130000Z
DTEND:20200917T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/14
DESCRIPTION:Title: Grassmanian categories of infinite rank\nby Jenny August (Max Plan
k Institut für Mathematik (MPIM)) as part of FD Seminar\n\n\nAbstract\nIn
this talk\, I’ll describe our work towards providing an infinite rank v
ersion of the Grassmanian cluster categories introduced by Jensen\, King a
nd Su. We develop a new combinatorial tool for determining when two k-subs
ets of the integers are “non-crossing”\, or equivalently when two Plü
cker coordinates of a Grassmanian cluster algebra of infinite rank are “
compatible”. We use this tool to show that there is a structure preservi
ng bijection between these Plücker coordinates and the generically free m
odules of rank 1 in our Grassmanian category of infinite rank\, mirroring
a result of Jensen\, King and Su in the finite case. This is joint work wi
th Man-Wai Cheung\, Eleonore Faber\, Sira Gratz and Sibylle Schroll.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (University of Science and Technology of China (USTC)
)
DTSTART:20200924T130000Z
DTEND:20200924T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/15
DESCRIPTION:Title: Leavitt path algebras\, B-infty-algebras and Keller’s conjecture for
singular Hochschild cohomology\nby Xiao-Wu Chen (University of Scienc
e and Technology of China (USTC)) as part of FD Seminar\n\n\nAbstract\nI w
ill first recall the relation between Leavitt path algebras and the singul
arity categories of radical-square-zero algebras. Using Leavitt path algeb
ras\, we confirm Keller’s conjecrure for any radical-square-zero algebra
: there is an isomorphism in the homotopy category of $B_\\infty$-algebras
between the Hochschild cochain complex of the dg singularity category and
the singular Hochschild cochain complex of the algebra. Moreover\, we pro
ve that Keller’s conjecture is invariant under one-point (co)extensions
and singular equivalences with levels. This is joint with Huanhuan Li and
Zhengfang Wang.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Zito (University of Connecticut)
DTSTART:20201001T130000Z
DTEND:20201001T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/16
DESCRIPTION:Title: tau-Tilting Finite Algebras With Non-Empty Left Or Right Parts Are Rep
resentation-Finite\nby Stephen Zito (University of Connecticut) as par
t of FD Seminar\n\n\nAbstract\nτ-tilting theory was introduced by Adachi\
, Iyama and Reiten as a far-reaching generalization of classical tilting t
heory for finite dimensional associative algebras. One of the main classes
of objects in the theory is that of τ\\tauτ-rigid modules: a module MMM
over an algebra Λ\\LambdaΛ is τ\\tauτ-rigid if HomΛ(M\,τM)=0\\op
eratorname{Hom}_{\\Lambda}(M\,\\tau M)=0HomΛ(M\,τM)=0\, where τM\\ta
u MτM denotes the Auslander-Reiten translation of MMM\; such a module MMM
is called τ\\tauτ-tilting if the number ∣M∣|M|∣M∣ of non-isomor
phic indecomposable summands of MMM equals the number of isomorphism class
es of simple Λ\\LambdaΛ-modules. Recently\, a new class of algebras was
introduced by Demonet\, Iyama\, Jasso called τ\\tauτ-tilting finite alge
bras. They are defined as finite dimensional algebras with only a finite n
umber of isomorphism classes of basic τ\\tauτ-tilting modules.\n\nAn obv
ious sufficient condition to be τ\\tauτ-tilting finite is to be represen
tation-finite. In general\, this condition is not necessary. The aim of th
is talk is to show for algebras Λ\\LambdaΛ such that LΛL_\\LambdaLΛ
or RΛ≠∅R_\\Lambda\\neq\\emptysetRΛ=∅ \, representation-f
initeness and τ\\tauτ-tilting finiteness are equivalent conditions.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lidia Angeleri Hügel (Università degli Studi di Verona)
DTSTART:20201217T140000Z
DTEND:20201217T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/17
DESCRIPTION:by Lidia Angeleri Hügel (Università degli Studi di Verona) a
s part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Muro (TBC) (Universidad de Sevilla)
DTSTART:20201210T140000Z
DTEND:20201210T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/18
DESCRIPTION:by Fernando Muro (TBC) (Universidad de Sevilla) as part of FD
Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (University of East Anglia)
DTSTART:20201022T130000Z
DTEND:20201022T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/20
DESCRIPTION:Title: Categorification of representation theory with an application to Soerg
el bimodules\nby Vanessa Miemietz (University of East Anglia) as part
of FD Seminar\n\n\nAbstract\nWe explain how to categorify various basic re
sults from the representation theory of finite-dimensional algebras\, whic
h are useful for classifying simple modules\, to the 2-representation theo
ry of fiat 2-categories. We then apply these in order to obtain a classifi
cation of simple 2-representations of the 2-category of Soergel bimodules.
\n
LOCATION:https://researchseminars.org/talk/fd-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitri Orlov (Steklov Mathematical Institute of Russian Academy of
Sciences)
DTSTART:20201029T140000Z
DTEND:20201029T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/21
DESCRIPTION:Title: Finite-dimensional DG algebras and their properties\nby Dmitri Orl
ov (Steklov Mathematical Institute of Russian Academy of Sciences) as part
of FD Seminar\n\n\nAbstract\nThe talk will focus on finite-dimensional DG
algebras and categories of perfect complexes over such DG algebras. These
categories can be considered as proper derived noncommutative schemes. We
are going to discuss basic properties of these noncommutative schemes and
to establish a connection between such categories and DG categories with
(semi)exceptional collections.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Hausdorff Research Institute for Mathematics (HIM)
)
DTSTART:20201203T140000Z
DTEND:20201203T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/22
DESCRIPTION:Title: Exact structures and degeneration of Hall algebras\nby Mikhail Gor
sky (Hausdorff Research Institute for Mathematics (HIM)) as part of FD Sem
inar\n\n\nAbstract\nHall algebras and various related structures play a pr
ominent role in the modern representation theory. I will explain the inter
play between different exact structures on an additive category and degene
rations of the associated Hall algebras. For the categories of representat
ions of Dynkin quivers\, this recovers degenerations of the negative part
of the corresponding quantum group. I will sketch the proofs of our result
s in the general case based on Auslander-Reiten theory. We will discuss fu
rther examples related to quantum doubles of quantum Borel subalgebras and
\, if time permits\, certain generalizations involving extriangulated cate
gories. (Based on joint work with Xin Fang.)\n
LOCATION:https://researchseminars.org/talk/fd-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Habermann (University College London (UCL))
DTSTART:20201008T130000Z
DTEND:20201008T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/23
DESCRIPTION:Title: Homological mirror symmetry for invertible polynomials in two variable
s\nby Matthew Habermann (University College London (UCL)) as part of F
D Seminar\n\n\nAbstract\nThe starting point for homological mirror symmetr
y for invertible polynomials is an n x n invertible matrix with non-negati
ve integer entries. To such a matrix\, as well as to its transpose\, one c
an associate polynomials. These polynomials are called invertible if they
are weighted homogeneous\, and both define isolated singularities at the o
rigin. Homological mirror symmetry for invertible polynomials is a series
of conjectures which posits the equivalence of the different flavours of F
ukaya category associated to the Lefschetz fibration defined by one polyno
mial with various flavours of graded matrix factorisations defined by the
transpose polynomial. Particular to the case of two variables is the fact
that the partially wrapped Fukaya category of a Milnor fibre corresponds t
o the derived category of modules of a gentle algebra\, and so HMS for inv
ertible polynomials in two variables allows one to study the latter catego
ry geometrically. In this talk I will explain my recent work\, part of whi
ch was done jointly with Jack Smith.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Grant (University of East Anglia)
DTSTART:20201015T130000Z
DTEND:20201015T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/24
DESCRIPTION:Title: Preprojective algebras and fractional Calabi-Yau algebras\nby Joe
Grant (University of East Anglia) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Mertens (Universiteit Antwerpen)
DTSTART:20201105T140000Z
DTEND:20201105T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/25
DESCRIPTION:Title: Linear quasi-categories as templicial modules\nby Arne Mertens (Un
iversiteit Antwerpen) as part of FD Seminar\n\n\nAbstract\nThis is joint w
ork with my supervisor Wendy Lowen. After laying out the basics of quasi-c
ategories as defined by Joyal\, we introduce a notion of linear quasi-cate
gories over a unital commutative ring. We make use of certain colax monoid
al functors\, which we call templicial modules\, as a variant of simplicia
l modules respecting the monoidal structure. It turns out that templicial
modules with a Frobenius monoidal structure are equivalent to (homological
ly) non-negatively graded dg-categories. Through this equivalence we can a
ssociate to any dg-category a linear quasi-category\, the linear dg-nerve\
, which enhances the classical dg-nerve.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ICRA2020 Research Snapshots
DTSTART:20201112T140000Z
DTEND:20201112T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/26
DESCRIPTION:by ICRA2020 Research Snapshots as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ICRA2020 Research Snapshots
DTSTART:20201119T140000Z
DTEND:20201119T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/27
DESCRIPTION:by ICRA2020 Research Snapshots as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ICRA2020 Research Snapshots
DTSTART:20201126T140000Z
DTEND:20201126T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/28
DESCRIPTION:by ICRA2020 Research Snapshots as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henning Krause (Universität Bielefeld)
DTSTART:20210107T140000Z
DTEND:20210107T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/29
DESCRIPTION:Title: The category of local representations of a finite group\nby Hennin
g Krause (Universität Bielefeld) as part of FD Seminar\n\n\nAbstract\nWe
consider modular representations of a finite group and focus for each prim
e ideal of the cohomology ring on the stable category of representations s
upported at that prime. This category is tensor triangulated\, but compact
and dualising objects do not coincide. For instance\, the tensor unit is
not compact. This is in contrast to the global category of representations
and leads to an interesting completion of the category of compact objects
. The talk presents recent progress from an ongoing collaboration with Dav
e Benson\, Srikanth Iyengar\, and Julia Pevtsova.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chrysostomos Psaroudakis (Aristotle University of Thessaloniki)
DTSTART:20210114T140000Z
DTEND:20210114T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/30
DESCRIPTION:by Chrysostomos Psaroudakis (Aristotle University of Thessalon
iki) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lo (California State University\, Northridge (CSUN))
DTSTART:20210121T140000Z
DTEND:20210121T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/31
DESCRIPTION:by Jason Lo (California State University\, Northridge (CSUN))
as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teresa Conde (Universität Stuttgart)
DTSTART:20210128T140000Z
DTEND:20210128T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/32
DESCRIPTION:by Teresa Conde (Universität Stuttgart) as part of FD Seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grzegorz Bobiński (Nicolaus Copernicus University)
DTSTART:20210204T140000Z
DTEND:20210204T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/33
DESCRIPTION:by Grzegorz Bobiński (Nicolaus Copernicus University) as part
of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Barnard (DePaul University)
DTSTART:20210211T140000Z
DTEND:20210211T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/34
DESCRIPTION:by Emily Barnard (DePaul University) as part of FD Seminar\n\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hipólito Treffinger (Rheinische Friedrich-Wilhelms-Universität B
onn)
DTSTART:20210218T140000Z
DTEND:20210218T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/35
DESCRIPTION:by Hipólito Treffinger (Rheinische Friedrich-Wilhelms-Univers
ität Bonn) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:İlke Çanakçı (Vrije Universiteit Amsterdam)
DTSTART:20210225T140000Z
DTEND:20210225T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/36
DESCRIPTION:by İlke Çanakçı (Vrije Universiteit Amsterdam) as part of
FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javad Asadollahi (University of Isfahan)
DTSTART:20210304T140000Z
DTEND:20210304T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/37
DESCRIPTION:by Javad Asadollahi (University of Isfahan) as part of FD Semi
nar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Franzen (Ruhr-Universität Bochum)
DTSTART:20210311T140000Z
DTEND:20210311T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/38
DESCRIPTION:by Hans Franzen (Ruhr-Universität Bochum) as part of FD Semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Gelinas
DTSTART:20210318T140000Z
DTEND:20210318T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/39
DESCRIPTION:by Vincent Gelinas as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Eckert (Universität Bielefeld)
DTSTART:20210325T140000Z
DTEND:20210325T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/40
DESCRIPTION:by Sebastian Eckert (Universität Bielefeld) as part of FD Sem
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Šťovíček (Charles University)
DTSTART:20210401T130000Z
DTEND:20210401T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/41
DESCRIPTION:by Jan Šťovíček (Charles University) as part of FD Seminar
\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Bodzenta-Skibińska (University of Warsaw)
DTSTART:20210415T130000Z
DTEND:20210415T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/42
DESCRIPTION:Title: Abelian envelopes of exact categories\nby Agnieszka Bodzenta-Skibi
ńska (University of Warsaw) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Hua (University of Hong Kong)
DTSTART:20210422T130000Z
DTEND:20210422T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/43
DESCRIPTION:Title: Cluster categories and rational curves\nby Zheng Hua (University o
f Hong Kong) as part of FD Seminar\n\n\nAbstract\nGiven a semi-simple coll
ection of rational curves on a smooth quasi-projective 3-fold\, its multip
ointed noncommutative deformation is represented by a negatively graded DG
A $\\Gamma$. The finite dimensionality of the cohomology of $\\Gamma$ seem
s to relate to contractibility of the collection of rational curves. For C
Y 3-folds\, $\\Gamma$ is a bimodule 3CY DG algebra. If we further assume c
ontractibility then $H^0\\Gamma$ is isomorphic to the contraction algebra
of Donovan and Wemyss. And the cluster category of $\\Gamma$ is dg-equival
ent to the singularity category of the contracted space. In some sense the
CY algebra $\\Gamma$ links the deformation theory of the exceptional fibr
es and the singularity theory of the contracted space. In this talk I will
present a joint work with Bernhard Keller\, where we prove that the deriv
ed Morita type of the contraction algebra together with a canonical class
in its 0-th Hochschild homology defined via CY structure determines the an
alytic type of the singularity of the contracted space.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magdalena Boos (Ruhr-Universität Bochum)
DTSTART:20210429T130000Z
DTEND:20210429T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/44
DESCRIPTION:Title: On symmetric quivers and their degenerations\nby Magdalena Boos (R
uhr-Universität Bochum) as part of FD Seminar\n\n\nAbstract\nWe introduce
the notion of a symmetric quiver as provided by Derksen and Weyman in 200
2 and discuss symmetric degenerations in this context (which correspond to
orbit closure relations in the symmetric representation variety). After m
otivating our particular interest in the latter by presenting connections
to group actions in algebraic Lie Theory\, we explain our main questions:
are symmetric degenerations induced by “usual” degenerations in the re
presentation variety of the underlying quiver? We look at (counter)example
s and recent results.\n\nThis is joint work with G. Cerulli Irelli and F.
