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:20260404T131145Z
UID:fd-seminar/1
DESCRIPTION:Title: Calabi–Yau properties of Postnikov diagrams\nby Matthew Pr
essland (University of Leeds) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pauksztello (Lancaster University)
DTSTART:20200528T130000Z
DTEND:20200528T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/2
DESCRIPTION:Title: Simple-mindedness: negativity and positivity\nby David Pauks
ztello (Lancaster University) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Labardini-Fragoso (UNAM)
DTSTART:20200604T130000Z
DTEND:20200604T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/3
DESCRIPTION:Title: Schemes of modules over gentle algebras and laminations of surfa
ces\nby Daniel Labardini-Fragoso (UNAM) as part of FD Seminar\n\nAbstr
act: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Nagoya University)
DTSTART:20200618T130000Z
DTEND:20200618T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/4
DESCRIPTION:Title: Simple objects in torsion-free classes over preprojective algebr
as of Dynkin type\nby Haruhisa Enomoto (Nagoya University) as part of
FD Seminar\n\n\nAbstract\nIn this talk\, I propose to study exact-categori
cal structures of torsion(-free) classes of module categories. For functor
ially finite torsion-free class\, indecomposable projective and injective
objects are easily described by \\tau^-τ \n−\n -tilting modules\, and i
n particular\, the numbers of them coincide. However\, there can be more s
imple objects in torsion-free class\, which I propose to study. I explain
that the number of simple objects controls the validity of the Jordan–H
ölder type theorem in a torsion-free class.\n\nThen I’ll talk about sim
ple objects in a torsion-free class over the preprojective algebra (and pa
th algebra) of Dynkin type\, which is also important in Lie theory due to
Geiss–Leclerc–Schröer’s categorification of the cluster structure.
By Mizuno’s result\, we can associate an element ww of the Weyl group to
each torsion-free class \\mathcal{F}F. By (extended) Gabriel’s theorem\
, \\mathcal{F}F roughly corresponds to the inversion set of ww\, the set o
f positive roots which are sent to negative by w^{-1}w \n−1\n . Then I s
how that simple objects in \\mathcal{F}F are in bijection with Bruhat inve
rsions of ww\, which are related to the Bruhat order of the Weyl group.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis-Philippe Thibault (NTNU)
DTSTART:20200611T130000Z
DTEND:20200611T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/5
DESCRIPTION:by Louis-Philippe Thibault (NTNU) as part of FD Seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Schiffler (University of Connecticut)
DTSTART:20200625T130000Z
DTEND:20200625T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/6
DESCRIPTION:Title: A geometric model for the syzygies over certain 2-Calabi--Yau ti
lted algebras\nby Ralf Schiffler (University of Connecticut) as part o
f FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Amiot (Université Joseph Fourier)
DTSTART:20200702T130000Z
DTEND:20200702T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/7
DESCRIPTION:Title: Derived equivalences for skew-gentle algebras\nby Claire Ami
ot (Université Joseph Fourier) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Baur (University of Leeds)
DTSTART:20200716T130000Z
DTEND:20200716T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/8
DESCRIPTION:Title: Postnikov diagrams and orbifolds\nby Karin Baur (University
of Leeds) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Špela Špenko (Université libre de Bruxelles)
DTSTART:20200730T130000Z
DTEND:20200730T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/9
DESCRIPTION:Title: GKZ systems and perverse schobers\nby Špela Špenko (Univer
sité libre de Bruxelles) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (Universidad de Buenos Aires)
DTSTART:20200709T130000Z
DTEND:20200709T140000Z
DTSTAMP:20260404T131145Z
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: T
BA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cris Negron (University of North Carolina)
DTSTART:20200723T130000Z
DTEND:20200723T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/11
DESCRIPTION:Title: Finite generation of cohomology for Drinfeld doubles of finite
group schemes\nby Cris Negron (University of North Carolina) as part o
f FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Université de Paris)
DTSTART:20200903T130000Z
DTEND:20200903T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/12
DESCRIPTION:Title: Relative Calabi-Yau completions and higher preprojective algebr
as\nby Bernhard Keller (Université de Paris) as part of FD Seminar\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shijie Zhu (The University of Iowa)
DTSTART:20200910T140000Z
DTEND:20200910T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/13
DESCRIPTION:Title: Hopf algebras of discrete representation type\nby Shijie Zh
u (The University of Iowa) as part of FD Seminar\n\n\nAbstract\nHopf algeb
ra is an important topic in geometric representation theory. A basic algeb
ra is of finite representation type if there are only finitely many non-is
omorphic indecomposable representations. Basic Hopf algebras of finite rep
resentation type have been classified by Liu and Li in 2004. As algebras\,
they are just copies of Nakayama algebras. A pointed coalgebra is of disc
rete representation type\, if there are only finitely many non-isomorphic
indecomposable representations for each dimension vector. In this talk\, I
am going to give a classification of pointed Hopf algebras of discrete re
presentation type. The main tool we are using is called “covering maps
” of (finite dimensional) coalgebras which comes from separable extensio
ns of the dual algebras. This is a joint work with Miodrag Iovanov\, Emre
Sen\, and Alexander Sistko.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jenny August (Max Plank Institut für Mathematik (MPIM))
DTSTART:20200917T130000Z
DTEND:20200917T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/14
DESCRIPTION:Title: Grassmanian categories of infinite rank\nby Jenny August (M
ax Plank Institut für Mathematik (MPIM)) as part of FD Seminar\n\n\nAbstr
act\nIn this talk\, I’ll describe our work towards providing an infinite
rank version of the Grassmanian cluster categories introduced by Jensen\,
King and Su. We develop a new combinatorial tool for determining when two
k-subsets of the integers are “non-crossing”\, or equivalently when t
wo Plücker coordinates of a Grassmanian cluster algebra of infinite rank
are “compatible”. We use this tool to show that there is a structure p
reserving bijection between these Plücker coordinates and the generically
free modules of rank 1 in our Grassmanian category of infinite rank\, mir
roring a result of Jensen\, King and Su in the finite case. This is joint
work with Man-Wai Cheung\, Eleonore Faber\, Sira Gratz and Sibylle Schroll
.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/15
DESCRIPTION:Title: Leavitt path algebras\, B-infty-algebras and Keller’s conject
ure for singular Hochschild cohomology\nby Xiao-Wu Chen (University of
Science and Technology of China (USTC)) as part of FD Seminar\n\n\nAbstra
ct\nI will first recall the relation between Leavitt path algebras and the
singularity categories of radical-square-zero algebras. Using Leavitt pat
h algebras\, we confirm Keller’s conjecrure for any radical-square-zero
algebra: there is an isomorphism in the homotopy category of $B_\\infty$-a
lgebras between the Hochschild cochain complex of the dg singularity categ
ory and the singular Hochschild cochain complex of the algebra. Moreover\,
we prove that Keller’s conjecture is invariant under one-point (co)exte
nsions and singular equivalences with levels. This is joint with Huanhuan
Li and Zhengfang Wang.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Zito (University of Connecticut)
DTSTART:20201001T130000Z
DTEND:20201001T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/16
DESCRIPTION:Title: tau-Tilting Finite Algebras With Non-Empty Left Or Right Parts
Are Representation-Finite\nby Stephen Zito (University of Connecticut)
as part of FD Seminar\n\n\nAbstract\nτ-tilting theory was introduced by
Adachi\, Iyama and Reiten as a far-reaching generalization of classical ti
lting theory for finite dimensional associative algebras. One of the main
classes of objects in the theory is that of τ\\tauτ-rigid modules: a mod
ule MMM over an algebra Λ\\LambdaΛ is τ\\tauτ-rigid if HomΛ(M\,τM
)=0\\operatorname{Hom}_{\\Lambda}(M\,\\tau M)=0HomΛ(M\,τM)=0\, where
τM\\tau MτM denotes the Auslander-Reiten translation of MMM\; such a mod
ule MMM is called τ\\tauτ-tilting if the number ∣M∣|M|∣M∣ of non
-isomorphic indecomposable summands of MMM equals the number of isomorphis
m classes of simple Λ\\LambdaΛ-modules. Recently\, a new class of algebr
as was introduced by Demonet\, Iyama\, Jasso called τ\\tauτ-tilting fini
te algebras. They are defined as finite dimensional algebras with only a f
inite number of isomorphism classes of basic τ\\tauτ-tilting modules.\n\
nAn obvious sufficient condition to be τ\\tauτ-tilting finite is to be r
epresentation-finite. In general\, this condition is not necessary. The ai
m of this talk is to show for algebras Λ\\LambdaΛ such that LΛL_\\Lambd
aLΛ or RΛ≠∅R_\\Lambda\\neq\\emptysetRΛ=∅ \, represent
ation-finiteness and τ\\tauτ-tilting finiteness are equivalent condition
s.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lidia Angeleri Hügel (Università degli Studi di Verona)
DTSTART:20201217T140000Z
DTEND:20201217T150000Z
DTSTAMP:20260404T131145Z
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://stable.researchseminars.org/talk/fd-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Muro (TBC) (Universidad de Sevilla)
DTSTART:20201210T140000Z
DTEND:20201210T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/18
DESCRIPTION:by Fernando Muro (TBC) (Universidad de Sevilla) as part of FD
Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (University of East Anglia)
DTSTART:20201022T130000Z
DTEND:20201022T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/20
DESCRIPTION:Title: Categorification of representation theory with an application t
o Soergel bimodules\nby Vanessa Miemietz (University of East Anglia) a
s part of FD Seminar\n\n\nAbstract\nWe explain how to categorify various b
asic results from the representation theory of finite-dimensional algebras
\, which are useful for classifying simple modules\, to the 2-representati
on theory of fiat 2-categories. We then apply these in order to obtain a c
lassification of simple 2-representations of the 2-category of Soergel bim
odules.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/21
DESCRIPTION:Title: Finite-dimensional DG algebras and their properties\nby Dmi
tri Orlov (Steklov Mathematical Institute of Russian Academy of Sciences)
as part of FD Seminar\n\n\nAbstract\nThe talk will focus on finite-dimensi
onal DG algebras and categories of perfect complexes over such DG algebras
. These categories can be considered as proper derived noncommutative sche
mes. We are going to discuss basic properties of these noncommutative sche
mes and to establish a connection between such categories and DG categorie
s with (semi)exceptional collections.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Hausdorff Research Institute for Mathematics (HIM)
)
DTSTART:20201203T140000Z
DTEND:20201203T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/22
DESCRIPTION:Title: Exact structures and degeneration of Hall algebras\nby Mikh
ail Gorsky (Hausdorff Research Institute for Mathematics (HIM)) as part of
FD Seminar\n\n\nAbstract\nHall algebras and various related structures pl
ay a prominent role in the modern representation theory. I will explain th
e interplay between different exact structures on an additive category and
degenerations of the associated Hall algebras. For the categories of repr
esentations of Dynkin quivers\, this recovers degenerations of the negativ
e part of the corresponding quantum group. I will sketch the proofs of our
results in the general case based on Auslander-Reiten theory. We will dis
cuss further examples related to quantum doubles of quantum Borel subalgeb
ras and\, if time permits\, certain generalizations involving extriangulat
ed categories. (Based on joint work with Xin Fang.)\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Habermann (University College London (UCL))
DTSTART:20201008T130000Z
DTEND:20201008T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/23
DESCRIPTION:Title: Homological mirror symmetry for invertible polynomials in two v
ariables\nby Matthew Habermann (University College London (UCL)) as pa
rt of FD Seminar\n\n\nAbstract\nThe starting point for homological mirror
symmetry for invertible polynomials is an n x n invertible matrix with non
-negative integer entries. To such a matrix\, as well as to its transpose\
, one can associate polynomials. These polynomials are called invertible i
f they are weighted homogeneous\, and both define isolated singularities a
t the origin. Homological mirror symmetry for invertible polynomials is a
series of conjectures which posits the equivalence of the different flavou
rs of Fukaya category associated to the Lefschetz fibration defined by one
polynomial with various flavours of graded matrix factorisations defined
by the transpose polynomial. Particular to the case of two variables is th
e fact that the partially wrapped Fukaya category of a Milnor fibre corres
ponds to the derived category of modules of a gentle algebra\, and so HMS
for invertible polynomials in two variables allows one to study the latter
category geometrically. In this talk I will explain my recent work\, part
of which was done jointly with Jack Smith.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Grant (University of East Anglia)
DTSTART:20201015T130000Z
DTEND:20201015T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/24
DESCRIPTION:Title: Preprojective algebras and fractional Calabi-Yau algebras\n
by Joe Grant (University of East Anglia) as part of FD Seminar\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Mertens (Universiteit Antwerpen)
DTSTART:20201105T140000Z
DTEND:20201105T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/25
DESCRIPTION:Title: Linear quasi-categories as templicial modules\nby Arne Mert
ens (Universiteit Antwerpen) as part of FD Seminar\n\n\nAbstract\nThis is
joint work with my supervisor Wendy Lowen. After laying out the basics of
quasi-categories as defined by Joyal\, we introduce a notion of linear qua
si-categories over a unital commutative ring. We make use of certain colax
monoidal functors\, which we call templicial modules\, as a variant of si
mplicial modules respecting the monoidal structure. It turns out that temp
licial modules with a Frobenius monoidal structure are equivalent to (homo
logically) non-negatively graded dg-categories. Through this equivalence w
e can associate to any dg-category a linear quasi-category\, the linear dg
-nerve\, which enhances the classical dg-nerve.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ICRA2020 Research Snapshots
DTSTART:20201112T140000Z
DTEND:20201112T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/26
DESCRIPTION:by ICRA2020 Research Snapshots as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ICRA2020 Research Snapshots
DTSTART:20201119T140000Z
DTEND:20201119T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/27
DESCRIPTION:by ICRA2020 Research Snapshots as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ICRA2020 Research Snapshots
DTSTART:20201126T140000Z
DTEND:20201126T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/28
DESCRIPTION:by ICRA2020 Research Snapshots as part of FD Seminar\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henning Krause (Universität Bielefeld)
DTSTART:20210107T140000Z
DTEND:20210107T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/29
DESCRIPTION:Title: The category of local representations of a finite group\nby
Henning Krause (Universität Bielefeld) as part of FD Seminar\n\n\nAbstra
ct\nWe consider modular representations of a finite group and focus for ea
ch prime ideal of the cohomology ring on the stable category of representa
tions supported at that prime. This category is tensor triangulated\, but
compact and dualising objects do not coincide. For instance\, the tensor u
nit is not compact. This is in contrast to the global category of represen
tations and leads to an interesting completion of the category of compact
objects. The talk presents recent progress from an ongoing collaboration w
ith Dave Benson\, Srikanth Iyengar\, and Julia Pevtsova.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chrysostomos Psaroudakis (Aristotle University of Thessaloniki)
DTSTART:20210114T140000Z
DTEND:20210114T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/30
DESCRIPTION:by Chrysostomos Psaroudakis (Aristotle University of Thessalon
iki) as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lo (California State University\, Northridge (CSUN))
DTSTART:20210121T140000Z
DTEND:20210121T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/31
DESCRIPTION:by Jason Lo (California State University\, Northridge (CSUN))
as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teresa Conde (Universität Stuttgart)
DTSTART:20210128T140000Z
DTEND:20210128T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/32
DESCRIPTION:by Teresa Conde (Universität Stuttgart) as part of FD Seminar
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grzegorz Bobiński (Nicolaus Copernicus University)
DTSTART:20210204T140000Z
DTEND:20210204T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/33
DESCRIPTION:by Grzegorz Bobiński (Nicolaus Copernicus University) as part
of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Barnard (DePaul University)
DTSTART:20210211T140000Z
DTEND:20210211T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/34
DESCRIPTION:by Emily Barnard (DePaul University) as part of FD Seminar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hipólito Treffinger (Rheinische Friedrich-Wilhelms-Universität B
onn)
DTSTART:20210218T140000Z
DTEND:20210218T150000Z
DTSTAMP:20260404T131145Z
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://stable.researchseminars.org/talk/fd-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:İlke Çanakçı (Vrije Universiteit Amsterdam)
DTSTART:20210225T140000Z
DTEND:20210225T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/36
DESCRIPTION:by İlke Çanakçı (Vrije Universiteit Amsterdam) as part of
FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javad Asadollahi (University of Isfahan)
DTSTART:20210304T140000Z
DTEND:20210304T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/37
DESCRIPTION:by Javad Asadollahi (University of Isfahan) as part of FD Semi
nar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Franzen (Ruhr-Universität Bochum)
DTSTART:20210311T140000Z
DTEND:20210311T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/38
DESCRIPTION:by Hans Franzen (Ruhr-Universität Bochum) as part of FD Semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Gelinas
DTSTART:20210318T140000Z
DTEND:20210318T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/39
DESCRIPTION:by Vincent Gelinas as part of FD Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Eckert (Universität Bielefeld)
DTSTART:20210325T140000Z
DTEND:20210325T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/40
DESCRIPTION:by Sebastian Eckert (Universität Bielefeld) as part of FD Sem
inar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Šťovíček (Charles University)
DTSTART:20210401T130000Z
DTEND:20210401T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/41
DESCRIPTION:by Jan Šťovíček (Charles University) as part of FD Seminar
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Bodzenta-Skibińska (University of Warsaw)
DTSTART:20210415T130000Z
DTEND:20210415T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/42
DESCRIPTION:Title: Abelian envelopes of exact categories\nby Agnieszka Bodzent
a-Skibińska (University of Warsaw) as part of FD Seminar\n\nAbstract: TBA
\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Hua (University of Hong Kong)
DTSTART:20210422T130000Z
DTEND:20210422T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/43
DESCRIPTION:Title: Cluster categories and rational curves\nby Zheng Hua (Unive
rsity of Hong Kong) as part of FD Seminar\n\n\nAbstract\nGiven a semi-simp
le collection of rational curves on a smooth quasi-projective 3-fold\, its
multipointed noncommutative deformation is represented by a negatively gr
aded DGA $\\Gamma$. The finite dimensionality of the cohomology of $\\Gamm
a$ seems to relate to contractibility of the collection of rational curves
. For CY 3-folds\, $\\Gamma$ is a bimodule 3CY DG algebra. If we further a
ssume contractibility then $H^0\\Gamma$ is isomorphic to the contraction a
lgebra of Donovan and Wemyss. And the cluster category of $\\Gamma$ is dg-
equivalent to the singularity category of the contracted space. In some se
nse the CY algebra $\\Gamma$ links the deformation theory of the exception
al fibres and the singularity theory of the contracted space. In this talk
I will present a joint work with Bernhard Keller\, where we prove that th
e derived Morita type of the contraction algebra together with a canonical
class in its 0-th Hochschild homology defined via CY structure determines
the analytic type of the singularity of the contracted space.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Magdalena Boos (Ruhr-Universität Bochum)
DTSTART:20210429T130000Z
DTEND:20210429T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/44
DESCRIPTION:Title: On symmetric quivers and their degenerations\nby Magdalena
Boos (Ruhr-Universität Bochum) as part of FD Seminar\n\n\nAbstract\nWe in
troduce the notion of a symmetric quiver as provided by Derksen and Weyman
in 2002 and discuss symmetric degenerations in this context (which corres
pond to orbit closure relations in the symmetric representation variety).