Esposito.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Iyama (The University of Tokyo)
DTSTART:20210513T130000Z
DTEND:20210513T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/45
DESCRIPTION:Title: Periodic trivial extension algebras and fractionally Calabi-Yau algebr
as\nby Osamu Iyama (The University of Tokyo) as part of FD Seminar\n\n
\nAbstract\nWe study periodicity and twisted periodicity of the trivial ex
tension algebra T(A) of a finite-dimensional algebra A. We prove that (twi
sted) periodicity of the trivial extension is equivalent to A being (twist
ed) fractionally Calabi–Yau. Moreover\, twisted periodicity of T(A) is e
quivalent to the d-representation-finiteness of the r-fold trivial extensi
on algebra Tr(A) for some positive integers r and d. These results allow u
s to construct a large number of new examples of periodic as well as fract
ionally Calabi–Yau algebras\, and give answers to several open questions
. This is a joint work with Aaron Chan\, Erik Darpö and René Marczinzik.
\n
LOCATION:https://researchseminars.org/talk/fd-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gordana Todorov (Northeastern University)
DTSTART:20210603T130000Z
DTEND:20210603T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/46
DESCRIPTION:Title: Cluster Structures and Cluster Theories\nby Gordana Todorov (North
eastern University) as part of FD Seminar\n\n\nAbstract\n(Joint work with
Kiyoshi Igusa and Job D. Rock)\n\nI will discuss continuous cluster catego
ries\, generalizations of those\, cluster structures\, examples when only
conditions for “cluster theories”\, but not “cluster structures” (
in the sense of BIRS) are satisfied. Also relations between various cluste
r theories will be stated (some known\, some naturally expected).\n
LOCATION:https://researchseminars.org/talk/fd-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Gelinas
DTSTART:20210610T130000Z
DTEND:20210610T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/47
DESCRIPTION:Title: Some invariants related to the finitistic dimension\nby Vincent Ge
linas as part of FD Seminar\n\n\nAbstract\nThe finitistic dimension of Art
in algebras is notoriously hard to understand. In this talk\, we’ll disc
uss an attempt to pin it down in terms of a new invariant\, defined more g
enerally over sufficiently nice Noetherian rings. Originally meant to mode
l the finitistic dimension of Iwanaga-Gorenstein rings\, it unexpectedly a
lso gave the correct answer for commutative local Noetherian rings\, Artin
algebras of radical square zero\, and (due to recent results of Ringel an
d Sen) Nakayama algebras. Given time\, we’ll also discuss links with the
notion of “finitistic” Auslander algebras recently introduced by Marc
zinzik.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Brüstle (Université de Sherbrooke)
DTSTART:20210617T130000Z
DTEND:20210617T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/48
DESCRIPTION:Title: On length functions for an exact category\nby Thomas Brüstle (Uni
versité de Sherbrooke) as part of FD Seminar\n\n\nAbstract\nThe notion of
an exact category has been introduced by Quillen to axiomatize homologica
l properties of abelian categories. It allows to define and study homologi
cal properties of an exact category\, and to define its derived category.
However\, it turns out that the fundamental concept of length\, as known f
or modules\, is less suitable to be studied in the context of an exact cat
egory. We aim in this talk to present some recent developments showing for
which kind of exact categories an analogue of the Jordan-Hölder property
holds\, and what one can expect from the notion of length in general. We
also present results on the lattice structure of the set of all exact stru
ctures that can be attached to a fixed additive category.\n\nSome of the p
resented results are joint work with Rose-Line Baillargeon\, Mikhail Gorsk
y\, Souheila Hassoun and Aran Tattar.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Universität Hamburg)
DTSTART:20210722T130000Z
DTEND:20210722T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/49
DESCRIPTION:Title: Geometric models of Ginzburg algebras via local-to-global principles\nby Merlin Christ (Universität Hamburg) as part of FD Seminar\n\n\nAbs
tract\nThe derived categories of different classes of algebras (e.g. gentl
e algebras) and dg-algebras (e.g. Ginzburg algebras of triangulated surfac
es) have recently been described in terms of surfaces\, in so-called geome
tric models. Results include the description of objects in terms of curves
in a surface and Hom’s in terms of intersections. These algebras have i
n common that they arise via gluing\, i.e. as the global sections of a con
structible cosheaf. In the talk\, we will describe the gluing construction
for (relative) Ginzburg algebras of triangulated surfaces and compare it
with the gluing construction for gentle algebras. We will then discuss how
the gluing constructions naturally lead to the geometric models of their
derived categories.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Van Nguyen (United States Naval Academy)
DTSTART:20210506T130000Z
DTEND:20210506T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/50
DESCRIPTION:Title: Quantum symmetries through the lens of linear algebra\nby Van Nguy
en (United States Naval Academy) as part of FD Seminar\n\n\nAbstract\nThe
McKay matrix $M_V$ records the result of tensoring the simple modules with
a finite-dimensional module $V$. In the case of finite groups\, the eigen
vectors for $M_V$ are the columns of the character table\, and the eigenva
lues come from evaluating the character of $V$ on conjugacy class represen
tatives.\n\nIn this talk\, we will explore what can be said about such eig
envectors when the McKay matrix is determined by modules over an arbitrary
finite-dimensional Hopf algebra $H$. Here\, the McKay matrix \n$M_V$ enco
des quantum symmetries coming from the actions of $H$. We prove general re
sults about $M_V$ by using the coproduct and the characters of simple and
projective $H$-modules\, and also obtain results for a different matrix th
at encodes the fusion rules for Hopf algebra $H$. We illustrate these resu
lts for the small quantum group $u_q(\\mathfrak{sl}_2)$\, where $q$ is a r
oot of unity (and generally for the Drinfeld double $D_n$ of the Taft alge
bra). In these examples\, the eigenvalues and eigenvectors for these matri
ces can be described in terms of several kinds of Chebyshev polynomials.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck
DTSTART:20210624T130000Z
DTEND:20210624T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/51
DESCRIPTION:Title: A surface and a threefold with equivalent singularity categories\n
by Martin Kalck as part of FD Seminar\n\n\nAbstract\nWe start with an intr
oduction to singularity categories and equivalences between them. In parti
cular\, we recall known results about singular equivalences between commut
ative rings\, which go back to Knörrer\, Yang\, Kawamata and a joint work
with Karmazyn. Then we explain a new singular equivalence between an affi
ne surface and an affine threefold. This seems to be the first (non-trivia
l) example of a singular equivalence involving rings of even and odd Krull
dimension.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khrystyna Serhiyenko (University of Kentucky)
DTSTART:20210715T130000Z
DTEND:20210715T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/52
DESCRIPTION:Title: Maximal green sequences for string algebras\nby Khrystyna Serhiyen
ko (University of Kentucky) as part of FD Seminar\n\n\nAbstract\nMaximal g
reen sequences are certain transformations of quivers that were first intr
oduced by Keller in the context of cluster algebras. Later they were gener
alized to the setting of finite dimensional algebras\, where a maximal gre
en sequence is a finite maximal chain in the lattice of torsion classes. M
ore recently\, it was shown that these sequences are in bijection with for
ward hom-orthogonal sequences of bricks in the module category. We use the
latter approach to study existence and number of maximal green sequences
for string algebras. This is joint work with Al Garver.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Jørgensen (Aarhus University)
DTSTART:20210729T130000Z
DTEND:20210729T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/53
DESCRIPTION:Title: Abelian subcategories of triangulated categories induced by simple min
ded systems\nby Peter Jørgensen (Aarhus University) as part of FD Sem
inar\n\n\nAbstract\nIf $k$ is a field\, $A$ a finite dimensional $k$-algeb
ra\, then the simple $A$-modules form a simple minded collection in the de
rived category $D^b(mod A)$. Their extension closure is $mod A$\; in parti
cular\, it is abelian. This situation is emulated by a general simple mind
ed collection $S$ in a suitable triangulated category $C$. In particular\,
the extension closure $\\langle S \\rangle$ is abelian\, and there is a t
ilting theory for such abelian subcategories of $C$. These statements foll
ow from $\\langle S \\rangle$ being the heart of a bounded t-structure.\n\
nIt is a defining characteristic of simple minded collections that their n
egative self extensions vanish in every degree. Relaxing this to vanishing
in degrees $\\{-w+1\, \\dots\, -1\\}$ where $w$ is a positive integer lea
ds to the rich\, parallel notion of $w$-simple minded systems\, which have
recently been the subject of vigorous interest within negative cluster ti
lting theory.\n\nIf $S$ is a $w$-simple minded system for some $w\\geq 2$\
, then $\\langle S \\rangle$ is typically not the heart of a t-structure.
However\, it is possible to prove by different means that $\\langle S \\ra
ngle$ is still abelian and that there is a tilting theory for such abelian
subcategories. We will explain the theory behind this\, which is based on
Quillen’s notion of exact categories.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana García-Elsener (Universidad Nacional de Mar del Plata)
DTSTART:20210701T130000Z
DTEND:20210701T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/54
DESCRIPTION:Title: Rigid indecomposable modules in Grassmannian cluster categories\nb
y Ana García-Elsener (Universidad Nacional de Mar del Plata) as part of F
D Seminar\n\n\nAbstract\nThe coordinate ring of the Grassmannian variety o
f $k$-dimensional subspaces in $\\mathbb{C^n}$ has a cluster algebra struc
ture with Plucker relations giving rise to exchange relations. We study in
decomposable modules of the corresponding Grassmannian cluster categories
of type $(k\,n)$. Jensen\, King\, and Su have associated a Kac-Moody root
system to the category and shown that in the finite types\, rigid indecomp
osable modules correspond to roots. We provide evidence for this associati
on in the infinite types: we show that every indecomposable rank $2$ modul
e corresponds to a root of the associated root system. We also study roots
and indecomposable rank $3$ modules for the case $(3\,n)$.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kent Vashaw (Louisiana State University)
DTSTART:20210708T130000Z
DTEND:20210708T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/55
DESCRIPTION:Title: Noncommutative Tensor Triangular Geometry and Cohomological Support Va
rieties\nby Kent Vashaw (Louisiana State University) as part of FD Sem
inar\n\n\nAbstract\nRecently\, there has been significant interest in the
tensor product property for cohomological support varieties of Hopf algebr
as and tensor categories. We will describe a method for approaching the te
nsor product property by way of a noncommutative version of Balmer’s ten
sor triangular geometry in the general setting of a monoidal triangulated
category. We prove related properties about the collections of thick one-s
ided and two-sided ideals of the category\, and then are often able to use
the universal properties of the Balmer support to obtain applications to
cohomological supports. Examples arising from the representation theory of
Hopf algebras will be discussed throughout. This is joint work with Danie
l Nakano and Milen Yakimov.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugh Thomas (Université du Québec à Montréal)
DTSTART:20210902T130000Z
DTEND:20210902T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/56
DESCRIPTION:Title: An algebraic variety related to tau-tilting theory\nby Hugh Thomas
(Université du Québec à Montréal) as part of FD Seminar\n\n\nAbstract
\nLet A be a finite-dimensional algebra of finite representation type. I w
ill describe an affine algebraic variety whose totally non-negative part r
eflects the combinatorics of the tau-tilting fan of A. Starting from a Dyn
kin quiver\, one obtains something closely related to the corresponding Fo
ck–Goncharov cluster X variety\, while in general\, points on (one compo
nent of) the variety can be given in terms of ratios of F-polynomials\; th
e upshot is that this construction can be viewed as an extension of some o
f the beautiful features of cluster algebras to a more general setting. No
netheless\, familiarity with cluster algebras will not be needed to unders
tand the talk. A conjecture related to functoriality properties of the con
struction will be discussed. This is part of a joint project with Nima Ark
ani-Hamed\, Hadleigh Frost\, Pierre-Guy Plamondon\, and Giulio Salvatori.\
n
LOCATION:https://researchseminars.org/talk/fd-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johanne Haugland (Norges teknisk-naturvitenskapelige universitet\,
NTNU)
DTSTART:20210909T130000Z
DTEND:20210909T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/57
DESCRIPTION:Title: Higher Koszul duality and connections with n-hereditary algebras\n
by Johanne Haugland (Norges teknisk-naturvitenskapelige universitet\, NTNU
) as part of FD Seminar\n\n\nAbstract\nWe discuss a connection between two
areas of independent interest in representation theory\, namely Koszul du
ality and higher homological algebra. This is studied through a generaliza
tion of the notion of T-Koszul algebras\, as introduced by Madsen and Gree
n–Reiten–Solberg. After giving an introduction to the relevant backgro
und material\, we present a higher version of classical Koszul duality and
sketch some applications for n-hereditary algebras. In particular\, we se
e that an important class of our generalized Koszul algebras can be charac
terized in terms of n-representation infinite algebras. As a consequence\,
we show that an algebra is n-representation infinite if and only if its t
rivial extension is (n+1)-Koszul with respect to its degree 0 part. A gene
ralized notion of almost Koszulity in the sense of Brenner–Butler–King
yields similar results in the n-representation finite case. \n\nThis talk
is based on joint work with Mads H. Sandøy.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Sistko (Manhattan College)
DTSTART:20210916T130000Z
DTEND:20210916T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/58
DESCRIPTION:Title: F1 Representations and Hall Algebras\nby Alexander Sistko (Manhatt
an College) as part of FD Seminar\n\n\nAbstract\nFor any quiver Q\, one ca
n associate a category of Q-representations over F1\, the so-called “fie
ld with one element.” This category\, and its associated Ringel-Hall alg
ebra\, retain many features of representations over fields while exhibitin
g interesting differences. In this talk\, we discuss recent advances in th
e study of F1-representations and their Hall algebras. After an overview o
f the fundamental background\, we describe how F1-representations may be s
tudied via coefficient quivers. This approach yields results on representa
tion type over F1 and new insights into the associated Hall algebras. With
the remaining time\, we discuss an ongoing project which applies F1-repre
sentation theory to compute the Euler characteristics of certain quiver Gr
assmannians. This is joint work with Jaiung Jun.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steffen Oppermann (Norges teknisk-naturvitenskapelige universitet\
, NTNU)
DTSTART:20210923T130000Z
DTEND:20210923T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/59
DESCRIPTION:Title: Rank decompositions and associated exact categories for multi-paramete
r persistence modules\nby Steffen Oppermann (Norges teknisk-naturviten
skapelige universitet\, NTNU) as part of FD Seminar\n\n\nAbstract\nThe mot
ivation for the work I am going to speak about comes from a recent field o
f application of representation theory: the study of persistent homology i
n topological data analysis.\n\nI will try to explain how and why one migh
t turn data into a quiver representation. Most classically this will be a
representation of a linearly ordered quiver of type A. Such a representati
on can be depicted as a collection of line segments\, corresponding to the
supports of the indecomposable summands. This depiction is known as a “
bar code”. One interprets the results by considering the longest bars mo
st significant.\n\nIn many applications\, it would be natural to consider
multiple parameters\, equivalently representation of tensor products of mu
ltiple type A quivers. These algebras are wild in almost all cases\, and i
ndecomposables are not determined by their support as in the one parameter
case.\n\nThe original part of my talk will be based on joint work with Ma
gnus Botnan and Steve Oudot. We introduce a candidate for a bar code of a
2-parameter persistence module\, and observe that it is closely related to
an exact structure on the representation category.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART:20210930T130000Z
DTEND:20210930T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/60
DESCRIPTION:Title: The Heisenberg category of a category\nby Timothy Logvinenko (Card
iff University) as part of FD Seminar\n\n\nAbstract\nIn 90s Nakajima and G
rojnowski identified the total cohomology of the Hilbert schemes of points
on a smooth projective surface with the Fock space representation of the
Heisenberg algebra associated to its cohomology lattice. Later\, Krug lift
ed this to derived categories\nand generalised it to the symmetric quotien
t stacks of any smooth projective variety.\n\nOn the other hand\, Khovanov
introduced a categorification of the free boson Heisenberg algebra\, i.e.
the one associated to the rank 1 lattice. It is a monoidal category whose
\nmorphisms are described by a certain planar diagram calculus which categ
orifies the Heisenberg relations. A similar categorification was construct
ed by Cautis and Licata for the Heisenberg algebras of ADE type root latti
ces.\n\nWe show how to associate the Heisenberg 2-category to any smooth a
nd proper DG category and then define its Fock space 2-representation. Thi
s construction unifies all the results above and extends them to what can
be viewed as the generality of arbitrary noncommutative smooth and proper
schemes.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Herschend (Uppsala University)
DTSTART:20211007T130000Z
DTEND:20211007T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/61
DESCRIPTION:Title: Double covers of quiver Heisenberg algebras as higher preprojective al
gebras\nby Martin Herschend (Uppsala University) as part of FD Seminar
\n\n\nAbstract\nLet Q be a finite acyclic quiver. In my talk I will discus
s several algebras associated to Q and how they are related. As a starting
point we’ll consider the path algebra of Q and how its representation t
heory is reflected in homological properties of the preprojective algebra
of Q. One immediate connection is that the preprojective algebra is graded
and its degree zero part is the path algebra.\n\nNext we turn to the quiv
er Heisenberg algebra of Q. This algebra is a particular case of the centr
al extensions of preprojective algebras introduced by Etingof-Rains. It ha
s many similar properties to the preprojective algebra. Finally\, we will
consider a certain double cover of the quiver Heisenberg algebra\, more pr
ecisely its second quasi-Veronese algebra. This algebra is also graded and
turns out to be a higher preprojective algebra of its degree zero part B.