After motivating our particular interest in the latter by presenting conne
ctions to group actions in algebraic Lie Theory\, we explain our main ques
tions: are symmetric degenerations induced by “usual” degenerations in
the representation variety of the underlying quiver? We look at (counter)
examples and recent results.\n\nThis is joint work with G. Cerulli Irelli
and F. Esposito.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Iyama (The University of Tokyo)
DTSTART:20210513T130000Z
DTEND:20210513T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/45
DESCRIPTION:Title: Periodic trivial extension algebras and fractionally Calabi-Yau
algebras\nby Osamu Iyama (The University of Tokyo) as part of FD Semi
nar\n\n\nAbstract\nWe study periodicity and twisted periodicity of the tri
vial extension algebra T(A) of a finite-dimensional algebra A. We prove th
at (twisted) periodicity of the trivial extension is equivalent to A being
(twisted) fractionally Calabi–Yau. Moreover\, twisted periodicity of T(
A) is equivalent to the d-representation-finiteness of the r-fold trivial
extension algebra Tr(A) for some positive integers r and d. These results
allow us to construct a large number of new examples of periodic as well a
s fractionally Calabi–Yau algebras\, and give answers to several open qu
estions. This is a joint work with Aaron Chan\, Erik Darpö and René Marc
zinzik.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gordana Todorov (Northeastern University)
DTSTART:20210603T130000Z
DTEND:20210603T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/46
DESCRIPTION:Title: Cluster Structures and Cluster Theories\nby Gordana Todorov
(Northeastern University) as part of FD Seminar\n\n\nAbstract\n(Joint wor
k with Kiyoshi Igusa and Job D. Rock)\n\nI will discuss continuous cluster
categories\, generalizations of those\, cluster structures\, examples whe
n only conditions for “cluster theories”\, but not “cluster structur
es” (in the sense of BIRS) are satisfied. Also relations between various
cluster theories will be stated (some known\, some naturally expected).\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincent Gelinas
DTSTART:20210610T130000Z
DTEND:20210610T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/47
DESCRIPTION:Title: Some invariants related to the finitistic dimension\nby Vin
cent Gelinas as part of FD Seminar\n\n\nAbstract\nThe finitistic dimension
of Artin algebras is notoriously hard to understand. In this talk\, we’
ll discuss an attempt to pin it down in terms of a new invariant\, defined
more generally over sufficiently nice Noetherian rings. Originally meant
to model the finitistic dimension of Iwanaga-Gorenstein rings\, it unexpec
tedly also gave the correct answer for commutative local Noetherian rings\
, Artin algebras of radical square zero\, and (due to recent results of Ri
ngel and Sen) Nakayama algebras. Given time\, we’ll also discuss links w
ith the notion of “finitistic” Auslander algebras recently introduced
by Marczinzik.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Brüstle (Université de Sherbrooke)
DTSTART:20210617T130000Z
DTEND:20210617T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/48
DESCRIPTION:Title: On length functions for an exact category\nby Thomas Brüst
le (Université de Sherbrooke) as part of FD Seminar\n\n\nAbstract\nThe no
tion of an exact category has been introduced by Quillen to axiomatize hom
ological properties of abelian categories. It allows to define and study h
omological properties of an exact category\, and to define its derived cat
egory. However\, it turns out that the fundamental concept of length\, as
known for modules\, is less suitable to be studied in the context of an ex
act category. We aim in this talk to present some recent developments show
ing for which kind of exact categories an analogue of the Jordan-Hölder p
roperty holds\, and what one can expect from the notion of length in gener
al. We also present results on the lattice structure of the set of all exa
ct structures that can be attached to a fixed additive category.\n\nSome o
f the presented results are joint work with Rose-Line Baillargeon\, Mikhai
l Gorsky\, Souheila Hassoun and Aran Tattar.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Universität Hamburg)
DTSTART:20210722T130000Z
DTEND:20210722T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/49
DESCRIPTION:Title: Geometric models of Ginzburg algebras via local-to-global princ
iples\nby Merlin Christ (Universität Hamburg) as part of FD Seminar\n
\n\nAbstract\nThe derived categories of different classes of algebras (e.g
. gentle algebras) and dg-algebras (e.g. Ginzburg algebras of triangulated
surfaces) have recently been described in terms of surfaces\, in so-calle
d geometric models. Results include the description of objects in terms of
curves in a surface and Hom’s in terms of intersections. These algebras
have in common that they arise via gluing\, i.e. as the global sections o
f a constructible cosheaf. In the talk\, we will describe the gluing const
ruction for (relative) Ginzburg algebras of triangulated surfaces and comp
are it with the gluing construction for gentle algebras. We will then disc
uss how the gluing constructions naturally lead to the geometric models of
their derived categories.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Van Nguyen (United States Naval Academy)
DTSTART:20210506T130000Z
DTEND:20210506T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/50
DESCRIPTION:Title: Quantum symmetries through the lens of linear algebra\nby V
an Nguyen (United States Naval Academy) as part of FD Seminar\n\n\nAbstrac
t\nThe McKay matrix $M_V$ records the result of tensoring the simple modul
es with a finite-dimensional module $V$. In the case of finite groups\, th
e eigenvectors for $M_V$ are the columns of the character table\, and the
eigenvalues come from evaluating the character of $V$ on conjugacy class r
epresentatives.\n\nIn this talk\, we will explore what can be said about s
uch eigenvectors when the McKay matrix is determined by modules over an ar
bitrary finite-dimensional Hopf algebra $H$. Here\, the McKay matrix \n$M_
V$ encodes quantum symmetries coming from the actions of $H$. We prove gen
eral results about $M_V$ by using the coproduct and the characters of simp
le and projective $H$-modules\, and also obtain results for a different ma
trix that encodes the fusion rules for Hopf algebra $H$. We illustrate the
se results for the small quantum group $u_q(\\mathfrak{sl}_2)$\, where $q$
is a root of unity (and generally for the Drinfeld double $D_n$ of the Ta
ft algebra). In these examples\, the eigenvalues and eigenvectors for thes
e matrices can be described in terms of several kinds of Chebyshev polynom
ials.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kalck
DTSTART:20210624T130000Z
DTEND:20210624T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/51
DESCRIPTION:Title: A surface and a threefold with equivalent singularity categorie
s\nby Martin Kalck as part of FD Seminar\n\n\nAbstract\nWe start with
an introduction to singularity categories and equivalences between them. I
n particular\, we recall known results about singular equivalences between
commutative rings\, which go back to Knörrer\, Yang\, Kawamata and a joi
nt work with Karmazyn. Then we explain a new singular equivalence between
an affine surface and an affine threefold. This seems to be the first (non
-trivial) example of a singular equivalence involving rings of even and od
d Krull dimension.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khrystyna Serhiyenko (University of Kentucky)
DTSTART:20210715T130000Z
DTEND:20210715T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/52
DESCRIPTION:Title: Maximal green sequences for string algebras\nby Khrystyna S
erhiyenko (University of Kentucky) as part of FD Seminar\n\n\nAbstract\nMa
ximal green sequences are certain transformations of quivers that were fir
st introduced by Keller in the context of cluster algebras. Later they wer
e generalized to the setting of finite dimensional algebras\, where a maxi
mal green sequence is a finite maximal chain in the lattice of torsion cla
sses. More recently\, it was shown that these sequences are in bijection w
ith forward hom-orthogonal sequences of bricks in the module category. We
use the latter approach to study existence and number of maximal green seq
uences for string algebras. This is joint work with Al Garver.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Jørgensen (Aarhus University)
DTSTART:20210729T130000Z
DTEND:20210729T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/53
DESCRIPTION:Title: Abelian subcategories of triangulated categories induced by sim
ple minded systems\nby Peter Jørgensen (Aarhus University) as part of
FD Seminar\n\n\nAbstract\nIf $k$ is a field\, $A$ a finite dimensional $k
$-algebra\, then the simple $A$-modules form a simple minded collection in
the derived category $D^b(mod A)$. Their extension closure is $mod A$\; i
n particular\, it is abelian. This situation is emulated by a general simp
le minded collection $S$ in a suitable triangulated category $C$. In parti
cular\, the extension closure $\\langle S \\rangle$ is abelian\, and there
is a tilting theory for such abelian subcategories of $C$. These statemen
ts follow from $\\langle S \\rangle$ being the heart of a bounded t-struct
ure.\n\nIt is a defining characteristic of simple minded collections that
their negative self extensions vanish in every degree. Relaxing this to va
nishing in degrees $\\{-w+1\, \\dots\, -1\\}$ where $w$ is a positive inte
ger leads to the rich\, parallel notion of $w$-simple minded systems\, whi
ch have recently been the subject of vigorous interest within negative clu
ster tilting 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-stru
cture. However\, it is possible to prove by different means that $\\langle
S \\rangle$ is still abelian and that there is a tilting theory for such
abelian subcategories. We will explain the theory behind this\, which is b
ased on Quillen’s notion of exact categories.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/54
DESCRIPTION:Title: Rigid indecomposable modules in Grassmannian cluster categories
\nby Ana García-Elsener (Universidad Nacional de Mar del Plata) as pa
rt of FD Seminar\n\n\nAbstract\nThe coordinate ring of the Grassmannian va
riety of $k$-dimensional subspaces in $\\mathbb{C^n}$ has a cluster algebr
a structure with Plucker relations giving rise to exchange relations. We s
tudy indecomposable modules of the corresponding Grassmannian cluster cate
gories of type $(k\,n)$. Jensen\, King\, and Su have associated a Kac-Mood
y root system to the category and shown that in the finite types\, rigid i
ndecomposable modules correspond to roots. We provide evidence for this as
sociation in the infinite types: we show that every indecomposable rank $2
$ module corresponds to a root of the associated root system. We also stud
y roots and indecomposable rank $3$ modules for the case $(3\,n)$.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kent Vashaw (Louisiana State University)
DTSTART:20210708T130000Z
DTEND:20210708T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/55
DESCRIPTION:Title: Noncommutative Tensor Triangular Geometry and Cohomological Sup
port Varieties\nby Kent Vashaw (Louisiana State University) as part of
FD Seminar\n\n\nAbstract\nRecently\, there has been significant interest