The algebra B has many similarities with the original path algebra. It ha
s global dimension 2 and is 2-hereditary algebra in the sense of Iyama’s
higher dimensional Auslander-Reiten theory.\n\nThis talk is based on ongo
ing joint work with Hiroyuki Minamoto.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Palu (Université UPJV Amiens)
DTSTART:20211014T130000Z
DTEND:20211014T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/62
DESCRIPTION:Title: Mutation in hereditary extriangulated categories\nby Yann Palu (Un
iversité UPJV Amiens) as part of FD Seminar\n\n\nAbstract\nMotivated by t
he categorification of cluster algebras\, Buan–Marsh–Reineke–Reiten
–Todorov introduced a theory of mutation for cluster-tilting objects in
certain 2-Calabi–Yau triangulated categories. This lead to many variatio
ns or generalisations\, such as tau-tilting\, 2-term silting or relative t
ilting.\n\nThe point-of-view of extriangulated categories\, introduced in
collaboration with Hiroyuki Nakaoka\, turns out to be relevant for the stu
dy of mutations. Indeed\, most mutation theories arising in representation
theory can be related to the existence of certain “good” extriangulat
ed structures. This is the point that I will try and make in this talk\, b
y introducing the notion of a 0-Auslander extriangulated category.\n\nThis
is based on joint works with Mikhail Gorsky\, Hiroyuki Nakaoka\, Arnau Pa
drol\, Vincent Pilaud and Pierre-Guy Plamondon.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroki Matsui (Tokushima University)
DTSTART:20211021T130000Z
DTEND:20211021T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/63
DESCRIPTION:Title: Prime thick subcategories of derived categories associated with noethe
rian schemes\nby Hiroki Matsui (Tokushima University) as part of FD Se
minar\n\n\nAbstract\nIn 2005\, Balmer introduced the notion of a prime thi
ck tensor ideal for a tensor triangulated category T as an analogous conce
pt to a prime ideal of a commutative ring. Using prime thick tensor ideals
\, Balmer established the epoch-making theory so-called the tensor-triangu
lar geometry which allows us to study T by commutative-algebraic/algebro-g
eometric approaches. On the other hand\, recently I have introduced the no
tion of prime thick subcategories to develop a similar theory to the tenso
r-triangular geometry for tensor triangulated categories without tensor st
ructures. In this talk\, we study prime thick subcategories of the perfect
derived category D^perf(X)\, the bounded derived category D^b(X)\, and th
e singularity category D^sg(X) of a noetherian scheme X. Especially\, we g
ive a characterization of a point x of X to be a complete intersection or
a hypersurface in terms of prime thick subcategories of such derived categ
ories.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calin Chindris (University of Missouri)
DTSTART:20211028T130000Z
DTEND:20211028T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/64
DESCRIPTION:Title: Sigma-critical quiver representations and applications to the Paulsen
Problem in Frame Theory\nby Calin Chindris (University of Missouri) as
part of FD Seminar\n\n\nAbstract\nSigma-critical representations are quiv
er representations that satisfy certain matrix equations. They arise natur
ally in the context of the Kempf-Ness theorem on closed orbits in Invarian
t Theory. After introducing all the relevant concepts\, I will first descr
ibe a result that gives necessary and sufficient conditions for the orbit
of a representation to contain a sigma-critical representation. I will the
n explain how this result can be used to solve the Paulsen Problem for mat
rix frames. This is based on joint work with Jasim Ismaeel.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changchang Xi (Capital Normal University)
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/65
DESCRIPTION:Title: Symmetric subcategories and good tilting modules\nby Changchang Xi
(Capital Normal University) as part of FD Seminar\n\n\nAbstract\nTilting
modules have played an important role in representation theory of algebras
. Especially\, infinitely generated tilting modules provide completely dif
ferent features. In this case\, recollements of triangulated categories in
the sense of Beilinson-Bernstein-Deligne enter into the play. In this tal
k\, we introduce symmetric subcategories and show that\, for any good tilt
ing module over an algebra\, the derived category of the endomorphism alge
bra of the tilting module is always a recollement of the derived categorie
s of the given algebra and a symmetric subcategory of a module category. E
xplicit examples of symmetric subcategories associated to 2-good tilting m
odules over commutative Gorenstein rings are presented. This talk reports
a joint work with Hongxing Chen.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emine Yıldırım (Isaac Newton Institute for Mathematical Science
s and University of Cambridg)
DTSTART:20211111T140000Z
DTEND:20211111T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/66
DESCRIPTION:Title: Periodic actions on distributive lattices and counterparts in algebra<
/a>\nby Emine Yıldırım (Isaac Newton Institute for Mathematical Science
s and University of Cambridg) as part of FD Seminar\n\n\nAbstract\nLet L b
e a distributive lattice and A be its incidence algebra. There is a celebr
ated combinatorial action on posets called “rowmotion”. Thanks to a re
sult of Iyama-Marczinzik\, we can think of this combinatorial action as th
e grade bijection defined on the algebra A. On the other hand\, the Coxete
r transformation plays an important role in representation theory of algeb
ras and in some cases it shows some periodicity. The periodicity of the Co
xeter transformation is motivated by the fractionally Calabi-Yau property
of a certain category. Motivated by these\, we show that the composition o
f the rowmotion and the Coxeter transformation is periodic for the algebra
A in a joint work with René Marczinzik and Hugh Thomas.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow)
DTSTART:20211118T140000Z
DTEND:20211118T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/67
DESCRIPTION:Title: Thick Subcategories and Lattices\nby Sira Gratz (University of Gla
sgow) as part of FD Seminar\n\n\nAbstract\nThe computation of lattices of
thick subcategories has emerged as a popular topic and serves as a more ac
hievable analogue of classifying objects. Often one understands such latti
ces by describing them in terms of some associated topological space. Howe
ver\, in many representation theoretic examples this is not possible. I’
ll explain what the obstruction is and mention work in progress aimed at a
ddressing this issue.\n\nThis talk is based on joint work with Greg Steven
son.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (University College London)
DTSTART:20211125T140000Z
DTEND:20211125T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/68
DESCRIPTION:Title: Dynamics in triangulated categories\nby Federico Barbacovi (Univer
sity College London) as part of FD Seminar\n\n\nAbstract\nIn topology a dy
namical system is given by a couple $(X\, f)$\, where $X$ is a topological
space and $f : X \\rightarrow X$ is a continuous map. Dimitrov — Haiden
— Katzarkov — Kontsevich generalised this notion to that of a categor
ical dynamical system. To measure the complexity of such system\, they als
o introduced the concept of categorical entropy. A famous theorem of Gromo
v and Yomdin relates the topological entropy of a holomorphic automorphism
of a complex manifold with the action of the automorphism in cohomology.
In this talk I will report on joint work with Jongmyeong Kim in which we p
rovide a sufficient condition that ensures that (a weaker version of) an a
nalogue theorem holds in categorical dynamics.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constanze Roitzheim (University of Kent)
DTSTART:20211202T140000Z
DTEND:20211202T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/69
DESCRIPTION:Title: Homotopy theory of finite total orders\, trees and chicken feet\nb
y Constanze Roitzheim (University of Kent) as part of FD Seminar\n\n\nAbst
ract\nA transfer system is a graph on a lattice satisfying certain restric
tion and composition properties. They were first studied on the lattice of
subgroups of a finite group in order to examine equivariant homotopy comm
utativity\, which then unlocked a wealth of links to combinatorial methods
. On a finite total order [n]\, transfer systems can be used to classify d
ifferent homotopy theories on [n]. The talk will involve plenty of example
s and not assume any background knowledge.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Coelho Simões (Lancaster University)
DTSTART:20211209T140000Z
DTEND:20211209T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/70
DESCRIPTION:Title: From gentle to string algebras: a geometric model\nby Raquel Coelh
o Simões (Lancaster University) as part of FD Seminar\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
and explain how to extend this model to a geometric model of the module ca
tegory of any string algebra. This is based on joint work in progress with
Karin Baur.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow)
DTSTART:20211216T140000Z
DTEND:20211216T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/71
DESCRIPTION:Title: Local Normal Forms of Noncommutative Functions\nby Michael Wemyss
(University of Glasgow) as part of FD Seminar\n\n\nAbstract\nIn algebraic
terms\, the purpose of the talk is to classify finite dimensional Jacobi a
lgebras arising on the d-loop quiver. The surprising thing is that a clas
sification should exist at all\, and it is even more surprising that ADE e
nters. I will spend most of my time explaining what the algebras are\, wh
y they classify\, and how to intrinsically extract ADE information from th
em. I will also say a little on why this should be viewed as an extension
of classical singularity theory\, since many of the ideas are inspired by
Arnold and others. At the end\, I’ll briefly explain why I’m really
interested in this problem\, the connection with different quivers\, and t
he applications of the above classification to curve counting and biration
al geometry. This is all joint work with Gavin Brown.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (University of Bonn)
DTSTART:20220113T140000Z
DTEND:20220113T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/72
DESCRIPTION:Title: Weight structures and (geometric) representation theory\nby Cathar
ina Stroppel (University of Bonn) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Woolf (University of Liverpool)
DTSTART:20220120T140000Z
DTEND:20220120T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/73
DESCRIPTION:Title: Bridgeland stability conditions with massless objects\nby Jon Wool
f (University of Liverpool) as part of FD Seminar\n\n\nAbstract\nThe Bridg
eland stability space of a triangulated category is a non-compact complex
manifold with a wall-and-chamber structure capturing interesting aspects o
f the category’s structure.\n\nI will describe joint work with Broomhead
\, Pauksztello and Ploog in which we partially compactify the stability sp
ace by allowing `degenerate’ stability conditions with massless objects.