in the tensor product property for cohomological support varieties of Hopf
algebras and tensor categories. We will describe a method for approaching
the tensor product property by way of a noncommutative version of Balmer
’s tensor triangular geometry in the general setting of a monoidal trian
gulated category. We prove related properties about the collections of thi
ck one-sided and two-sided ideals of the category\, and then are often abl
e to use the universal properties of the Balmer support to obtain applicat
ions to cohomological supports. Examples arising from the representation t
heory of Hopf algebras will be discussed throughout. This is joint work wi
th Daniel Nakano and Milen Yakimov.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hugh Thomas (Université du Québec à Montréal)
DTSTART:20210902T130000Z
DTEND:20210902T140000Z
DTSTAMP:20260404T131145Z
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\nA
bstract\nLet A be a finite-dimensional algebra of finite representation ty
pe. I will describe an affine algebraic variety whose totally non-negative
part reflects the combinatorics of the tau-tilting fan of A. Starting fro
m a Dynkin quiver\, one obtains something closely related to the correspon
ding Fock–Goncharov cluster X variety\, while in general\, points on (on
e component of) the variety can be given in terms of ratios of F-polynomia
ls\; the upshot is that this construction can be viewed as an extension of
some of the beautiful features of cluster algebras to a more general sett
ing. Nonetheless\, familiarity with cluster algebras will not be needed to
understand the talk. A conjecture related to functoriality properties of
the construction will be discussed. This is part of a joint project with N
ima Arkani-Hamed\, Hadleigh Frost\, Pierre-Guy Plamondon\, and Giulio Salv
atori.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johanne Haugland (Norges teknisk-naturvitenskapelige universitet\,
NTNU)
DTSTART:20210909T130000Z
DTEND:20210909T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/57
DESCRIPTION:Title: Higher Koszul duality and connections with n-hereditary algebra
s\nby Johanne Haugland (Norges teknisk-naturvitenskapelige universitet
\, NTNU) as part of FD Seminar\n\n\nAbstract\nWe discuss a connection betw
een two areas of independent interest in representation theory\, namely Ko
szul duality and higher homological algebra. This is studied through a gen
eralization of the notion of T-Koszul algebras\, as introduced by Madsen a
nd Green–Reiten–Solberg. After giving an introduction to the relevant
background material\, we present a higher version of classical Koszul dual
ity and sketch some applications for n-hereditary algebras. In particular\
, we see that an important class of our generalized Koszul algebras can be
characterized in terms of n-representation infinite algebras. As a conseq
uence\, we show that an algebra is n-representation infinite if and only i
f its trivial extension is (n+1)-Koszul with respect to its degree 0 part.
A generalized notion of almost Koszulity in the sense of Brenner–Butler
–King yields similar results in the n-representation finite case. \n\nTh
is talk is based on joint work with Mads H. Sandøy.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Sistko (Manhattan College)
DTSTART:20210916T130000Z
DTEND:20210916T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/58
DESCRIPTION:Title: F1 Representations and Hall Algebras\nby Alexander Sistko (
Manhattan College) as part of FD Seminar\n\n\nAbstract\nFor any quiver Q\,
one can associate a category of Q-representations over F1\, the so-called
“field with one element.” This category\, and its associated Ringel-H
all algebra\, retain many features of representations over fields while ex
hibiting interesting differences. In this talk\, we discuss recent advance
s in the study of F1-representations and their Hall algebras. After an ove
rview of the fundamental background\, we describe how F1-representations m
ay be studied via coefficient quivers. This approach yields results on rep
resentation type over F1 and new insights into the associated Hall algebra
s. With the remaining time\, we discuss an ongoing project which applies F
1-representation theory to compute the Euler characteristics of certain qu
iver Grassmannians. This is joint work with Jaiung Jun.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steffen Oppermann (Norges teknisk-naturvitenskapelige universitet\
, NTNU)
DTSTART:20210923T130000Z
DTEND:20210923T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/59
DESCRIPTION:Title: Rank decompositions and associated exact categories for multi-p
arameter persistence modules\nby Steffen Oppermann (Norges teknisk-nat
urvitenskapelige universitet\, NTNU) as part of FD Seminar\n\n\nAbstract\n
The motivation for the work I am going to speak about comes from a recent
field of application of representation theory: the study of persistent hom
ology in topological data analysis.\n\nI will try to explain how and why o
ne might turn data into a quiver representation. Most classically this wil
l be a representation of a linearly ordered quiver of type A. Such a repre
sentation can be depicted as a collection of line segments\, corresponding
to the supports of the indecomposable summands. This depiction is known a
s a “bar code”. One interprets the results by considering the longest
bars most significant.\n\nIn many applications\, it would be natural to co
nsider multiple parameters\, equivalently representation of tensor product
s of multiple type A quivers. These algebras are wild in almost all cases\
, and indecomposables are not determined by their support as in the one pa
rameter case.\n\nThe original part of my talk will be based on joint work
with Magnus Botnan and Steve Oudot. We introduce a candidate for a bar cod
e of a 2-parameter persistence module\, and observe that it is closely rel
ated to an exact structure on the representation category.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART:20210930T130000Z
DTEND:20210930T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/60
DESCRIPTION:Title: The Heisenberg category of a category\nby Timothy Logvinenk
o (Cardiff University) as part of FD Seminar\n\n\nAbstract\nIn 90s Nakajim
a and Grojnowski 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\, Kr
ug lifted this to derived categories\nand generalised it to the symmetric
quotient stacks of any smooth projective variety.\n\nOn the other hand\, K
hovanov introduced a categorification of the free boson Heisenberg algebra
\, i.e. the one associated to the rank 1 lattice. It is a monoidal categor
y whose\nmorphisms are described by a certain planar diagram calculus whic
h categorifies the Heisenberg relations. A similar categorification was co
nstructed by Cautis and Licata for the Heisenberg algebras of ADE type roo
t lattices.\n\nWe show how to associate the Heisenberg 2-category to any s
mooth and proper DG category and then define its Fock space 2-representati
on. This construction unifies all the results above and extends them to wh
at can be viewed as the generality of arbitrary noncommutative smooth and
proper schemes.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Herschend (Uppsala University)
DTSTART:20211007T130000Z
DTEND:20211007T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/61
DESCRIPTION:Title: Double covers of quiver Heisenberg algebras as higher preprojec
tive algebras\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
discuss several algebras associated to Q and how they are related. As a s
tarting point we’ll consider the path algebra of Q and how its represent
ation theory is reflected in homological properties of the preprojective a
lgebra 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 t
he quiver Heisenberg algebra of Q. This algebra is a particular case of th
e central extensions of preprojective algebras introduced by Etingof-Rains
. It has many similar properties to the preprojective algebra. Finally\, w
e will consider a certain double cover of the quiver Heisenberg algebra\,
more precisely its second quasi-Veronese algebra. This algebra is also gra
ded 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 has global dimension 2 and is 2-hereditary algebra in the sense of Iy
ama’s higher dimensional Auslander-Reiten theory.\n\nThis talk is based
on ongoing joint work with Hiroyuki Minamoto.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Palu (Université UPJV Amiens)
DTSTART:20211014T130000Z
DTEND:20211014T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/62
DESCRIPTION:Title: Mutation in hereditary extriangulated categories\nby Yann P
alu (Université UPJV Amiens) as part of FD Seminar\n\n\nAbstract\nMotivat
ed by the categorification of cluster algebras\, Buan–Marsh–Reineke–
Reiten–Todorov introduced a theory of mutation for cluster-tilting objec
ts in certain 2-Calabi–Yau triangulated categories. This lead to many va
riations or generalisations\, such as tau-tilting\, 2-term silting or rela
tive tilting.\n\nThe point-of-view of extriangulated categories\, introduc
ed in collaboration with Hiroyuki Nakaoka\, turns out to be relevant for t
he study of mutations. Indeed\, most mutation theories arising in represen
tation theory can be related to the existence of certain “good” extria
ngulated structures. This is the point that I will try and make in this ta
lk\, by introducing the notion of a 0-Auslander extriangulated category.\n
\nThis is based on joint works with Mikhail Gorsky\, Hiroyuki Nakaoka\, Ar
nau Padrol\, Vincent Pilaud and Pierre-Guy Plamondon.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroki Matsui (Tokushima University)
DTSTART:20211021T130000Z
DTEND:20211021T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/63
DESCRIPTION:Title: Prime thick subcategories of derived categories associated with
noetherian schemes\nby Hiroki Matsui (Tokushima University) as part o
f FD Seminar\n\n\nAbstract\nIn 2005\, Balmer introduced the notion of a pr
ime thick tensor ideal for a tensor triangulated category T as an analogou
s concept to a prime ideal of a commutative ring. Using prime thick tensor
ideals\, Balmer established the epoch-making theory so-called the tensor-
triangular geometry which allows us to study T by commutative-algebraic/al
gebro-geometric approaches. On the other hand\, recently I have introduced
the notion of prime thick subcategories to develop a similar theory to th
e tensor-triangular geometry for tensor triangulated categories without te
nsor structures. In this talk\, we study prime thick subcategories of the
perfect derived category D^perf(X)\, the bounded derived category D^b(X)\,
and the singularity category D^sg(X) of a noetherian scheme X. Especially
\, we give a characterization of a point x of X to be a complete intersect
ion or a hypersurface in terms of prime thick subcategories of such derive
d categories.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calin Chindris (University of Missouri)
DTSTART:20211028T130000Z
DTEND:20211028T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/64
DESCRIPTION:Title: Sigma-critical quiver representations and applications to the P
aulsen Problem in Frame Theory\nby Calin Chindris (University of Misso
uri) as part of FD Seminar\n\n\nAbstract\nSigma-critical representations a
re quiver representations that satisfy certain matrix equations. They aris
e naturally in the context of the Kempf-Ness theorem on closed orbits in I
nvariant Theory. After introducing all the relevant concepts\, I will firs