\n\nOne reason this is interesting is that the added boundary points are c
losely related to the walls. I will illustrate this connection in low-dime
nsional examples arising from quivers with two vertices.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Genovese (Charles University)
DTSTART:20220127T140000Z
DTEND:20220127T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/74
DESCRIPTION:Title: A derived Gabriel-Popescu theorem for t-structures\nby Francesco G
enovese (Charles University) as part of FD Seminar\n\n\nAbstract\nThe Gabr
iel-Popescu theorem exhibits any Grothendieck abelian category as an exact
localization of a category of modules over a suitable ring. Generalizing
to the derived framework\, we replace abelian categories with (enhanced) t
riangulated categories endowed with a t-structure. Such categories\, under
appropriate “Grothendieck-like” assumptions\, can be exhibited as t-e
xact quotients of derived categories of suitable dg-algebras concentrated
in nonpositive degrees\, hence yielding a “derived Gabriel-Popescu theor
em”. In this talk\, we describe a proof of this result which exploits th
e underlying philosophy that “(enhanced) triangulated categories with t-
structures really behave like abelian categories”. We shall encounter su
itably defined “derived epi-mono factorizations” and derived injective
objects. This is joint work with Julia Ramos González.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (Universidad Nacional Autónoma de México
)
DTSTART:20220203T140000Z
DTEND:20220203T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/75
DESCRIPTION:Title: Deformation theory for finite cluster complexes\nby Alfredo Nájer
a Chávez (Universidad Nacional Autónoma de México) as part of FD Semina
r\n\n\nAbstract\nCluster complexes are a certain class of simplicial compl
exes that naturally arise in the theory of cluster algebras. They codify a
wealth of fundamental information about cluster algebras. The purpose of
this talk is to elaborate on a geometric relationship between cluster alge
bras and cluster complexes. In vague words this relationship is the follow
ing: cluster algebras of finite cluster type with universal coefficients m
ay be obtained via a torus action on a Hilbert scheme. In particular\, we
will discuss the deformation theory of the Stanley-Reisner ring associated
to a finite cluster complex and present some applications related to the
Gröbner theory of the ideal of relations among cluster and frozen variabl
es of a cluster algebra of finite cluster type. Time permitting I will ela
borate on how to generalize this approach to the context of tau-tilting fi
nite algebras. This is based on a joint project with Nathan Ilten and Hipo
lito Treffinger whose first outcome is the preprint arXiv:2111.02566.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsutomu Nakamura (The University of Tokyo)
DTSTART:20220210T140000Z
DTEND:20220210T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/76
DESCRIPTION:Title: The definable subcategory induced by a large canonical module\nby
Tsutomu Nakamura (The University of Tokyo) as part of FD Seminar\n\n\nAbst
ract\nAuslander and Buchweitz (1989) showed that the class of maximal Cohe
n-Macaulay modules over a Cohen-Macaulay local ring with a canonical modul
e is part of a complete cotorsion pair in the category of finitely generat
ed modules. As shown by Miyachi (1998)\, this fact holds more generally fo
r an R-order over a Cohen-Macaulay ring R with a (pointwise) canonical mod
ule. On the other hand\, Holm (2017) established a perfect cotorsion pair
(X\, Y) in the category of all modules over a Cohen-Macaulay local ring wi
th a canonical module such that X is the smallest definable subcategory co
ntaining all maximal Cohen-Macaulay modules. This result was deduced by sh
owing a Govorov-Lazard type result for X\, and the modules in X are those
called weak balanced big Cohen-Macaulay. In my talk\, I will suggest an in
finitely generated version of a canonical module\, and explain how this co
ncept makes sense to generalize Holm’s results to a non-commutative and
non-local setup like Miyachi’s work. It is also possible to partly avoid
the existence of a canonical module\, so that some results on balanced bi
g Cohen-Macaulay approximation due to Simon (2009) and Holm (2017) can be
unified. This work is inspired by ongoing joint work with Michal Hrbek and
Jan Stovicek about large (co)tilting complexes over a commutative noether
ian ring\, and related to recent joint work with Ryo Kanda about flat coto
rsion modules over Noether algebras.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Latyntsev (University of Oxford)
DTSTART:20220217T140000Z
DTEND:20220217T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/77
DESCRIPTION:Title: Quantum vertex algebras and cohomological Hall algebras\nby Alexei
Latyntsev (University of Oxford) as part of FD Seminar\n\n\nAbstract\nThe
re is an extremely rich history of interaction between string theory and t
he mathematics of moduli spaces\, for instance cohomological Hall algebras
/algebras of BPS states\, or vertex/chiral algebras.\n\nIn this talk\, I w
ill explain a link between two of these: Joyce’s vertex algebras attache
d to the moduli stack of objects in an abelian category\, and one dimensio
nal CoHAs. This is based on my recent paper 2110.14356\, whose main result
says that the cohomologies of such stacks are “quantum vertex algebras
”: the factorisation/vertex analogues of quasitriangular bialgebras. The
main technical tool is a “bivariant” Euler class which makes torus lo
calisation work in this context. I will discuss applications of these tech
niques to CoHAs of coherent sheaves on a curve and future directions.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Janina C. Letz (Universität Bielefeld)
DTSTART:20220224T140000Z
DTEND:20220224T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/78
DESCRIPTION:by Janina C. Letz (Universität Bielefeld) as part of FD Semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (Universität Stuttgart)
DTSTART:20220303T140000Z
DTEND:20220303T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/79
DESCRIPTION:by Zhengfang Wang (Universität Stuttgart) as part of FD Semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Schenfisch (Montana State University)
DTSTART:20220310T140000Z
DTEND:20220310T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/80
DESCRIPTION:Title: Algebraic K-Theory of Zig-Zag Persistence Modules\nby Anna Schenfi
sch (Montana State University) as part of FD Seminar\n\n\nAbstract\nIn thi
s talk\, we will first see how persistence modules (a primary tool in topo
logical data analysis) have a natural home in the setting of stratified sp
aces and constructible cosheaves. In particular\, we focus on zig-zag modu
les\, which correspond to one-parameter filtrations. We then outline how t
he algebraic K-theory of zig-zag modules can be computed via an additivity
result\, aided by an equivalence between the category of zig-zag modules
and the combinatorial entrance path category on a stratified $\\mathbb{R}$
. Once equipped with the K-theory of zig-zag modules\, we see other one-pa
rameter topological summaries (such as Euler characteristic curves) as cla
sses of $K_0$.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (The University of Tokyo)
DTSTART:20220317T140000Z
DTEND:20220317T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/81
DESCRIPTION:Title: Classifying torsion classes of Noetherian algebras\nby Yuta Kimura
(The University of Tokyo) as part of FD Seminar\n\n\nAbstract\nLet R be a
commutative Noetherian ring. A Noetherian algebra A is an R-algebra which
is finitely generated as an R-module. In this talk\, we study classificat
ion problem of torsion classes and related subcategories of the category m
od A of finitely generated A-modules. In the case where R is a field\, the
re are many studies of subcategories of mod A. τ-tilting modules\, introd
uced by Adachi-Iyama-Reiten\, play a central role in the recent developmen
t of such studies. We see that silting modules also play an important role
for classification problem of torsion classes of Noetherian algebras. In
the case where A is commutative\, Serre subcategories\, torsion classes an
d torsionfree classes are classified by using subsets of the prime spectru
m of R by Gabriel\, Stanley-Wang and Takahashi. We see that our results re
cover their results. This is joint work with Osamu Iyama.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charley Cummings (University of Bristol)
DTSTART:20220324T140000Z
DTEND:20220324T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/82
DESCRIPTION:Title: Left-right symmetry of the finitistic dimension\nby Charley Cummin
gs (University of Bristol) as part of FD Seminar\n\n\nAbstract\nThe finiti
stic dimension conjecture is the assertion that the finitistic dimension o
f a finite dimensional algebra is finite. This dimension can be defined in
terms of left or right modules. In general\, the left and right finitisti
c dimensions of an algebra are not equal\, but it is unknown if the finite
ness of the two dimensions is connected. In this talk\, we will translate
the conjecture into a question about the connection between the left and r
ight finitistic dimensions of an algebra using quiver operations.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlie Beil (University of Graz)
DTSTART:20220331T130000Z
DTEND:20220331T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/83
DESCRIPTION:Title: Dimer quivers on genus g surfaces and noncommutative desingularization
s\nby Charlie Beil (University of Graz) as part of FD Seminar\n\n\nAbs
tract\nA dimer algebra is a type of Jacobian algebra whose quiver $Q$ embe
ds in a surface $S$\, such that each connected component of $S\\backslash
Q$ is simply connected and bounded by an oriented cycle of $Q$. It was sh
own in 2009 that noetherian dimer algebras on a torus are noncommutative d
esingularizations of their centers\; in particular\, they are ‘homologic
ally smooth’ endomorphism rings. On higher genus surfaces\, however\, th
ese nice properties disappear. I will introduce special quotients of dimer
algebras\, called ‘ghor algebras’\, where the relations come from the
quiver’s perfect matchings rather than a potential. On a torus\, a dime
r algebra coincides with its ghor algebra if and only if it is noetherian\
, whereas ghor algebras are almost never noetherian on higher genus surfac
es. Nevertheless\, I will describe how a ghor algebra\, on any genus gg su
rface\, may be viewed as a noncommutative desingularization of its center.
This is joint work with Karin Baur.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (University of Strasbourg)
DTSTART:20220407T130000Z
DTEND:20220407T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/84
DESCRIPTION:Title: Rational homotopy type of the moduli space of stable rational curves\nby Vladimir Dotsenko (University of Strasbourg) as part of FD Seminar\
n\n\nAbstract\nIn 2004\, Manin asked whether the cohomology of the moduli
space of stable rational curves with n marked points (= the Deligne-Mumfor
d compactification of the moduli space of smooth genus zero curves with n
marked points) is a Koszul algebra. This question remained open since. I s
hall present a solution to it\, proving that the answer is positive for al
l n. An immediate consequence of my result is an explicit description of t
he rational homotopy Lie algebras of these spaces by generators and relati
ons. Time permitting\, I shall discuss some generalizations and modificati
ons of this result.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Giunti (Graz University of Technology)
DTSTART:20220414T130000Z
DTEND:20220414T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/85
DESCRIPTION:Title: Persistence modules and amplitudes\nby Barbara Giunti (Graz Univer
sity of Technology) as part of FD Seminar\n\n\nAbstract\nPersistence theor
y is a powerful branch of Topological Data Analysis with many applications
. In this seminar\, I will briefly introduce it\, presupposing no previous
knowledge of the topic. In particular\, I will discuss some finiteness co
nditions on persistence modules. I will then introduce amplitudes\, a spec
ial type of invariants that capture the idea of ‘‘size of persistence
’’. Amplitudes can be defined on any abelian category and are particul
arly useful in the so-called multiparameter persistence\, where there exis
ts no discrete complete invariant. I will present some examples of amplitu
des and discuss some of their properties.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sota Asai (Osaka University)
DTSTART:20220421T130000Z
DTEND:20220421T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/86
DESCRIPTION:Title: TF equivalence classes constructed from canonical decompositions\n
by Sota Asai (Osaka University) as part of FD Seminar\n\n\nAbstract\nThis
talk is based on joint work with Osamu Iyama. Let $A$ be a finite dimensio
nal algebra over an algebraically closed field. Brüstle-Smith-Treffinger
introduced a wall-chamber structure on the real Grothendieck group $K_0(\\
operatorname{proj} A)_R$ via stability conditions of King. It is strongly
related to TF equivalence\, which is an equivalence relation on $K_0(\\ope
ratorname{proj} A)_R$ defined by numerical torsion pairs of Baumann-Kamnit
zer-Tingley. Thanks to results by Yurikusa and Brüstle-Smith-Treffinger\,
I showed that the $g$-vector cone $C^+(U)$ associated to each 2-term pres
ilting complex $U$ in $K^b(\\operatorname{proj} A)$ is a TF equivalence cl
ass in my previous study\, but we cannot obtain all TF equivalence classes
in this way unless $A$ is $\\tau$-tilting finite. In this joint work with
Iyama\, we obtained a generalization of this construction of TF equivalen
ce classes by using canonical decompositions of elements in $K_0(\\operato
rname{proj} A)$ introduced by Derksen-Fei in the case that $A$ satisfies t
he condition called EE-tameness. I will talk about this result.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (The Australian National University)
DTSTART:20220428T130000Z
DTEND:20220428T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/87
DESCRIPTION:Title: Bridgeland stability conditions\, spherical objects\, and autoequivale
nces\nby Asilata Bapat (The Australian National University) as part of
FD Seminar\n\n\nAbstract\nConsider the space of Bridgeland stability cond
itions of a suitably nice triangulated category. Autoequivalences of the t
riangulated category act on the space of stability conditions. Fixing a st
ability condition imposes extra combinatorial structure on the category\,
that can be used to study the group of autoequivalences in various differe
nt ways. This talk will showcase some of the fascinating structure that em
erges via this idea\, particularly for 2-Calabi–Yau categories associate
d to quivers. This is based on joint work with Anand Deopurkar and Anthony
M. Licata.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (Tsinghua University)
DTSTART:20220505T130000Z
DTEND:20220505T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/88
DESCRIPTION:Title: Geometric classification of totally stable stability spaces\nby Yu
Qiu (Tsinghua University) as part of FD Seminar\n\n\nAbstract\nWe constru
ct a geometric model for the root category of any Dynkin diagram $Q$\, whi
ch is an $h$-gon $V$ with cores\, where $h$ is the Coxeter number. As an a
pplication\, we classify all spaces $ToSt(D)$ of totally stable stability
conditions on triangulated categories $D$\, where $D$ must be of the form
$D^b(Q)$. More precisely\, we prove that $ToStD^b(Q)/C$ is isomorphic to t
he moduli spaces of stable $h$-gons of type $Q$. In particular\, an $h$-go
n $V$ of type $D_n$ is a centrally symmetric doubly punctured $2(n−1)$-g
on. $V$ is stable if it is convex and the punctures are inside the level-$
(n−2)$ diagonal-gon. Another interesting case is $E_6$\, where the (stab
le) $12$-gon can be realized as a pair of planar tiling pattern. This is a
joint work with Xiaoting Zhang.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Ruhr-Universität Bochum)
DTSTART:20220519T130000Z
DTEND:20220519T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/89
DESCRIPTION:Title: Dimension expanders via quiver representations\nby Markus Reineke
(Ruhr-Universität Bochum) as part of FD Seminar\n\n\nAbstract\nDimension
expanders\, introduced by Wigderson and Lubotzky-Zelmanov\, are a linear a
lgebra analogue of the notion of expander graphs. We interpret this notion
in terms of quiver representations\, as a quantitative variant of stabilt
y. We use Schofield’s recursive description of general subrepresentation
s to re-derive existence of dimension expanders and to determine optimal e
xpansion coefficients.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Cruz (Universität Stuttgart)
DTSTART:20220512T130000Z
DTEND:20220512T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/90
DESCRIPTION:Title: Relative dominant dimension and quasi-hereditary covers\nby Tiago
Cruz (Universität Stuttgart) as part of FD Seminar\n\n\nAbstract\nEvery f
inite-dimensional algebra can be written as the endomorphism algebra of a
projective module over a quasi-hereditary algebra. Moreover\, every finite
-dimensional algebra over an algebraically closed field admits a (split) q
uasi-hereditary cover in the sense of Rouquier. So we may wonder how close
ly connected the module category of a finite-dimensional algebra is to the
module category of one of its quasi-hereditary covers.\n\nIn this talk\,
we discuss how a generalisation of dominant dimension can be used as a too
l to measure the quality of (split) quasi-hereditary covers of Noetherian
algebras and how it can be used to construct new quasi-hereditary covers.\
n
LOCATION:https://researchseminars.org/talk/fd-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sentieri (Università degli Studi di Verona)
DTSTART:20220526T130000Z
DTEND:20220526T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/91
DESCRIPTION:Title: Wide subcategories obtained from cosilting pairs\nby Francesco Sen
tieri (Università degli Studi di Verona) as part of FD Seminar\n\n\nAbstr
act\nIngalls and Thomas introduced a construction relating torsion pairs a
nd wide subcategories in the context of finite-dimensional modules over he
reditary algebras. Their work was later generalized by Marks and Stovicek
to arbitrary algebras. We apply this construction to cosilting torsion pai
rs in the category of all modules and give a description of the resulting
wide subcategories as some generalized perpendicular categories. We show t
hat all the wide subcategories we obtain are coreflective and discuss the
case in which they are bireflective. We conclude with an application to th
e study of torsion pairs in the category of finite-dimensional modules. Th
is is joint work with Lidia Angeleri.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rene Marczinzik
DTSTART:20220602T130000Z
DTEND:20220602T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/92
DESCRIPTION:Title: Dominant Auslander regular algebras and minimal Auslander-Cohen-Macaul
ay algebras\nby Rene Marczinzik as part of FD Seminar\n\n\nAbstract\nW
e introduce dominant Auslander regular algebras and minimal Auslander-Cohe
n-Macaulay algebras as a generalisation of higher Auslander algebras. As a
n application we show how those two new classes of algebras can be used to
answer a question by Green and another question by Auslander and Reiten.
This is joint work in progress with Aaron Chan and Osamu Iyama.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Paquette (Royal Military College of Canada)
DTSTART:20220609T130000Z
DTEND:20220609T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/93
DESCRIPTION:Title: Free products of semi-simple algebras via quivers\nby Charles Paqu
ette (Royal Military College of Canada) as part of FD Seminar\n\n\nAbstrac
t\nWe will see how quiver representation theory and stability allow us to
understand the (finite dimensional) representation theory of a free produc
t of semi-simple (associative) k-algebras. In particular\, we will study t
he simple modules and modules in general position. We will see that a modu
le in general position is always semisimple\, and give an explicit numeral
equation to decide when it is simple. If time permits\, we will comment o
n the representation type (tame\, wild) and discuss how to use moduli spac
es of quivers to compute the number of parameters for the simple modules i
n a given dimension. This is joint work with A. Buchanan\, I. Dimitrov\, O
. Grace\, D. Wehlau and T. Xu.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (The University of Tokyo)
DTSTART:20220616T130000Z
DTEND:20220616T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/94
DESCRIPTION:Title: Mutating cluster-tilting objects in (d + 2)-angulated cluster categori
es\nby Nicholas Williams (The University of Tokyo) as part of FD Semin
ar\n\n\nAbstract\nOppermann and Thomas introduced the (d + 2)-angulated cl
uster category to generalise the classical cluster category to higher homo
logical algebra. A great difficulty that arises in these categories is tha
t cluster-tilting objects are no longer mutable at every summand\, in cont
rast to the classical setting. In this talk we give two new ways of unders
tanding mutability in these higher cluster categories: one from an algebra
ic perspective\, and the other from a combinatorial perspective\, for the
particular case of the higher Auslander algebras of type A.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kaplan (Hasselt University)
DTSTART:20220623T130000Z
DTEND:20220623T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/95
DESCRIPTION:Title: Relating properties of homological dimension two algebras\nby Dani
el Kaplan (Hasselt University) as part of FD Seminar\n\n\nAbstract\nLet Q
be a connected\, non-ADE quiver. The preprojective algebra of Q is well-be
haved in the following sense: it is 2-Calabi–Yau\, a noncommutative comp
lete intersection (NCCI)\, and prime. If further Q is extended ADE then th
e preprojective algebra of Q is a noncommutative crepant resolution (NCCR)
over its center\, which is isomorphic to functions on the corresponding d
u Val singularity. In this talk\, I will explain joint work with Travis Sc
hedler which proves these properties for a multiplicative analogue of the
preprojective algebra\, defined by Crawley-Boevey and Shaw\, in the case Q
contains a cycle. Current work in progress aims to prove this for general
Q. The technique involves defining a new notion\, the strong free product
property (SFPP)\, which implies these notions. One then proves the SFPP u
sing multiple applications of Bergman’s Diamond Lemma for ring theory. A
pplications to topology and geometry include computations of certain Cheka
nov–Eliashberg dg-algebras / wrapped Fukaya categories following Etgü
–Lekili\, and a description of the formal local structure of quiver vari
eties.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Charles University)
DTSTART:20220630T130000Z
DTEND:20220630T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/96
DESCRIPTION:Title: Finitistic dimensions of differential graded rings\nby Liran Shaul
(Charles University) as part of FD Seminar\n\n\nAbstract\nFinitistic dime
nsions are important homological numerical invariants associated to a ring
. In this talk we explain how to define these invariants over differential
graded rings. We then explain how to extend previous results about finiti
stic dimensions from commutative noetherian rings to commutative noetheria
n differential graded rings. Finally\, we discuss the noncommutative case
and its relation to the finitistic dimension conjecture.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Université de Versailles Saint-Quentin)
DTSTART:20220901T130000Z
DTEND:20220901T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/97
DESCRIPTION:Title: On some configurations spaces related to algebras of finite representa
tion type\nby Pierre-Guy Plamondon (Université de Versailles Saint-Qu
entin) as part of FD Seminar\n\n\nAbstract\nThe representation theory of a
n algebra gives rise to various\ninteresting geometrical objects\, such as
the g-vector fan and Newton\npolytopes of representations. Classical obje
cts such as the associahedron\ncan be realized in this way\, and these con
structions have interesting\napplications in the categorification of clust
er algebras.\n\nIn this talk\, I will associate to any representation-fini
te algebra\nanother geometrical object\, an affine variety which is closel
y related to\nthe polytopes mentioned above. We will see how this variety
reflects the\ntau-tilting theory of the algebra\, and how F-polynomials of
\nrepresentations give a parametrization of it.\n\nThis is a report on ong
oing work with Nima Arkani-Hamed\, Hadleigh Frost\,\nGiulio Salvatori and
Hugh Thomas.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cody Gilbert (University of Iowa)
DTSTART:20220908T130000Z
DTEND:20220908T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/98
DESCRIPTION:Title: Moduli of Representations of Clannish Algebras\nby Cody Gilbert (U
niversity of Iowa) as part of FD Seminar\n\n\nAbstract\nWe prove irreducib
le components of moduli spaces of semistable representations of clannish a
lgebras are isomorphic to products of projective spaces. This is achieved
by showing irreducible components of varieties of representations of clann
ish algebras can be viewed as irreducible components of skewed-gentle alge
bras\, which we show are always normal. The main theorem generalizes an an
alogous result for moduli of representations of special biserial algebras
proven by Carroll-Chindris-Kinser-Weyman.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (University of Cambridge)
DTSTART:20220915T130000Z
DTEND:20220915T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/99
DESCRIPTION:Title: Locally free Caldero-Chapoton functions\nby Lang Mou (University o
f Cambridge) as part of FD Seminar\n\n\nAbstract\nLocally free Caldero-Cha
poton functions are introduced by Geiss-Leclerc-Schröer for locally free
representations of certain quivers with relations associated to skew-symme
trizable matrices. They show that for Dynkin types these functions give fo
rmulas for cluster variables\, generalizing Caldero-Chapoton’s formula i
n simply laced cases. We extend this formula to rank 2 cluster algebras an
d those associated to unpunctured marked bordered surfaces with orbifold p
oints. Part of this talk is based on joint work with Daniel Labardini-Frag
oso.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Bennett-Tennenhaus (Bielefeld University)
DTSTART:20221006T130000Z
DTEND:20221006T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/100
DESCRIPTION:Title: Semilinear clannish algebras\nby Raphael Bennett-Tennenhaus (Biel
efeld University) as part of FD Seminar\n\n\nAbstract\nString algebras are
monomial algebras introduced by Butler and Ringel\, where they showed any
indecomposable representation is: a string module\, given by a relation-a
voiding walk in the quiver\; or a band module\, given by a cyclic walk and
some module over the Laurent polynomial ring. Clannish algebras\, introdu
ced by Crawley-Boevey\, generalise string algebras - in addition to monomi
al relations\, one specifies a set of special loops\, each bounded by some
monic quadratic polynomial. Butler and Ringel’s classification was then
adapted\, where the class of string (or band) modules splits into asymmet
ric and symmetric subclasses. Said symmetry is a reflection of the walk ab
out a special loop\, and symmetric strings and bands are parameterised by
replacements for the Laurent polynomial ring.\n\nBoth string algebras and
clannish algebras are defined over a field\, and the quadratics bounding s
pecial loops must factor with distinct roots in this field. This talk is b
ased on joint work with Crawley-Boevey (2204.12138)\, where we generalise
the module classification for clannish algebras. We replace the ground fie
ld with a division ring\, we equip each arrow with an automorphism of this
division ring\, and we allow irreducible quadratics to bound the special
loops. The resulting notion of a semilinear clannish algebra specifies to
a generalisation of string algebras considered by Ringel\, where the map a
ssociated to an arrow in any representation must be semilinear with respec
t to its automorphism.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Simental Rodríguez
DTSTART:20221013T130000Z
DTEND:20221013T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/101
DESCRIPTION:Title: Cluster structures on braid varieties\nby José Simental Rodrígu
ez as part of FD Seminar\n\n\nAbstract\nGiven a simple algebraic group G a
nd an element β of its positive braid monoid we consider an affine\, smoo
th algebraic variety X(β) that generalizes some well-known varieties in L
ie theory\, including open Richardson varieties and double Bott-Samelson c
ells. In this talk\, we will construct a cluster algebra structure on the
coordinate ring of X(β) using combinatorial objects called algebraic weav
es and tropicalization of Lusztig’s coordinates. We will also give prope
rties of this cluster structure\, including local acyclicity and the exist
ence of reddening sequences. This is based on joint work with R. Casals\,
E. Gorsky\, M. Gorsky\, L. Shen and I. Le.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Fedele (University of Leeds)
DTSTART:20221020T130000Z
DTEND:20221020T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/102
DESCRIPTION:Title: Universal localizations of d-homological pairs\nby Francesca Fede
le (University of Leeds) as part of FD Seminar\n\n\nAbstract\nLet $k$ be a
n algebraically closed field and $A$ a finite dimensional $k$-algebra. The
universal localization of $A$ with respect to a set of morphisms between
finitely generated projective $A$-modules always exists. When $A$ is hered
itary\, Krause and Stovicek proved that the universal localizations of $A$
are in bijection with various natural structures.\n\nIn this talk I will
introduce the higher analogue of universal localizations\, that is univers
al localizations of $d$-homological pairs with respect to certain wide sub
categories\, and show a (partial) generalisation of Krause and Stovicek re
sult in the higher setup.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haibo Jin (Universität zu Köln)
DTSTART:20221027T130000Z
DTEND:20221027T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/103
DESCRIPTION:Title: Recollements and localisation theorems\nby Haibo Jin (Universitä
t zu Köln) as part of FD Seminar\n\n\nAbstract\nA localisation theorem by
A. Neeman states that any recollement of compactly generated triangulated
categories induces a short exact sequence of subcategories of compact obj
ects up to direct summands. In this talk\, we consider recollements of unb
ounded derived categories of dg algebras\, and we give several localisatio
n theorems with respect to different sub (sub-quotient) categories of the
derived categories (e.g. perfect derived categories\, perfect valued deriv
ed categories\, singularity categories\, etc.). This is an ongoing joint w
ork with Dong Yang and Guodong Zhou.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther Banaian (Aarhus University)
DTSTART:20221103T140000Z
DTEND:20221103T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/104
DESCRIPTION:Title: Algebras from Orbifolds\nby Esther Banaian (Aarhus University) as
part of FD Seminar\n\n\nAbstract\nWe discuss two algebras associated to t
riangulated unpunctured orbifolds with all orbifold points of order three
- a gentle algebra and a generalized cluster algebra\, in the sense of Che
khov and Shapiro. To each algebra\, we associate a map which can be seen a
s taking arcs on the orbifold to Laurent polynomials. The first map was de
fined by Caldero and Chapoton\; the second is the snake graph map\, define
d for surfaces by Musiker-Schiffler-Williams and for orbifolds by B.-Kelle
y. We show that the outputs of these two maps agree. This talk is based on
joint work with Yadira Valdivieso.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (University Laval)
DTSTART:20221110T140000Z
DTEND:20221110T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/105
DESCRIPTION:Title: Quasi-cluster algebras\nby Véronique Bazier-Matte (University La
val) as part of FD Seminar\n\n\nAbstract\nQuasi-cluster algebras were defi
ned in 2015 by Dupont and Palesi and are an analogous of cluster algebras
for non-orientable surfaces. In this talk\, we will first give an introduc
tion on these quasi-cluster algebras and list some of their properties (fi
nite-type classification\, skein relations\, among others). Then\, we will
associate a quiver with potential to triangulations of non-orientable sur
faces and study the algebra given by this. More precisely\, we use the clu
ster category associated to an orientable double cover of our non-orientab
le surface to give a correspondence between quasi-triangulations of a non-
orientable surface and an analogue of cluster-tilting objects.\n\nJoint wo
rk with Aaron Chan and Kayla Wright\n
LOCATION:https://researchseminars.org/talk/fd-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Stevenson (Aarhus University)
DTSTART:20221117T140000Z
DTEND:20221117T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/106
DESCRIPTION:Title: Life hacks for dgas with finite dimensional cohomology\nby Greg S
tevenson (Aarhus University) as part of FD Seminar\n\n\nAbstract\nIt is no
t necessarily the case that a dg algebra with finite dimensional cohomolog
y is quasi-isomorphic to one which is honestly finite dimensional\, i.e. a
finite dimensional algebra with a compatible differential. However\, prov
ided the cohomology is concentrated in non-positive degrees one can always
find such a quasi-isomorphism. Such finite dimensional dg algebras have m
any amusing properties\, and I will explain some of them.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lleonard Rubio y Degrassi (Uppsala University)
DTSTART:20221124T140000Z
DTEND:20221124T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/107
DESCRIPTION:Title: On the Lie algebra structure of integrable derivations\nby Lleona
rd Rubio y Degrassi (Uppsala University) as part of FD Seminar\n\n\nAbstra
ct\nThe space of integrable derivations was introduced by Hasse and Schmid
t\, and has since been used in geometry and commutative algebra. More rece
ntly\, integrable derivations have been used as a source of invariants in
representation theory.\n\nIn this talk I will show that the space of integ
rable classes in the first Hochschild cohomology of a finite dimensional a
lgebra forms a (restricted) Lie algebra that is invariant under derived eq
uivalences\, and under stable equivalences of Morita type between self-inj
ective algebras. I will also provide negative answers to questions posed b
y Linckelmann and by Farkas\, Geiss and Marcos regarding integrable deriva
tions. This is joint work with Benjamin Briggs.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederik Marks (Universität Stuttgart)
DTSTART:20221201T140000Z
DTEND:20221201T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/108
DESCRIPTION:Title: A functorial approach to rank functions on triangulated categories\nby Frederik Marks (Universität Stuttgart) as part of FD Seminar\n\n\nA
bstract\nMotivated by work of Cohn and Schofield on Sylvester rank functio
ns\, Chuang and Lazarev have recently introduced the notion of a rank func
tion on a triangulated category. They show that Verdier quotients into sim
ple triangulated categories are classified by a certain type of rank funct
ions\, and that such rank functions on the perfect derived category of a d
g algebra describe derived localisations into dg skew-fields. In this talk
\, we suggest interpreting rank functions as certain additive functions on
the functor category. As a consequence\, we obtain that every integral ra
nk function decomposes uniquely as a sum of irreducible ones. In the follo
wing\, we focus on compactly generated triangulated categories\, where bas
ic rank functions on the compacts are length functions with respect to cer
tain endofinite objects. We show that rank functions in this context are c
losely related to definable subcategories and smashing localisations\, whi
ch allows us to extend the aforementioned results by Chuang and Lazarev. T
his talk is based on joint work with Teresa Conde\, Mikhail Gorsky and Ale
xandra Zvonareva.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lutz Hille (Universität Münster)
DTSTART:20221208T140000Z
DTEND:20221208T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/109
DESCRIPTION:Title: Polynomial Invariants for Triangulated Categories with Exceptional Se
quences\nby Lutz Hille (Universität Münster) as part of FD Seminar\n
\n\nAbstract\nGiven two triangulated categories\, it is desirable to decid
e\, whether they are equivalent as triangulated categories. Essentially th
ere are two aspects\, a combinatorial aspect and a geometric aspect. The f
irst one corresponds to an isomorphism on the level of the Grothendieck gr
oup together with its Euler form. The solution for triangulated categories
of finite dimensional (hereditary or even quasi-hereditary) wild algebras
with three vertices is known\, the only free parameter is the largest eig
en value of the Coxeter transformation (for hereditary algebras)\, or equi
valently\, its trace (that works also for quasi-hereditary algebras). This
idea was used also for cluster algebras with three vertices (in a joint w
ork with Beineke and Brüstle) to decide\, whether it is acyclic or not (w
ith some exceptions). It is classically known as an equation between the r
anks of eceptional sequences on the projective plane (Drezet\, le Potier a
nd later also Rudakov).\n\nFor the general problem\, triangulated categori
es with a full exceptional sequence of length n we determine a finite set
of polynomials\, called polynomial invariants\, so that we can generically
solve this problem (there are some exceptions one should consider in more
detail) in terms of the values of these polynomials\, they generalize the
Markov equation for n=3.\n\nIn this talk we review some of the history\,
formulate the problem over arbitrary fields and solve it using so-called p
olynomial invariants. We also discuss\, what can be decided using polynomi
al invariants and what is the remaining open problem\, in particular\, wha
t to expect for the geometric aspects of the question.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala University)
DTSTART:20221215T140000Z
DTEND:20221215T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/110
DESCRIPTION:Title: Graded extensions of Verma modules\nby Volodymyr Mazorchuk (Uppsa
la University) as part of FD Seminar\n\n\nAbstract\nThe aim of this talk i
s to report on some recent progress related to the classical problem of de
scription of extensions of Verma modules in BGG category O. In particular\
, looking at the refined picture provided by graded extensions and using s
ome classical results of Delorme\, we determine the role the R-polynomials
play in this theory. Consequently\, we determine many cases in which exte
nsions can be described by the Gabber-Joseph formula and construct explici
t examples where this formula fails.\n\nBased on a joint work with Hankyun
g Ko.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laertis Vaso (Norges teknisk-naturvitenskapelige universitet\, NTN
U)
DTSTART:20230119T140000Z
DTEND:20230119T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/111
DESCRIPTION:by Laertis Vaso (Norges teknisk-naturvitenskapelige universite
t\, NTNU) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/fd-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuya Mizuno (Osaka Metropolitan University)
DTSTART:20230126T140000Z
DTEND:20230126T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/112
DESCRIPTION:Title: Complete $g$-fans of rank 2\nby Yuya Mizuno (Osaka Metropolitan U
niversity) as part of FD Seminar\n\n\nAbstract\n$g$-fan of a finite dimens
ional algebra is a fan in its real Grothendieck group defined by tilting t
heory. We give a classification of complete $g$-fans of rank 2. More expli
citly\, our main result asserts that every complete sign-coherent fan of r
ank 2 is a $g$-fan of some finite dimensional algebra. Our proof is based
on three fundamental results\, Gluing Theorem\, Rotation Theorem and Subdi
vision Theorem\, which realize basic operations on fans in the level of fi
nite dimensional algebras. This is a joint work with T. Aoki\, A. Higashit
ani\, O. Iyama and R. Kase.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongxing Chen (Capital Normal University)
DTSTART:20230202T140000Z
DTEND:20230202T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/113
DESCRIPTION:Title: Homological theory of orthogonal modules\nby Hongxing Chen (Capit
al Normal University) as part of FD Seminar\n\n\nAbstract\nTachikawa’s s
econd conjecture predicts that a finitely generated\, orthogonal module ov
er a finite-dimensional self-injective algebra is projective. This conject
ure is an important part of the Nakayama conjecture. In the talk\, we intr
oduce a systematic study of finitely generated\, orthogonal generators ove
r a self-injective Artin algebra from the view point of stable module cate
gories. For an orthogonal generator $M$\, we establish a recollement of th
e $M$-relative stable categories\, describe compact objects of the right t
erm of the recollement\, and give equivalent characterizations of Tachikaw
a’s second conjecture in terms of $M$-Gorenstein categories. Further\, w
e introduce Gorenstein-Morita algebras and show that the Nakayama conjectu
re holds true for them. This is joint work with Changchang Xi.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (Universität zu Köln)
DTSTART:20230209T140000Z
DTEND:20230209T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/114
DESCRIPTION:Title: $A_\\infty$ deformations of extended Khovanov arc algebras and Stropp
el’s Conjecture\nby Severin Barmeier (Universität zu Köln) as part
of FD Seminar\n\n\nAbstract\nExtended Khovanov arc algebras are graded fi
nite-dimensional algebras which appear at the confluence of representation
theory\, link homology and symplectic geometry. In this talk I will expla
in how to obtain explicit $A_\\infty$ deformations of these algebras by pr
esenting their Koszul duals as path algebras of quivers with relations and
using a combinatorial method via reduction systems to determine their def
ormations. This settles a conjecture by Catharina Stroppel (ICM 2010) on t
he bigraded Hochschild cohomology groups of extended Khovanov arc algebras
and produces explicit $A_\\infty$ deformations of Fukaya-Seidel categorie
s associated to Hilbert schemes of points on nilpotent slices of type $A$
singularities constructed recently by Cheuk Yu Mak and Ivan Smith. This ta
lk is based on https://arxiv.org/abs/2211.03354 joint with Zhengfang Wang.