t describe a result that gives necessary and sufficient conditions for the
orbit of a representation to contain a sigma-critical representation. I w
ill then explain how this result can be used to solve the Paulsen Problem
for matrix frames. This is based on joint work with Jasim Ismaeel.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changchang Xi (Capital Normal University)
DTSTART:20211104T140000Z
DTEND:20211104T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/65
DESCRIPTION:Title: Symmetric subcategories and good tilting modules\nby Changc
hang Xi (Capital Normal University) as part of FD Seminar\n\n\nAbstract\nT
ilting modules have played an important role in representation theory of a
lgebras. Especially\, infinitely generated tilting modules provide complet
ely different features. In this case\, recollements of triangulated catego
ries in the sense of Beilinson-Bernstein-Deligne enter into the play. In t
his talk\, we introduce symmetric subcategories and show that\, for any go
od tilting module over an algebra\, the derived category of the endomorphi
sm algebra of the tilting module is always a recollement of the derived ca
tegories of the given algebra and a symmetric subcategory of a module cate
gory. Explicit examples of symmetric subcategories associated to 2-good ti
lting modules over commutative Gorenstein rings are presented. This talk r
eports a joint work with Hongxing Chen.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/66
DESCRIPTION:Title: Periodic actions on distributive lattices and counterparts in a
lgebra\nby Emine Yıldırım (Isaac Newton Institute for Mathematical
Sciences and University of Cambridg) as part of FD Seminar\n\n\nAbstract\n
Let L be a distributive lattice and A be its incidence algebra. There is a
celebrated combinatorial action on posets called “rowmotion”. Thanks
to a result of Iyama-Marczinzik\, we can think of this combinatorial actio
n as the grade bijection defined on the algebra A. On the other hand\, the
Coxeter transformation plays an important role in representation theory o
f algebras and in some cases it shows some periodicity. The periodicity of
the Coxeter transformation is motivated by the fractionally Calabi-Yau pr
operty of a certain category. Motivated by these\, we show that the compos
ition of 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://stable.researchseminars.org/talk/fd-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow)
DTSTART:20211118T140000Z
DTEND:20211118T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/67
DESCRIPTION:Title: Thick Subcategories and Lattices\nby Sira Gratz (University
of Glasgow) as part of FD Seminar\n\n\nAbstract\nThe computation of latti
ces of thick subcategories has emerged as a popular topic and serves as a
more achievable analogue of classifying objects. Often one understands suc
h lattices by describing them in terms of some associated topological spac
e. However\, in many representation theoretic examples this is not possibl
e. I’ll explain what the obstruction is and mention work in progress aim
ed at addressing this issue.\n\nThis talk is based on joint work with Greg
Stevenson.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Federico Barbacovi (University College London)
DTSTART:20211125T140000Z
DTEND:20211125T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/68
DESCRIPTION:Title: Dynamics in triangulated categories\nby Federico Barbacovi
(University College London) as part of FD Seminar\n\n\nAbstract\nIn topolo
gy a dynamical system is given by a couple $(X\, f)$\, where $X$ is a topo
logical space and $f : X \\rightarrow X$ is a continuous map. Dimitrov —
Haiden — Katzarkov — Kontsevich generalised this notion to that of a
categorical dynamical system. To measure the complexity of such system\, t
hey also introduced the concept of categorical entropy. A famous theorem o
f Gromov and Yomdin relates the topological entropy of a holomorphic autom
orphism of a complex manifold with the action of the automorphism in cohom
ology. In this talk I will report on joint work with Jongmyeong Kim in whi
ch we provide a sufficient condition that ensures that (a weaker version o
f) an analogue theorem holds in categorical dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constanze Roitzheim (University of Kent)
DTSTART:20211202T140000Z
DTEND:20211202T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/69
DESCRIPTION:Title: Homotopy theory of finite total orders\, trees and chicken feet
\nby Constanze Roitzheim (University of Kent) as part of FD Seminar\n\
n\nAbstract\nA transfer system is a graph on a lattice satisfying certain
restriction and composition properties. They were first studied on the lat
tice of subgroups of a finite group in order to examine equivariant homoto
py commutativity\, which then unlocked a wealth of links to combinatorial
methods. On a finite total order [n]\, transfer systems can be used to cla
ssify different homotopy theories on [n]. The talk will involve plenty of
examples and not assume any background knowledge.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Coelho Simões (Lancaster University)
DTSTART:20211209T140000Z
DTEND:20211209T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/70
DESCRIPTION:Title: From gentle to string algebras: a geometric model\nby Raque
l Coelho Simões (Lancaster University) as part of FD Seminar\n\n\nAbstrac
t\nGeometric models associated to triangulations of Riemann surfaces arose
in the context of cluster algebras and have since been used as an importa
nt tool to study representation theory of algebras and provide connections
with algebraic geometry and symplectic geometry.\n\nSignificant applicati
ons of geometric models include a description of extensions and a classifi
cation of support tau-tilting modules over gentle algebras. Gentle algebra
s are a particular subclass of string algebras\, which are of tame represe
ntation type\, meaning it is often possible to get a global understanding
of their representation theory.\n\nIn this talk I will describe the module
category of a gentle algebra via partial triangulations of unpunctured su
rfaces and explain how to extend this model to a geometric model of the mo
dule category of any string algebra. This is based on joint work in progre
ss with Karin Baur.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (University of Glasgow)
DTSTART:20211216T140000Z
DTEND:20211216T150000Z
DTSTAMP:20260404T131145Z
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 alg
ebraic terms\, the purpose of the talk is to classify finite dimensional J
acobi algebras arising on the d-loop quiver. The surprising thing is that
a classification should exist at all\, and it is even more surprising tha
t ADE enters. I will spend most of my time explaining what the algebras a
re\, why they classify\, and how to intrinsically extract ADE information
from them. I will also say a little on why this should be viewed as an ex
tension of classical singularity theory\, since many of the ideas are insp
ired 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 the applications of the above classification to curve counting and b
irational geometry. This is all joint work with Gavin Brown.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (University of Bonn)
DTSTART:20220113T140000Z
DTEND:20220113T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/72
DESCRIPTION:Title: Weight structures and (geometric) representation theory\nby
Catharina Stroppel (University of Bonn) as part of FD Seminar\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jon Woolf (University of Liverpool)
DTSTART:20220120T140000Z
DTEND:20220120T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/73
DESCRIPTION:Title: Bridgeland stability conditions with massless objects\nby J
on Woolf (University of Liverpool) as part of FD Seminar\n\n\nAbstract\nTh
e Bridgeland stability space of a triangulated category is a non-compact c
omplex manifold with a wall-and-chamber structure capturing interesting as
pects of the category’s structure.\n\nI will describe joint work with Br
oomhead\, Pauksztello and Ploog in which we partially compactify the stabi
lity space by allowing `degenerate’ stability conditions with massless o
bjects.\n\nOne reason this is interesting is that the added boundary point
s are closely related to the walls. I will illustrate this connection in l
ow-dimensional examples arising from quivers with two vertices.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Genovese (Charles University)
DTSTART:20220127T140000Z
DTEND:20220127T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/74
DESCRIPTION:Title: A derived Gabriel-Popescu theorem for t-structures\nby Fran
cesco Genovese (Charles University) as part of FD Seminar\n\n\nAbstract\nT
he Gabriel-Popescu theorem exhibits any Grothendieck abelian category as a
n exact localization of a category of modules over a suitable ring. Genera
lizing to the derived framework\, we replace abelian categories with (enha
nced) triangulated categories endowed with a t-structure. Such categories\
, under appropriate “Grothendieck-like” assumptions\, can be exhibited
as t-exact quotients of derived categories of suitable dg-algebras concen
trated in nonpositive degrees\, hence yielding a “derived Gabriel-Popesc
u theorem”. In this talk\, we describe a proof of this result which expl
oits the underlying philosophy that “(enhanced) triangulated categories
with t-structures really behave like abelian categories”. We shall encou
nter suitably defined “derived epi-mono factorizations” and derived in
jective objects. This is joint work with Julia Ramos González.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (Universidad Nacional Autónoma de México
)
DTSTART:20220203T140000Z
DTEND:20220203T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/75
DESCRIPTION:Title: Deformation theory for finite cluster complexes\nby Alfredo
Nájera Chávez (Universidad Nacional Autónoma de México) as part of FD
Seminar\n\n\nAbstract\nCluster complexes are a certain class of simplicia
l complexes that naturally arise in the theory of cluster algebras. They c
odify a wealth of fundamental information about cluster algebras. The purp
ose of this talk is to elaborate on a geometric relationship between clust
er algebras and cluster complexes. In vague words this relationship is the
following: cluster algebras of finite cluster type with universal coeffic
ients may be obtained via a torus action on a Hilbert scheme. In particula
r\, we will discuss the deformation theory of the Stanley-Reisner ring ass
ociated to a finite cluster complex and present some applications related
to the Gröbner theory of the ideal of relations among cluster and frozen
variables of a cluster algebra of finite cluster type. Time permitting I w
ill elaborate on how to generalize this approach to the context of tau-til
ting finite algebras. This is based on a joint project with Nathan Ilten a
nd Hipolito Treffinger whose first outcome is the preprint arXiv:2111.0256
6.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tsutomu Nakamura (The University of Tokyo)
DTSTART:20220210T140000Z
DTEND:20220210T150000Z
DTSTAMP:20260404T131145Z
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\nAbstract\nAuslander and Buchweitz (1989) showed that the class of maxim
al Cohen-Macaulay modules over a Cohen-Macaulay local ring with a canonica
l module is part of a complete cotorsion pair in the category of finitely
generated modules. As shown by Miyachi (1998)\, this fact holds more gener
ally for an R-order over a Cohen-Macaulay ring R with a (pointwise) canoni
cal module. On the other hand\, Holm (2017) established a perfect cotorsio
n pair (X\, Y) in the category of all modules over a Cohen-Macaulay local
ring with a canonical module such that X is the smallest definable subcate
gory containing all maximal Cohen-Macaulay modules. This result was deduce
d by showing 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 sugges
t an infinitely generated version of a canonical module\, and explain how
this concept makes sense to generalize Holm’s results to a non-commutati
ve and non-local setup like Miyachi’s work. It is also possible to partl
y avoid the existence of a canonical module\, so that some results on bala
nced big Cohen-Macaulay approximation due to Simon (2009) and Holm (2017)
can be unified. This work is inspired by ongoing joint work with Michal Hr
bek and Jan Stovicek about large (co)tilting complexes over a commutative
noetherian ring\, and related to recent joint work with Ryo Kanda about fl
at cotorsion modules over Noether algebras.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Latyntsev (University of Oxford)
DTSTART:20220217T140000Z
DTEND:20220217T150000Z
DTSTAMP:20260404T131145Z
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\nAbstra
ct\nThere is an extremely rich history of interaction between string theor
y and the mathematics of moduli spaces\, for instance cohomological Hall a
lgebras/algebras of BPS states\, or vertex/chiral algebras.\n\nIn this tal
k\, I will explain a link between two of these: Joyce’s vertex algebras
attached to the moduli stack of objects in an abelian category\, and one d
imensional CoHAs. This is based on my recent paper 2110.14356\, whose main
result says that the cohomologies of such stacks are “quantum vertex al
gebras”: the factorisation/vertex analogues of quasitriangular bialgebra
s. The main technical tool is a “bivariant” Euler class which makes to
rus localisation work in this context. I will discuss applications of thes
e techniques to CoHAs of coherent sheaves on a curve and future directions
.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Janina C. Letz (Universität Bielefeld)
DTSTART:20220224T140000Z
DTEND:20220224T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/78
DESCRIPTION:by Janina C. Letz (Universität Bielefeld) as part of FD Semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (Universität Stuttgart)
DTSTART:20220303T140000Z
DTEND:20220303T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/79
DESCRIPTION:by Zhengfang Wang (Universität Stuttgart) as part of FD Semin
ar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Schenfisch (Montana State University)
DTSTART:20220310T140000Z
DTEND:20220310T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/80
DESCRIPTION:Title: Algebraic K-Theory of Zig-Zag Persistence Modules\nby Anna
Schenfisch (Montana State University) as part of FD Seminar\n\n\nAbstract\
nIn this talk\, we will first see how persistence modules (a primary tool
in topological data analysis) have a natural home in the setting of strati
fied spaces and constructible cosheaves. In particular\, we focus on zig-z
ag modules\, which correspond to one-parameter filtrations. We then outlin
e how the algebraic K-theory of zig-zag modules can be computed via an add
itivity result\, aided by an equivalence between the category of zig-zag m
odules and the combinatorial entrance path category on a stratified $\\mat
hbb{R}$. Once equipped with the K-theory of zig-zag modules\, we see other
one-parameter topological summaries (such as Euler characteristic curves)
as classes of $K_0$.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (The University of Tokyo)
DTSTART:20220317T140000Z
DTEND:20220317T150000Z
DTSTAMP:20260404T131145Z
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-algebr
a which is finitely generated as an R-module. In this talk\, we study clas
sification problem of torsion classes and related subcategories of the cat
egory mod A of finitely generated A-modules. In the case where R is a fiel
d\, there are many studies of subcategories of mod A. τ-tilting modules\,
introduced by Adachi-Iyama-Reiten\, play a central role in the recent dev
elopment of such studies. We see that silting modules also play an importa
nt role for classification problem of torsion classes of Noetherian algebr
as. In the case where A is commutative\, Serre subcategories\, torsion cla
sses and torsionfree classes are classified by using subsets of the prime
spectrum of R by Gabriel\, Stanley-Wang and Takahashi. We see that our res
ults recover their results. This is joint work with Osamu Iyama.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charley Cummings (University of Bristol)
DTSTART:20220324T140000Z
DTEND:20220324T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/82
DESCRIPTION:Title: Left-right symmetry of the finitistic dimension\nby Charley
Cummings (University of Bristol) as part of FD Seminar\n\n\nAbstract\nThe
finitistic dimension conjecture is the assertion that the finitistic dime
nsion of a finite dimensional algebra is finite. This dimension can be def
ined in terms of left or right modules. In general\, the left and right fi
nitistic dimensions of an algebra are not equal\, but it is unknown if the
finiteness of the two dimensions is connected. In this talk\, we will tra
nslate the conjecture into a question about the connection between the lef
t and right finitistic dimensions of an algebra using quiver operations.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlie Beil (University of Graz)
DTSTART:20220331T130000Z
DTEND:20220331T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/83
DESCRIPTION:Title: Dimer quivers on genus g surfaces and noncommutative desingular
izations\nby Charlie Beil (University of Graz) as part of FD Seminar\n
\n\nAbstract\nA dimer algebra is a type of Jacobian algebra whose quiver $
Q$ embeds in a surface $S$\, such that each connected component of $S\\bac
kslash Q$ is simply connected and bounded by an oriented cycle of $Q$. It
was shown in 2009 that noetherian dimer algebras on a torus are noncommut
ative desingularizations of their centers\; in particular\, they are ‘ho
mologically smooth’ endomorphism rings. On higher genus surfaces\, howev
er\, these nice properties disappear. I will introduce special quotients o
f dimer algebras\, called ‘ghor algebras’\, where the relations come f
rom the quiver’s perfect matchings rather than a potential. On a torus\,
a dimer algebra coincides with its ghor algebra if and only if it is noet
herian\, whereas ghor algebras are almost never noetherian on higher genus
surfaces. Nevertheless\, I will describe how a ghor algebra\, on any genu
s gg surface\, may be viewed as a noncommutative desingularization of its
center. This is joint work with Karin Baur.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (University of Strasbourg)
DTSTART:20220407T130000Z
DTEND:20220407T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/84
DESCRIPTION:Title: Rational homotopy type of the moduli space of stable rational c
urves\nby Vladimir Dotsenko (University of Strasbourg) as part of FD S
eminar\n\n\nAbstract\nIn 2004\, Manin asked whether the cohomology of the
moduli space of stable rational curves with n marked points (= the Deligne
-Mumford compactification of the moduli space of smooth genus zero curves
with n marked points) is a Koszul algebra. This question remained open sin
ce. I shall present a solution to it\, proving that the answer is positive
for all n. An immediate consequence of my result is an explicit descripti
on of the rational homotopy Lie algebras of these spaces by generators and
relations. Time permitting\, I shall discuss some generalizations and mod
ifications of this result.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Giunti (Graz University of Technology)
DTSTART:20220414T130000Z
DTEND:20220414T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/85
DESCRIPTION:Title: Persistence modules and amplitudes\nby Barbara Giunti (Graz
University of Technology) as part of FD Seminar\n\n\nAbstract\nPersistenc
e theory is a powerful branch of Topological Data Analysis with many appli
cations. In this seminar\, I will briefly introduce it\, presupposing no p
revious knowledge of the topic. In particular\, I will discuss some finite
ness conditions on persistence modules. I will then introduce amplitudes\,
a special type of invariants that capture the idea of ‘‘size of persi
stence’’. Amplitudes can be defined on any abelian category and are pa
rticularly useful in the so-called multiparameter persistence\, where ther
e exists no discrete complete invariant. I will present some examples of a
mplitudes and discuss some of their properties.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sota Asai (Osaka University)
DTSTART:20220421T130000Z
DTEND:20220421T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/86
DESCRIPTION:Title: TF equivalence classes constructed from canonical decomposition
s\nby 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 d
imensional algebra over an algebraically closed field. Brüstle-Smith-Tref
finger introduced a wall-chamber structure on the real Grothendieck group
$K_0(\\operatorname{proj} A)_R$ via stability conditions of King. It is st
rongly related to TF equivalence\, which is an equivalence relation on $K_
0(\\operatorname{proj} A)_R$ defined by numerical torsion pairs of Baumann
-Kamnitzer-Tingley. Thanks to results by Yurikusa and Brüstle-Smith-Treff
inger\, I showed that the $g$-vector cone $C^+(U)$ associated to each 2-te
rm presilting complex $U$ in $K^b(\\operatorname{proj} A)$ is a TF equival
ence class in my previous study\, but we cannot obtain all TF equivalence
classes in this way unless $A$ is $\\tau$-tilting finite. In this joint wo
rk with Iyama\, we obtained a generalization of this construction of TF eq
uivalence classes by using canonical decompositions of elements in $K_0(\\
operatorname{proj} A)$ introduced by Derksen-Fei in the case that $A$ sati
sfies the condition called EE-tameness. I will talk about this result.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (The Australian National University)
DTSTART:20220428T130000Z
DTEND:20220428T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/87
DESCRIPTION:Title: Bridgeland stability conditions\, spherical objects\, and autoe
quivalences\nby Asilata Bapat (The Australian National University) as
part of FD Seminar\n\n\nAbstract\nConsider the space of Bridgeland stabili
ty conditions of a suitably nice triangulated category. Autoequivalences o
f the triangulated category act on the space of stability conditions. Fixi
ng a stability condition imposes extra combinatorial structure on the cate
gory\, that can be used to study the group of autoequivalences in various
different ways. This talk will showcase some of the fascinating structure
that emerges via this idea\, particularly for 2-Calabi–Yau categories as
sociated to quivers. This is based on joint work with Anand Deopurkar and
Anthony M. Licata.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (Tsinghua University)
DTSTART:20220505T130000Z
DTEND:20220505T140000Z
DTSTAMP:20260404T131145Z
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
construct a geometric model for the root category of any Dynkin diagram $Q
$\, which is an $h$-gon $V$ with cores\, where $h$ is the Coxeter number.