\n
LOCATION:https://researchseminars.org/talk/fd-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicja Jaworska-Pastuszak (Nicolaus Copernicus University)
DTSTART:20230223T140000Z
DTEND:20230223T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/115
DESCRIPTION:Title: On Krull-Gabriel dimension of cluster repetitive categories and clust
er-tilted algebras\nby Alicja Jaworska-Pastuszak (Nicolaus Copernicus
University) as part of FD Seminar\n\n\nAbstract\nLet $K$ be an algebraical
ly closed field\, $R$ a locally support-finite locally bounded $K$-categor
y and $G$ a torsion-free admissible group of $K$-linear automorphisms of $
R$. Recently Pastuszak showed that the induced Galois covering $R\\rightar
row R/ G$\, where $R/ G$ denotes the orbit category\, preserves the Krull-
Gabriel dimension\, i.e. $\\mathrm{KG}(R)=\\mathrm{KG}(R/ G)$. Therefore\,
in order to determine Krull-Gabriel dimensions of tame standard self-inje
ctive algebras it was sufficient to determine Krull-Gabriel dimensions of
repetitive categories of tilted algebras of\nDynkin type\, tilted of Eucli
dean type or tubular algebras.\n\nIn this talk we recall the above results
and show how they can be adapted to the case of cluster repetitive catego
ries and cluster-tilted algebras which are their orbit categories. We will
also give some background on the Galois coverings of functor categories\,
since it is the main tool used in these results\, as well as present some
related problems and applications. This is a report of a joint work with
Grzegorz Pastuszak.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHÉS)
DTSTART:20230302T140000Z
DTEND:20230302T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/116
DESCRIPTION:Title: Pre-Calabi-Yau structures and string topology\nby Alex Takeda (IH
ÉS) as part of FD Seminar\n\n\nAbstract\nPre-Calabi-Yau structures are no
ncommutative versions of Poisson structures appearing in homological mirro
r symmetry\, and can be used to describe certain types of TQFT operations
on Hochschild homology. In this talk\, I will recall the definitions and a
pplications of these structures\, and then describe how to use these struc
tures to give a certain algebraic model for the string topology of non-sim
ply connected manifolds. This talk is based on a current joint project wit
h Manuel Rivera and Zhengfang Wang.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair King (University of Bath)
DTSTART:20230309T140000Z
DTEND:20230309T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/117
DESCRIPTION:Title: Twisted surfaces and clusters of curves\nby Alastair King (Univer
sity of Bath) as part of FD Seminar\n\n\nAbstract\nI will describe a combi
natorial way to associate to a (tagged) triangulation of a surface with ma
rked points and punctures a “twisted surface” together with a “clust
er of curves” whose intersection matrix is the corresponding exchange ma
trix. The twisted surface roughly models the spectral curve associated to
quadratic differentials\, as in [Bridgeland-Smith]\, but the combinatorial
construction has some subtle differences. This is joint work with Qiu-Yu.
\n
LOCATION:https://researchseminars.org/talk/fd-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Lanini (Università degli Studi di Roma Tor Vergata)
DTSTART:20230413T130000Z
DTEND:20230413T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/118
DESCRIPTION:Title: Symmetric quivers and symmetric varieties\nby Martina Lanini (Uni
versità degli Studi di Roma Tor Vergata) as part of FD Seminar\n\n\nAbstr
act\nIn this talk I will report on ongoing joint work with Ryan Kinser and
Jenna Rajchgot on varieties of symmetric quiver representations. These va
rieties are acted upon by a reductive group via change of basis\, and it i
s natural to ask for a parametrisation of the orbits\, for the closure inc
lusion relation among them\, for information about the singularities arisi
ng in orbit closures. Since the Eighties\, same (and further) questions ab
out representation varieties for type A quivers have been attached by rela
ting such varieties to Schubert varieties in type A flag varieties (Zelevi
nsky\, Bobinski-Zwara\, ...). I will explain that in the symmetric setting
it is possible to interpret the above questions in terms of certain symme
tric varieties. More precisely\, we show that singularities of an orbit cl
osure of a symmetric quiver representation variety are smoothly equivalent
to singularities of an appropriate Borel orbit closure in a symmetric var
iety.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Julia Redondo (Universidad Nacional del Sur)
DTSTART:20230420T130000Z
DTEND:20230420T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/119
DESCRIPTION:Title: The Ext-Algebra for infinitesimal deformations\nby Maria Julia Re
dondo (Universidad Nacional del Sur) as part of FD Seminar\n\n\nAbstract\n
Let $f$ be a Hochschild $2$-cocycle and $A_f$ an infinitesimal deformat
ion of a finite-dimensional associative $k$-algebra $A$. We describe\, und
er some conditions on $f$\, the algebra structure of the Ext-algebra of $A
_f$ in terms of the Ext-algebra of $A$. We achieve this description by
getting an explicit construction of minimal projective resolutions. This i
s based on joint work with L. Román and F. Rossi Bertone.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Cipriani (Università degli Studi di Verona)
DTSTART:20230427T130000Z
DTEND:20230427T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/120
DESCRIPTION:Title: Highest weight perverse sheaves\nby Alessio Cipriani (Università
degli Studi di Verona) as part of FD Seminar\n\n\nAbstract\nGiven a topol
ogically stratified space $X$ and a perversity function $p$ on it\, one ca
n build the category of $p$-perverse sheaves on $X$ by considering the hea
rt of a certain t-structure. Under suitable topological assumptions on $X$
perverse sheaves are finite dimensional modules over a finite dimensional
algebra independently on the chosen perversity function. It is then natur
al to ask under which further assumptions on the topology of the considere
d space perverse sheaves are highest weight. In this talk\, based on ongoi
ng joint work with Jon Woolf\, I will explain some sufficient (topological
) conditions on $X$ which ensure that perverse sheaves are highest weight.
\n
LOCATION:https://researchseminars.org/talk/fd-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Marie Jacobsen (Aarhus University)
DTSTART:20230504T130000Z
DTEND:20230504T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/121
DESCRIPTION:Title: Correspondences from tilting theory in higher homological algebra
\nby Karin Marie Jacobsen (Aarhus University) as part of FD Seminar\n\n\nA
bstract\nAdachi\, Iyama and Reiten developed $\\tau$-tilting theory to mir
ror the properties of mutation seen in cluster algebras. The theory gives
a generalisation of classical tilting modules using the Auslander-Reiten t
ranslation $\\tau$\, and one studies distinguished pairs of objects in the
module category of a finite-dimensional algebra known as $\\tau$-rigid pa
irs. An important result from the theory is the correspondence between fun
ctorially finite torsion classes\, maximal $\\tau$-rigid pairs and 2-term
silting complexes\, amongst others.\n\nMeanwhile\, higher homological alge
bra has since its introduction by Iyama become a very active field of rese
arch\, and many authors have generalised notions to the higher homological
setting\, including both torsion classes and $\\tau$-rigid pairs. This ta
lk is a report on work in progress investigating the relationship between
higher torsion classes\, silting objects and maximal $\\tau_d$-rigid pairs
. We describe explicit correspondences\, and also show computational resul
ts.\n\nThe talk is based on joint work with August\, Haugland\, Kvamme\, P
alu and Treffinger\n
LOCATION:https://researchseminars.org/talk/fd-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sondre Kvamme (Norges teknisk-naturvitenskapelige universitet\, NT
NU)
DTSTART:20230511T130000Z
DTEND:20230511T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/122
DESCRIPTION:Title: Indecomposables in the monomorphism category\nby Sondre Kvamme (N
orges teknisk-naturvitenskapelige universitet\, NTNU) as part of FD Semina
r\n\n\nAbstract\nThe study of submodule categories is an old subject in re
presentation theory going all the way back to beginning of the 20th centur
y by work of Miller and Hilton. It has connections to\, for example\, Litt
lewood—Richardson tableaux\, valuated p-groups and metabelian groups. In
2004 Ringel and Schmidmeier studied such categories using modern tools li
ke Auslander—Reiten theory and covering theory.\n\nA generalization of s
ubmodule categories\, called (separated) monomorphism categories\, has als
o been actively studied by several authors. They have found connections to
for example cotorsion pairs\, Gorenstein homological algebra\, singularit
y theory and topological data analysis.\n\nIn this talk I will define subm
odule and monomorphism categories\, and mention some of the known results
about them. Then I will explain how they can be related to representations
over stable categories via epivalences (also called representation equiva
lences)\, and how this can often be used to determine their indecomposable
s. I will also say something about our proof\, which uses free monads on a
belian categories. If time permits\, I will discuss analogues of monomorph
ism categories for species. In particular\, I will explain how our result
can be used to give a characterization of Cohen-Macaulay finiteness for th
e algebras H associated to symmetrizable Cartan matrices introduced by Gei
ss-Leclerc-Schröer\, assuming the terms in the symmetrizer are less than
or equal to 2.\n\nThis is joint work with Nan Gao\, Julian Külshammer and
Chrysostomos Psaroudakis.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhou (Tsinghua University)
DTSTART:20230518T130000Z
DTEND:20230518T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/123
DESCRIPTION:Title: Surfaces with binary and skew-gentle algebras\nby Yu Zhou (Tsingh
ua University) as part of FD Seminar\n\n\nAbstract\nIndecomposable objects
in the bounded derived category of a skew-gentle algebra have been classi
fied by many authors in an algebraic\, combinatorial or geometric way\, wh
ile a description of morphisms has not been given. In this talk\, we use a
new geometric model\, namely a graded marked surface with binary\, to inv
estigate a non-positive graded skew-gentle algebra. For any graded unknott
ed curve on the surface\, we associate an object in the perfect derived ca
tegory of the algebra\, and for any oriented intersection between unknotte
d curves\, we construct a morphism\, which form a basis of the correspondi
ng morphism space. This is based on joint work with Yu Qiu and Chao Zhang.
\n
LOCATION:https://researchseminars.org/talk/fd-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Syddansk University)
DTSTART:20230525T130000Z
DTEND:20230525T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/124
DESCRIPTION:Title: Algebras from surfaces: deformation\, duality\, quotients\nby Fab
ian Haiden (Syddansk University) as part of FD Seminar\n\n\nAbstract\nTher
e are a number of constructions which start with a (suitably decorated) su
rface together with a triangulation or more general system of arcs and pro
duce an algebra\, possibly differential-graded or A-infinity. Examples inc
lude: gentle algebras\, Jacobian and Ginzburg algebras of surfaces\, Braue
r graph algebras\, as well as generalizations of these. I will review some
of these constructions and discuss recently discovered connections betwee
n them\, involving deformation\, Koszul duality\, and cyclic group quotien
ts. Based on joint work with Merlin Christ and Yu Qiu (arXiv:2303.18249).\
n
LOCATION:https://researchseminars.org/talk/fd-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Garcia (Université Paris-Saclay)
DTSTART:20230601T130000Z
DTEND:20230601T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/125
DESCRIPTION:Title: Thick subcategories and semistability for projective presentations\nby Monica Garcia (Université Paris-Saclay) as part of FD Seminar\n\n\n
Abstract\nFor every finite dimensional algebra\, there are correspondences
between support $\\tau$-tilting modules\, functorially finite torsion pai
rs\, and left finite wide subcategories of the module category. The first
two classes of objects have “mirror” versions in the category of proje
ctive presentations\, namely\, 2-term silting complexes and cotorsion pair
s. In this talk\, we propose that the analog of the third class of objects
is that of thick subcategories. We will recall the notion of a thick subc
ategory of the category of projective presentations and show that those wi
th enough injectives are in bijection with left finite wide subcategories.
We will explain how thick subcategories arise from an attempt to define s
emistability for projective presentations.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erlend D. Børve (Norges teknisk-naturvitenskapelige universitet\,
NTNU)
DTSTART:20230608T130000Z
DTEND:20230608T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/126
DESCRIPTION:Title: Two-term silting and τ-cluster morphism categories\nby Erlend D.
Børve (Norges teknisk-naturvitenskapelige universitet\, NTNU) as part of
FD Seminar\n\n\nAbstract\nWe explain how Iyama—Yang’s silting reducti
on is compatible with Buan—Marsh’s reduction of $\\tau$-rigid pairs. T
hen\, we reconstruct the $\\tau$-cluster morphism category of a finite-dim
ensional algebra\, or more generally of a non-positive proper differential
graded algebra. Approaching $\\tau$-cluster morphism categories in terms
of silting theory\, as opposed to $\\tau$-tilting theory\, has the advanta
ge that the associativity of composition is proved more neatly. Time permi
tting\, we explore the cubical structure of $\\tau$-cluster morphism categ
ories and discuss alternative ways of defining them.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiarui Fei (Shanghai Jiao Tong University)
DTSTART:20230615T130000Z
DTEND:20230615T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/127
DESCRIPTION:Title: Crystal Structure of Upper Cluster Algebras\nby Jiarui Fei (Shang
hai Jiao Tong University) as part of FD Seminar\n\n\nAbstract\nWe describe
the (weaker) upper seminormal crystal structure for the $\\mu$-supported
$\\delta$-vectors for any ice quiver with potential\, or equivalently for
the tropical points of the corresponding cluster $\\mathcal{X}$-variety. W
e show that the crystal structure can be algebraically lifted to a biperfe
ct basis of the upper cluster algebra. This can be viewed as an additive c
ategorification of the crystal structure arising from cluster algebras. Al
l such biperfect bases are parametrized by lattice points in a product of
polytopes. We find that the requirement for upgrading to a (semi)normal cr
ystal is almost minimal in some sense. We illustrate this theory from clas
sical examples and new examples.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Burban (Universität Paderborn)
DTSTART:20230622T130000Z
DTEND:20230622T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/128
DESCRIPTION:Title: Derived-tame algebras\nby Igor Burban (Universität Paderborn) as
part of FD Seminar\n\n\nAbstract\nI shall first give a survey of known cl
asses of derived-tame finite dimensional algebras (gentle\, skew-gentle) e
xplaing the origin of the corresponding combinatorics of indecomposable ob
jects from the point of view of matrix problems (representations of bunche
s of (semi-)chains). Then I discuss another class of derived-tame algebras
which can be approached by a similar method. This is a joint work in prog
ress with Yuriy Drozd.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yadira Valdivieso (University of the Americas Puebla)
DTSTART:20230914T130000Z
DTEND:20230914T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/129
DESCRIPTION:Title: Skew-Brauer algebras and admissible cuts\nby Yadira Valdivieso (U
niversity of the Americas Puebla) as part of FD Seminar\n\n\nAbstract\nIn
this talk\, we define skew-Brauer graph algebras\, a generalization of the
well-known Brauer graph algebras.\n\nWe show that in the same way\, a Bra
uer graph algebras is defined from a graph with extra data on each vertex
and the edges attached to it\, a skew-Brauer graph algebra is also defined
from a graph with some extra data that captures an $\\mathbb{Z}_2$-action
on gentle algebras. We also show that the trivial extension of any skew-g
entle algebra is a skew-Brauer graph algebra. Finally\, we present a geome
tric interpretation of the notion of admissible cuts of a trivial extensio
n of skew-gentle algebras using dissections of orbifild surfaces.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Gunawan (University of Massachusetts Lowell)
DTSTART:20230921T130000Z
DTEND:20230921T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/130
DESCRIPTION:Title: Triangulations and maximal almost rigid modules over gentle algebras<
/a>\nby Emily Gunawan (University of Massachusetts Lowell) as part of FD S
eminar\n\n\nAbstract\nA type $A$ path algebra is an algebra whose basis is
the set of all paths in an orientation of a type $A$ Dynkin diagram. We i
ntroduce a new class of modules over a type $A$ path algebra and call them
maximal almost rigid (MAR). They are counted by the Catalan numbers and a
re naturally modeled by triangulations of a polygon. The endomorphism alge
bras of the MAR modules are classical tilted algebras of type $A$. Further
more\, their oriented flip graph is the oriented exchange graph of a small
er type $A$ cluster algebra which is known to define a Tamari or Cambrian
poset.\n\nThe type $A$ path algebras are special cases of gentle algebras\
, a family of finite-dimensional algebras whose indecomposable modules are
classified by certain walks called strings and bands. We generalize the n
otion of MAR to this setting. First\, we use the surface models studied by
Opper\, Plamondon\, and Schroll and by Baur and Coelho Simões to show th
at the MAR modules correspond bijectively to triangulations of a marked su
rface. We then show that the endomorphism algebra of a MAR module is the e
ndomorphism algebra of a tilting module over a bigger gentle algebra. Fina
lly\, we define an oriented flip graph of the MAR modules and conjecture t
hat it is acyclic.\n\nThis talk is based on joint projects with Emily Barn
ard\, Raquel Coelho Simões\, Emily Meehan\, and Ralf Schiffler.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (University of Glasgow)
DTSTART:20230928T130000Z
DTEND:20230928T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/131
DESCRIPTION:Title: Positroid varieties via representation theory\nby Matthew Pressla
nd (University of Glasgow) as part of FD Seminar\n\n\nAbstract\nTotal posi
tivity is by now a classical subject in linear algebra\, having begun in e
arnest with the work of Gantmacher and Krein from 1937. Recent results of
Postnikov and others have emphasised the importance of positivity in flag
varieties\, particularly the Grassmannian. A key tool in this area is Post
nikov’s positroid stratification of the Grassmannian\, and the cluster a
lgebra structures on its various (open) cells\, recently confirmed to exis
t by Galashin and Lam.\n\nIn this talk\, I will explain this story in the
language of representation theory\, with the positroid varieties and their
cluster algebra structures being encoded by the representation theory of
various non-commutative orders over the power series ring in one variable.
Except for the top-dimensional stratum\, Galashin and Lam’s constructio
n produces two different cluster algebra structures on each open positroid
\, and an application of this representation theoretic approach is a proof
that these two structures quasi-coincide\, as conjectured by Muller and S
peyer in 2017. In particular\, this means that these structures are equiva
lent from the point of view of total positivity.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (Universität Hamburg)
DTSTART:20230907T130000Z
DTEND:20230907T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/132
DESCRIPTION:Title: Complexes of stable infinity-categories\nby Tobias Dyckerhoff (Un
iversität Hamburg) as part of FD Seminar\n\n\nAbstract\nDerived categorie
s have come to play a decisive role in a wide range of topics. Several rec
ent developments\, in particular in the context of topological Fukaya cate
gories\, arouse the desire to study not just single categories\, but rathe
r complexes of categories. In this talk\, we will discuss examples of such
complexes in algebra\, topology\, algebraic geometry\, and symplectic geo
metry\, along with some results and conjectures involving them.\n\nBased o
n joint work with Merlin Christ and Tashi Walde.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calvin Pfeifer (University of Southern Denmark)
DTSTART:20231005T130000Z
DTEND:20231005T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/133
DESCRIPTION:Title: On $\\tau$-representation types with examples from the representation
theory of valued quivers\nby Calvin Pfeifer (University of Southern D
enmark) as part of FD Seminar\n\n\nAbstract\nIn this talk\, we propose a s
table and a τ-reduced version of the second Brauer-Thrall conjecture. The
former is a slight strengthening of a brick version of the second Brauer-
Thrall conjecture introduced by Mousavand and Schroll-Treffinger-Valdivies
o. The latter is stated in terms of Geiß-Leclerc-Schröer’s generically
τ-reduced components and provides a geometric interpretation of a questi
on raised by Demonet. We outline implications among these conjectures and
relate them to recent variations of tameness in stability and τ-tilting t
heory. It follows from Schroll-Treffinger-Valdivieso’s work that the con
jectures are true for special biserial algebras\, and we confirm them for
Geiß-Leclerc-Schröer’s (GLS) algebras associated to valued quivers. If
time permits\, we demonstrate that the in general representation wild GLS
algebras of affine type are still „tame“ from a $\\tau$-tilting persp
ective.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wu (University of Science and Technology of China)
DTSTART:20231012T130000Z
DTEND:20231012T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/134
DESCRIPTION:Title: Relative cluster categories and Higgs categories with infinite-dimens
ional morphism spaces\nby Yilin Wu (University of Science and Technolo
gy of China) as part of FD Seminar\n\n\nAbstract\nCluster categories were
introduced in 2006 by Buan–Marsh–Reineke–Reiten–Todorov in order t
o categorify acyclic cluster algebras without coefficients. Their construc
tion was generalized by Amiot to Jacobi-finite quivers with potential (200
9). Later\, Plamondon generalized it to arbitrary cluster algebras associa
ted with quivers (2009 and 2011). Cluster algebras with coefficients are i
mportant since they appear in nature as coordinate algebras of varieties l
ike Grassmannians\, double Bruhat cells\, unipotent cells\, … The work o
f Geiss-Leclerc-Schröer often yields Frobenius exact categories which all
ow to categorify such cluster algebras.\n\nIn previous work\, we have cons
tructed Higgs categories and relative cluster categories in the relative J
acobi-finite setting (arXiv:2109.03707). Higgs categories generalize the F
robenius categories used by Geiss-Leclerc-Schröer. In this talk\, we give
the construction of the Higgs category and of the relative cluster catego
ry in the relative Jacobi-infinite setting under suitable hypotheses. As i
n the relative Jacobi-finite case\, the Higgs category is no longer exact
but still extriangulated in the sense of Nakaoka-Palu (2019). We also give
the construction of a cluster character in this setting.\n\nThis is a joi
nt work with Chris Fraser and Bernhard Keller (arXiv:2307.12279).\n
LOCATION:https://researchseminars.org/talk/fd-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanna Le Gros (Universitat Autónoma de Barcelona)
DTSTART:20231019T130000Z
DTEND:20231019T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/135
DESCRIPTION:Title: Serre’s conditions and the finite type of classes of modules of bou
nded projective dimension\nby Giovanna Le Gros (Universitat Autónoma
de Barcelona) as part of FD Seminar\n\n\nAbstract\nThe class of modules of
projective dimension at most $n$\, denoted $\\mathcal{P}_n$\, is said to
be of finite type when its right $\\mathsf{Ext}$-orthogonal is exactly the
right $\\mathsf{Ext}$-orthogonal of the subclass of strongly finitely pre
sented modules in $\\mathcal{P}_n$ (recall that the strongly finitely pres
ented modules are the modules with a projective resolution consisting of f
initely generated modules). In particular\, the finite type of $\\mathcal{
P}_n$ is equivalent to the right $\\mathsf{Ext}$-orthogonal of $\\mathcal{
P}_n$ being an $n$-tilting class.\n\nThe classes $\\mathcal{P}_n$ which ar
e of finite type enjoy many additional properties with respect to those wh
ich are not\, so a next aim is to characterise the rings over which $\\mat
hcal{P}_n$ is of finite type for some $n$. In this talk\, we plan to addre
ss this question for commutative noetherian rings\, and relate this questi
on to a classical criterion of Serre. Explicitly\, over a commutative noet
herian ring\, the class $\\mathcal{P}_n$ is of finite type if and only if
Serre’s condition $(S_n)$ holds. Additionally\, we will also consider th
e slightly weaker condition of when the class of modules of flat dimension
at most $n$ coincides with the direct limit closure of the strongly finit
ely presented modules in $\\mathcal{P}_n$ over commutative noetherian ring
s\, or\, in other words\, when a ``higher’’ Govorov-Lazard Theorem hol
ds over these rings.\n\nThis talk is based on joint work with Michal Hrbek
.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Booth (Lancaster University)
DTSTART:20231026T130000Z
DTEND:20231026T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/136
DESCRIPTION:Title: Singularity categories via the derived quotient\nby Matt Booth (L
ancaster University) as part of FD Seminar\n\n\nAbstract\nGiven a reasonab
le commutative ring R and a noncommutative partial resolution A of R\, the
singularity category of A relative to R is controlled by a connective dg
algebra\, the derived exceptional locus\, which can be obtained as a deriv
ed quotient of A. In fact\, one can identify the derived exceptional locus
as the connective cover of an endomorphism dg algebra of an object in the
singularity category of R. When R is a complete local hypersurface\, the
derived exceptional locus in fact recovers the dg singularity category of
R\, which - by a result of Hua and Keller - recovers the isomorphism type
of R itself. I’ll talk about the above before giving an application: the
classification of singular threefold flops via their derived contraction
algebras. Derived methods must come into play here since\, in the singular
setting\, the usual contraction algebra does not classify\, in contrast t
o a recent theorem of Jasso\, Keller\, and Muro in the smooth setting.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Bird (Charles University)
DTSTART:20231102T140000Z
DTEND:20231102T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/137
DESCRIPTION:Title: Coherent and definable functors for triangulated categories\nby I
saac Bird (Charles University) as part of FD Seminar\n\n\nAbstract\nIn thi
s talk\, I shall introduce coherent and definable functors for triangulate
d categories. The former are the purity preserving functors into finitely
accessible categories with products\, and generalise their namesakes as in
troduced by Krause. It will be shown that the restricted Yoneda embedding
is the universal coherent functor. I will then introduce definable functor
s between triangulated categories\, which will be shown to be those which
preserve the pure structure. Their properties will be discussed and exampl
es given. I will then give some applications to representation theory. Thi
s is based on joint work with Jordan Williamson.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (University of Science and Technology of China)
DTSTART:20231116T140000Z
DTEND:20231116T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/138
DESCRIPTION:Title: On exact dg categories\nby Xiaofa Chen (University of Science and
Technology of China) as part of FD Seminar\n\n\nAbstract\nIn this talk\,
I will provide a brief introduction to exact dg categories and then explor
e their application to various correspondences in representation theory. W
e will generalize the Auslander–Iyama correspondence\, the Iyama–Solbe
rg correspondence\, and a correspondence considered in a paper by Iyama in
2005 to the setting of exact dg categories. The slogan is that solving co
rrespondence-type problems becomes easier using dg categories\, and intere
sting phenomena emerge when the dg category is concentrated in degree zero
or is abelian.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University)
DTSTART:20231109T140000Z
DTEND:20231109T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/139
DESCRIPTION:Title: Derived Picard groups of graded gentle algebras and integration of Ho
chschild classes\nby Sebastian Opper (Charles University) as part of F
D Seminar\n\n\nAbstract\nThe talk is based on my ongoing project concernin
g the derived Picard groups of graded gentle algebras\, or equivalently\,
partially wrapped Fukaya categories of surfaces in the sense of Haiden-Kat