As an application\, we classify all spaces $ToSt(D)$ of totally stable sta
bility conditions on triangulated categories $D$\, where $D$ must be of th
e form $D^b(Q)$. More precisely\, we prove that $ToStD^b(Q)/C$ is isomorph
ic to the moduli spaces of stable $h$-gons of type $Q$. In particular\, an
$h$-gon $V$ of type $D_n$ is a centrally symmetric doubly punctured $2(n
−1)$-gon. $V$ is stable if it is convex and the punctures are inside the
level-$(n−2)$ diagonal-gon. Another interesting case is $E_6$\, where t
he (stable) $12$-gon can be realized as a pair of planar tiling pattern. T
his is a joint work with Xiaoting Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Ruhr-Universität Bochum)
DTSTART:20220519T130000Z
DTEND:20220519T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/89
DESCRIPTION:Title: Dimension expanders via quiver representations\nby Markus R
eineke (Ruhr-Universität Bochum) as part of FD Seminar\n\n\nAbstract\nDim
ension expanders\, introduced by Wigderson and Lubotzky-Zelmanov\, are a l
inear algebra analogue of the notion of expander graphs. We interpret this
notion in terms of quiver representations\, as a quantitative variant of
stabilty. We use Schofield’s recursive description of general subreprese
ntations to re-derive existence of dimension expanders and to determine op
timal expansion coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Cruz (Universität Stuttgart)
DTSTART:20220512T130000Z
DTEND:20220512T140000Z
DTSTAMP:20260404T131145Z
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\n
Every finite-dimensional algebra can be written as the endomorphism algebr
a of a projective module over a quasi-hereditary algebra. Moreover\, every
finite-dimensional algebra over an algebraically closed field admits a (s
plit) quasi-hereditary cover in the sense of Rouquier. So we may wonder ho
w closely 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 a
s a tool to measure the quality of (split) quasi-hereditary covers of Noet
herian algebras and how it can be used to construct new quasi-hereditary c
overs.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sentieri (Università degli Studi di Verona)
DTSTART:20220526T130000Z
DTEND:20220526T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/91
DESCRIPTION:Title: Wide subcategories obtained from cosilting pairs\nby France
sco Sentieri (Università degli Studi di Verona) as part of FD Seminar\n\n
\nAbstract\nIngalls and Thomas introduced a construction relating torsion
pairs and wide subcategories in the context of finite-dimensional modules
over hereditary algebras. Their work was later generalized by Marks and St
ovicek to arbitrary algebras. We apply this construction to cosilting tors
ion pairs in the category of all modules and give a description of the res
ulting wide subcategories as some generalized perpendicular categories. We
show that all the wide subcategories we obtain are coreflective and discu
ss the case in which they are bireflective. We conclude with an applicatio
n to the study of torsion pairs in the category of finite-dimensional modu
les. This is joint work with Lidia Angeleri.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rene Marczinzik
DTSTART:20220602T130000Z
DTEND:20220602T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/92
DESCRIPTION:Title: Dominant Auslander regular algebras and minimal Auslander-Cohen
-Macaulay algebras\nby Rene Marczinzik as part of FD Seminar\n\n\nAbst
ract\nWe introduce dominant Auslander regular algebras and minimal Ausland
er-Cohen-Macaulay algebras as a generalisation of higher Auslander algebra
s. As an 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 R
eiten. This is joint work in progress with Aaron Chan and Osamu Iyama.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Paquette (Royal Military College of Canada)
DTSTART:20220609T130000Z
DTEND:20220609T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/93
DESCRIPTION:Title: Free products of semi-simple algebras via quivers\nby Charl
es Paquette (Royal Military College of Canada) as part of FD Seminar\n\n\n
Abstract\nWe will see how quiver representation theory and stability allow
us to understand the (finite dimensional) representation theory of a free
product of semi-simple (associative) k-algebras. In particular\, we will
study the simple modules and modules in general position. We will see that
a module in general position is always semisimple\, and give an explicit
numeral equation to decide when it is simple. If time permits\, we will co
mment on the representation type (tame\, wild) and discuss how to use modu
li spaces of quivers to compute the number of parameters for the simple mo
dules in a given dimension. This is joint work with A. Buchanan\, I. Dimit
rov\, O. Grace\, D. Wehlau and T. Xu.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (The University of Tokyo)
DTSTART:20220616T130000Z
DTEND:20220616T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/94
DESCRIPTION:Title: Mutating cluster-tilting objects in (d + 2)-angulated cluster c
ategories\nby Nicholas Williams (The University of Tokyo) as part of F
D Seminar\n\n\nAbstract\nOppermann and Thomas introduced the (d + 2)-angul
ated cluster category to generalise the classical cluster category to high
er homological algebra. A great difficulty that arises in these categories
is that cluster-tilting objects are no longer mutable at every summand\,
in contrast to the classical setting. In this talk we give two new ways of
understanding mutability in these higher cluster categories: one from an
algebraic perspective\, and the other from a combinatorial perspective\, f
or the particular case of the higher Auslander algebras of type A.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Kaplan (Hasselt University)
DTSTART:20220623T130000Z
DTEND:20220623T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/95
DESCRIPTION:Title: Relating properties of homological dimension two algebras\n
by Daniel 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-behaved in the following sense: it is 2-Calabi–Yau\, a noncommutati
ve complete intersection (NCCI)\, and prime. If further Q is extended ADE
then the preprojective algebra of Q is a noncommutative crepant resolution
(NCCR) over its center\, which is isomorphic to functions on the correspo
nding du Val singularity. In this talk\, I will explain joint work with Tr
avis Schedler 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 using multiple applications of Bergman’s Diamond Lemma for ring th
eory. Applications to topology and geometry include computations of certai
n Chekanov–Eliashberg dg-algebras / wrapped Fukaya categories following
Etgü–Lekili\, and a description of the formal local structure of quiver
varieties.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Charles University)
DTSTART:20220630T130000Z
DTEND:20220630T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/96
DESCRIPTION:Title: Finitistic dimensions of differential graded rings\nby Lira
n Shaul (Charles University) as part of FD Seminar\n\n\nAbstract\nFinitist
ic dimensions are important homological numerical invariants associated to
a ring. In this talk we explain how to define these invariants over diffe
rential graded rings. We then explain how to extend previous results about
finitistic dimensions from commutative noetherian rings to commutative no
etherian differential graded rings. Finally\, we discuss the noncommutativ
e case and its relation to the finitistic dimension conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Université de Versailles Saint-Quentin)
DTSTART:20220901T130000Z
DTEND:20220901T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/97
DESCRIPTION:Title: On some configurations spaces related to algebras of finite rep
resentation type\nby Pierre-Guy Plamondon (Université de Versailles S
aint-Quentin) as part of FD Seminar\n\n\nAbstract\nThe representation theo
ry of an algebra gives rise to various\ninteresting geometrical objects\,
such as the g-vector fan and Newton\npolytopes of representations. Classic
al objects such as the associahedron\ncan be realized in this way\, and th
ese constructions have interesting\napplications in the categorification o
f cluster algebras.\n\nIn this talk\, I will associate to any representati
on-finite algebra\nanother geometrical object\, an affine variety which is
closely related to\nthe polytopes mentioned above. We will see how this v
ariety reflects the\ntau-tilting theory of the algebra\, and how F-polynom
ials of\nrepresentations give a parametrization of it.\n\nThis is a report
on ongoing work with Nima Arkani-Hamed\, Hadleigh Frost\,\nGiulio Salvato
ri and Hugh Thomas.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cody Gilbert (University of Iowa)
DTSTART:20220908T130000Z
DTEND:20220908T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/98
DESCRIPTION:Title: Moduli of Representations of Clannish Algebras\nby Cody Gil
bert (University of Iowa) as part of FD Seminar\n\n\nAbstract\nWe prove ir
reducible components of moduli spaces of semistable representations of cla
nnish algebras are isomorphic to products of projective spaces. This is ac
hieved by showing irreducible components of varieties of representations o
f clannish algebras can be viewed as irreducible components of skewed-gent
le algebras\, which we show are always normal. The main theorem generalize
s an analogous result for moduli of representations of special biserial al
gebras proven by Carroll-Chindris-Kinser-Weyman.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (University of Cambridge)
DTSTART:20220915T130000Z
DTEND:20220915T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/99
DESCRIPTION:Title: Locally free Caldero-Chapoton functions\nby Lang Mou (Unive