zarkov-Kontsevich. After recalling some previous results in the ungraded c
ase\, I will explain the structure of these groups and the main ingredient
s of this result. As such\, we discuss a projection map from the derived P
icard group to the mapping class group and mapping class group actions on
these categories. The last ingredient is the use of exponential maps to de
termine the kernel of the projection map. I will explain how they allow us
to integrate certain Hochschild classes of any A-Infinity-algebra over a
field of characteristic 0\, to elements in its derived Picard group.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Gallauer (University of Warwick)
DTSTART:20231123T140000Z
DTEND:20231123T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/140
DESCRIPTION:Title: On dense cohomological invariants\nby Martin Gallauer (University
of Warwick) as part of FD Seminar\n\n\nAbstract\nA classical theorem of Q
uillen expresses the mod-p cohomology of a finite group in terms of its el
ementary abelian p-subgroups\, up to inseparable isogeny. In this talk I w
ill discuss variations on this theme: “going pro-finite” and “going
Mackey”. I will then explain how these are all linked to “dense invari
ants” in tensor-triangular geometry. Based on joint work with Paul Balme
r.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Barbieri (Università degli Studi di Verona)
DTSTART:20231207T140000Z
DTEND:20231207T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/142
DESCRIPTION:Title: Multi-scale stability conditions on A_n- Ginzburg categories\nby
Anna Barbieri (Università degli Studi di Verona) as part of FD Seminar\n\
n\nAbstract\nI will introduce a notion of “multi-scale stability conditi
ons” that\, under some finiteness assumptions\, generalise the notion of
Bridgeland stability for a triangulated category. For Ginzburg categories
of type A_n\, multi-scale stability conditions can be used to construct a
smooth compactification of an appropriate quotient of the usual stability
manifold. Based on joint work with M.Moeller and J.So.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss (Universidad Nacional Autónoma de México\, UNAM)
DTSTART:20231214T140000Z
DTEND:20231214T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/143
DESCRIPTION:Title: MSW-bangle functions are generic bases for marked surfaces\nby Ch
ristof Geiss (Universidad Nacional Autónoma de México\, UNAM) as part of
FD Seminar\n\n\nAbstract\nThis is a report on a joint project with Daniel
Labardini and Jon Wilson. We extend our previous result\, joint with Dani
el Labardini and Jan Schröer from unpunctured surfaces to punctured surfa
ces with non-empty boundaries. Let T be a tagged triangulation of such a m
arked surface and A(T) the corresponding Jacobian algebra for the Labardin
i potential. A(T) is finite-dimensional and tame\, however it is only gent
le if the surface has no punctures. More precisely\, A(T) is skewed-gentle
if T is of signature 0\, otherwise there is no explicit classification of
the indecomposable representations known. Moreover\, the correspondence b
etween curves and indecomposable representations is complicated by the pre
sence of kinks. We sketch briefly\, how to deal with these difficulties.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bethany Marsh (University of Leeds)
DTSTART:20240125T140000Z
DTEND:20240125T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/144
DESCRIPTION:Title: An introduction to tau-exceptional sequences\nby Bethany Marsh (U
niversity of Leeds) as part of FD Seminar\n\n\nAbstract\nJoint work with A
slak Bakke Buan.\n\nExceptional sequences in module categories over heredi
tary algebras (e.g. path algebras of quivers) were introduced and studied
by W. Crawley-Boevey and C. M. Ringel in the early 1990s\, as a way of und
erstanding the structure of such categories. They were motivated by the co
nsideration of exceptional sequences in algebraic geometry by A. I. Bondal
\, A. L. Gorodontsev and A. N. Rudakov.\n\nExceptional sequences can also
be considered over arbitrary finite dimensional algebras\, but their behav
iour is not so good in general: for example\, complete exceptional sequenc
es may not exist. We look at different ways of generalising to the heredit
ary case\, with a focus on tau-exceptional sequences\, recently introduced
in joint work with A. B. Buan (NTNU)\, motivated by the tau-tilting theor
y of T. Adachi\, O. Iyama and I. Reiten\, and signed exceptional sequences
in the hereditary case defined by K. Igusa and G. Todorov.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasper van de Kreeke (Universiteit van Amsterdam)
DTSTART:20240201T140000Z
DTEND:20240201T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/145
DESCRIPTION:Title: Namikawa-Weyl groups of quiver varieties\nby Jasper van de Kreeke
(Universiteit van Amsterdam) as part of FD Seminar\n\n\nAbstract\nNakajim
a’s quiver varieties are moduli spaces of quiver representations which b
ear an additional symplectic structure. Out of such a symplectic singulari
ty\, Namikawa constructs a “Namikawa-Weyl group” by means of deformati
on theory\, but implementing his construction in case of quiver varieties
remains open until today. In this talk\, I recapitulate how quiver varieti
es arise from representation theory\, what is already known about Namikawa
-Weyl groups of other symplectic singularities\, and how Raf Bocklandt and
I almost succeeded in the case of quiver varieties during my 2018 master
thesis. I will highlight some remaining technical problems\, which concern
the difference between the algebraic and analytic world and how to constr
uct non-affine GIT quotients.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hankyung Ko (Uppsala University)
DTSTART:20240208T140000Z
DTEND:20240208T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/146
DESCRIPTION:Title: Atoms in Singularland\nby Hankyung Ko (Uppsala University) as par
t of FD Seminar\n\n\nAbstract\nThe talk explains singular Coxeter combinat
orics\, i.e.\, combinatorics of parabolic double cosets in a Coxeter group
. In particular\, we give a generators and relations presentation (or two)
of the double cosets. Here appears a singular analogue of the simple refl
ections\, called atoms. Atoms generate a new combinatorial structure which
\, by a work of Iyama and Wemyss\, describes the tilting theory of contrac
ted (i.e. idempotent subalgebras of) preprojective algebras.\n\nBased on a
joint project with Ben Elias\, Nico Libedinsky\, Leonardo Patimo.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Hrbek (Czech Academy of Sciences)
DTSTART:20240215T140000Z
DTEND:20240215T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/147
DESCRIPTION:Title: Telescope conjecture via homological residue fields with applications
to schemes\nby Michal Hrbek (Czech Academy of Sciences) as part of FD
Seminar\n\n\nAbstract\nIn his landmark ‘00 paper\, Krause gave an abstr
act model theory characterization of when the Telescope Conjecture (TC) ho
lds in a compactly generated triangulated category. Restricting to the ten
sor-triangulated (tt) setting\, the tt version of (TC) can then be transla
ted as “every definable ideal is the orthogonal to a set of compact obje
cts”\, as explained by R. Wagstaffe. (TC) was originally formulated for
the case of the stable homotopy category of spectra\, where it had been a
conjecture for 40 years until the announcement of the negative answer last
year. Our results are motivated by the case of D(X)\, the derived categor
y of a concentrated scheme X\, where (TC) is a property which often holds
but fails for some X.\n\nBalmer and Favi showed that (TC) is an affine-loc
al property on the Balmer spectrum of a big tt-category. In the present wo
rk (arXiv:2311.00601)\, we show that under very mild (and conjecturally va
cuous) conditions\, (TC) is even stalk-local in a very strong sense: For (
TC) to hold\, it is enough to check that each of the Balmer’s homologica
l residue field objects generates the local tt-category over the correspon
ding stalk as a definable ideal.\n\nIn the case of D(X)\, this ties (TC) s
trongly with separation properties of the adic topology of the stalk rings
. We apply this to recover most known examples of validity or failure of (
TC) in D(X)\, as well as to construct some new ones. Moreover\, we show th
at certain restriction of (TC) can be characterized in terms of pseudoflat
ring epimorphisms over R\, yielding a surprising example of a non-surject
ive pseudoflat local ring morphism.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorna Gregory (University of East Anglia)
DTSTART:20240222T140000Z
DTEND:20240222T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/148
DESCRIPTION:Title: Representation Type and Pseudofinite-dimensional Modules over Finite-
dimensional Algebras\nby Lorna Gregory (University of East Anglia) as
part of FD Seminar\n\n\nAbstract\nThe (theory of) a class of modules is sa
id to be decidable if there is an algorithm which given a sentence in the
language of modules (a sentence is a particular kind of statement about mo
dules) answers whether it is true in all modules in that class. A long-sta
nding conjecture of Mike Prest claims that the (theory of) the class of al
l modules over a finite-dimensional algebra is decidable theory if and onl
y if it is of tame representation type. The reverse direction of this conj
ecture is often hard to prove even in particular examples. One difficulty
is that the conjecture talks about all modules rather than just finite-dim
ensional ones. In this talk I will present work in progress around and in
support of a new conjecture\, inspired by Prest’s conjecture\, which cla
ims that the (theory of) the class of finite-dimensional modules over a fi
nite-dimensional algebra is decidable if and only if it is of tame represe
ntation type.\n\nNo background knowledge in logic or model theory will be
assumed.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20240229T140000Z
DTEND:20240229T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/149
DESCRIPTION:Title: Okounkov's conjecture via BPS Lie algebras\nby Ben Davison (Unive
rsity of Edinburgh) as part of FD Seminar\n\n\nAbstract\nGiven an arbitrar
y finite quiver Q\, Maulik and Okounkov defined a new Yangian-style quantu
m group. It is built from the FRT formalism and their construction of R ma
trices on the cohomology of Nakajima quiver varieties\, via the stable env
elopes that they also defined. Just as in the case of ordinary Yangians\,
there is a Lie algebra g_Q inside their new algebra\, and the Yangian is a
deformation of the current algebra of this Lie algebra.\n\nOutside of ext
ended ADE type\, numerous basic features of g_Q have remained mysterious s
ince the outset of the subject\, for example\, the dimensions of the grade
d pieces. A conjecture of Okounkov predicts that these dimensions are give
n by the coefficients of Kac’s polynomials\, which count isomorphism cla
sses of absolutely indecomposable Q-representations over finite fields. I
will explain a recent proof\, with Botta\, of the result that the Maulik-O
kounkov Lie algebra is isomorphic to the “BPS Lie algebra” associated
to the tripled quiver with potential\, defined in joint work with Meinhard
t\, following the work of Kontsevich and Soibelman on critical cohomologic
al Hall algebras\, and then completely described in joint work with Hennec
art and Schlegel-Mejia. A corollary of these results is that Okounkov’s
conjecture is true.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Broomhead (University of Plymouth)
DTSTART:20240314T140000Z
DTEND:20240314T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/150
DESCRIPTION:Title: Convex geometry for fans of triangulated categories\nby Nathan Br
oomhead (University of Plymouth) as part of FD Seminar\n\n\nAbstract\nFans
and other convex-geometric objects have recently appeared in homological
algebra in several related contexts. For example\, as g-fans in the siltin
g theory of finite-dimensional algebras and as scattering diagrams in Brid
geland stability theory. I will discuss joint work with David Pauksztello\
, David Ploog and Jon Woolf on a general construction which we hope will p
rovide a natural and unifying framework. Starting with a triangulated cate
gory D and a finite rank quotient lattice L of its Grothendieck group\, we
show that each heart H in D determines a closed convex heart cone' in the
dual vector space V=Hom(L\,R). The heart cones of H and all its forward t
ilts form a heart fan’ in V. If H is `algebraic’\, i.e. is a length ca
tegory with finitely many simple objects\, then the heart cone is simplici
al and the heart fan is complete.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Linckelmann (City\, University of London)
DTSTART:20240321T140000Z
DTEND:20240321T150000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/151
DESCRIPTION:Title: Generating functions for the Hochschild cohomology of symmetric group
s\nby Markus Linckelmann (City\, University of London) as part of FD S
eminar\n\n\nAbstract\nWe start out by reviewing some classical material on
the representation theory of symmetric groups and the Hochschild cohomolo
gy of finite-dimensional algebras. We describe generating functions for th
e dimensions of the Hochschild cohomology of symmetric groups in each degr
ee.\n\nWhile it is known\, using the classification of finite simple group
s\, that the first Hochschild cohomology of a non-semisimple finite group
algebra is non-zero\, it remains an open question whether this is true for
non-simple blocks of finite groups.\n\nWe use generating functions to sho
w that the first Hochschild cohomology of any non-simple block of a symmet
ric group algebra is non-zero. This is joint work with Dave Benson and Rad
ha Kessar.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (Institut des Hautes Études Scientifiques)
DTSTART:20240411T130000Z
DTEND:20240411T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/152
DESCRIPTION:Title: Fusion-equivariant stability conditions and Morita duality\nby Ed
mund Heng (Institut des Hautes Études Scientifiques) as part of FD Semina
r\n\n\nAbstract\nClassically\, finite symmetries are captured by the actio
n of a finite group. Moving to the quantum world\, one has to allow for (p
ossibly non-invertible) quantum symmetries — these are instead captured
by the action of a more general algebraic structure\, known as a fusion ca
tegory. Such quantum symmetries are actually ubiquitous in mathematics\; f
or example\, given a category with an action of a finite group G (e.g. rep
(Q)\, Coh(X) etc.)\, its G-equivariant category has instead the action of
the category of representations rep(G)\, where rep(G) has the structure of
a fusion category.\nThe aim of this talk is to study the role of fusion c
ategories as “quantum symmetries” in relation to (Bridgeland) stabilit
y conditions. Given a triangulated category equipped an action of a fusion
category C\, we introduce the notion of “C-equivariant stability condit
ions”\, a generalisation of “G-invariant stability conditions”. The
first result is that these stability conditions form a closed submanifold
of the stability manifold\, just as the G-invariant stability conditions d
o. Moreover\, given a triangulated D with a G-action\, so that its G-equiv
ariant category D^G has a rep(G)-action\, we will see the following (Morit
a) duality result for stability conditions: the complex manifold of G-inva
riant stability conditions (associated to D) is homeomorphic to the comple
x manifold of rep(G)-equivariant stability conditions (associated to D^G).
\nThis is part of joint work with Hannah Dell and Anthony Licata.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azzurra Ciliberti (University of Rome La Sapienza)
DTSTART:20240502T130000Z
DTEND:20240502T140000Z
DTSTAMP:20260315T015631Z
UID:fd-seminar/153
DESCRIPTION:Title: Categorification of cluster algebras of type B and C through symmetri
c quivers and their representations\nby Azzurra Ciliberti (University
of Rome La Sapienza) as part of FD Seminar\n\n\nAbstract\nAfter recalling
the combinatorial description of their cluster complex\, we will state a c
luster expansion formula for cluster algebras of type B and C in terms of
cluster variables of type A. Then\, we will explain how to associate a sym
metric quiver with relations Q to any seed of a cluster algebra of type B
and C. Under this correspondence\, cluster variables of type B (resp. C) c
orrespond to orthogonal (resp. symplectic) indecomposable representations
of Q. Finally\, we will give a categorical interpretation of the cluster e
xpansion formula in the case of acyclic quivers.\n
LOCATION:https://researchseminars.org/talk/fd-seminar/153/
END:VEVENT
END:VCALENDAR