rsity of Cambridge) as part of FD Seminar\n\n\nAbstract\nLocally free Cald
ero-Chapoton functions are introduced by Geiss-Leclerc-Schröer for locall
y free representations of certain quivers with relations associated to ske
w-symmetrizable matrices. They show that for Dynkin types these functions
give formulas for cluster variables\, generalizing Caldero-Chapoton’s fo
rmula in simply laced cases. We extend this formula to rank 2 cluster alge
bras and those associated to unpunctured marked bordered surfaces with orb
ifold points. Part of this talk is based on joint work with Daniel Labardi
ni-Fragoso.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Bennett-Tennenhaus (Bielefeld University)
DTSTART:20221006T130000Z
DTEND:20221006T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/100
DESCRIPTION:Title: Semilinear clannish algebras\nby Raphael Bennett-Tennenhau
s (Bielefeld University) as part of FD Seminar\n\n\nAbstract\nString algeb
ras are monomial algebras introduced by Butler and Ringel\, where they sho
wed any indecomposable representation is: a string module\, given by a rel
ation-avoiding walk in the quiver\; or a band module\, given by a cyclic w
alk and some module over the Laurent polynomial ring. Clannish algebras\,
introduced by Crawley-Boevey\, generalise string algebras - in addition to
monomial relations\, one specifies a set of special loops\, each bounded
by some monic quadratic polynomial. Butler and Ringel’s classification w
as then adapted\, where the class of string (or band) modules splits into
asymmetric and symmetric subclasses. Said symmetry is a reflection of the
walk about a special loop\, and symmetric strings and bands are parameteri
sed by replacements for the Laurent polynomial ring.\n\nBoth string algebr
as and clannish algebras are defined over a field\, and the quadratics bou
nding special loops must factor with distinct roots in this field. This ta
lk is based on joint work with Crawley-Boevey (2204.12138)\, where we gene
ralise the module classification for clannish algebras. We replace the gro
und field with a division ring\, we equip each arrow with an automorphism
of this division ring\, and we allow irreducible quadratics to bound the s
pecial loops. The resulting notion of a semilinear clannish algebra specif
ies to a generalisation of string algebras considered by Ringel\, where th
e map associated to an arrow in any representation must be semilinear with
respect to its automorphism.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Simental Rodríguez
DTSTART:20221013T130000Z
DTEND:20221013T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/101
DESCRIPTION:Title: Cluster structures on braid varieties\nby José Simental R
odríguez as part of FD Seminar\n\n\nAbstract\nGiven a simple algebraic gr
oup G and an element β of its positive braid monoid we consider an affine
\, smooth algebraic variety X(β) that generalizes some well-known varieti
es in Lie theory\, including open Richardson varieties and double Bott-Sam
elson cells. In this talk\, we will construct a cluster algebra structure
on the coordinate ring of X(β) using combinatorial objects called algebra
ic weaves and tropicalization of Lusztig’s coordinates. We will also giv
e properties of this cluster structure\, including local acyclicity and th
e existence of reddening sequences. This is based on joint work with R. Ca
sals\, E. Gorsky\, M. Gorsky\, L. Shen and I. Le.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Fedele (University of Leeds)
DTSTART:20221020T130000Z
DTEND:20221020T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/102
DESCRIPTION:Title: Universal localizations of d-homological pairs\nby Frances
ca Fedele (University of Leeds) as part of FD Seminar\n\n\nAbstract\nLet $
k$ be an algebraically closed field and $A$ a finite dimensional $k$-algeb
ra. The universal localization of $A$ with respect to a set of morphisms b
etween finitely generated projective $A$-modules always exists. When $A$ i
s hereditary\, 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
universal localizations of $d$-homological pairs with respect to certain w
ide subcategories\, and show a (partial) generalisation of Krause and Stov
icek result in the higher setup.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haibo Jin (Universität zu Köln)
DTSTART:20221027T130000Z
DTEND:20221027T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/103
DESCRIPTION:Title: Recollements and localisation theorems\nby Haibo Jin (Univ
ersität zu Köln) as part of FD Seminar\n\n\nAbstract\nA localisation the
orem by A. Neeman states that any recollement of compactly generated trian
gulated categories induces a short exact sequence of subcategories of comp
act objects up to direct summands. In this talk\, we consider recollements
of unbounded derived categories of dg algebras\, and we give several loca
lisation theorems with respect to different sub (sub-quotient) categories
of the derived categories (e.g. perfect derived categories\, perfect value
d derived categories\, singularity categories\, etc.). This is an ongoing
joint work with Dong Yang and Guodong Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther Banaian (Aarhus University)
DTSTART:20221103T140000Z
DTEND:20221103T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/104
DESCRIPTION:Title: Algebras from Orbifolds\nby Esther Banaian (Aarhus Univers
ity) as part of FD Seminar\n\n\nAbstract\nWe discuss two algebras associat
ed to triangulated unpunctured orbifolds with all orbifold points of order
three - a gentle algebra and a generalized cluster algebra\, in the sense
of Chekhov and Shapiro. To each algebra\, we associate a map which can be
seen as taking arcs on the orbifold to Laurent polynomials. The first map
was defined by Caldero and Chapoton\; the second is the snake graph map\,
defined for surfaces by Musiker-Schiffler-Williams and for orbifolds by B
.-Kelley. We show that the outputs of these two maps agree. This talk is b
ased on joint work with Yadira Valdivieso.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (University Laval)
DTSTART:20221110T140000Z
DTEND:20221110T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/105
DESCRIPTION:Title: Quasi-cluster algebras\nby Véronique Bazier-Matte (Univer
sity Laval) as part of FD Seminar\n\n\nAbstract\nQuasi-cluster algebras we
re defined in 2015 by Dupont and Palesi and are an analogous of cluster al
gebras for non-orientable surfaces. In this talk\, we will first give an i
ntroduction on these quasi-cluster algebras and list some of their propert
ies (finite-type classification\, skein relations\, among others). Then\,
we will associate a quiver with potential to triangulations of non-orienta
ble surfaces and study the algebra given by this. More precisely\, we use
the cluster category associated to an orientable double cover of our non-o
rientable surface to give a correspondence between quasi-triangulations of
a non-orientable surface and an analogue of cluster-tilting objects.\n\nJ
oint work with Aaron Chan and Kayla Wright\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Stevenson (Aarhus University)
DTSTART:20221117T140000Z
DTEND:20221117T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/106
DESCRIPTION:Title: Life hacks for dgas with finite dimensional cohomology\nby
Greg Stevenson (Aarhus University) as part of FD Seminar\n\n\nAbstract\nI
t is not necessarily the case that a dg algebra with finite dimensional co
homology is quasi-isomorphic to one which is honestly finite dimensional\,
i.e. a finite dimensional algebra with a compatible differential. However
\, provided the cohomology is concentrated in non-positive degrees one can
always find such a quasi-isomorphism. Such finite dimensional dg algebras
have many amusing properties\, and I will explain some of them.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lleonard Rubio y Degrassi (Uppsala University)
DTSTART:20221124T140000Z
DTEND:20221124T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/107
DESCRIPTION:Title: On the Lie algebra structure of integrable derivations\nby
Lleonard Rubio y Degrassi (Uppsala University) as part of FD Seminar\n\n\
nAbstract\nThe space of integrable derivations was introduced by Hasse and
Schmidt\, and has since been used in geometry and commutative algebra. Mo
re recently\, integrable derivations have been used as a source of invaria
nts in representation theory.\n\nIn this talk I will show that the space o
f integrable classes in the first Hochschild cohomology of a finite dimens
ional algebra forms a (restricted) Lie algebra that is invariant under der
ived equivalences\, and under stable equivalences of Morita type between s
elf-injective algebras. I will also provide negative answers to questions
posed by Linckelmann and by Farkas\, Geiss and Marcos regarding integrable
derivations. This is joint work with Benjamin Briggs.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederik Marks (Universität Stuttgart)
DTSTART:20221201T140000Z
DTEND:20221201T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/108
DESCRIPTION:Title: A functorial approach to rank functions on triangulated catego
ries\nby Frederik Marks (Universität Stuttgart) as part of FD Seminar
\n\n\nAbstract\nMotivated by work of Cohn and Schofield on Sylvester rank
functions\, Chuang and Lazarev have recently introduced the notion of a ra
nk function on a triangulated category. They show that Verdier quotients i
nto simple triangulated categories are classified by a certain type of ran
k functions\, and that such rank functions on the perfect derived category
of a dg algebra describe derived localisations into dg skew-fields. In th
is talk\, we suggest interpreting rank functions as certain additive funct
ions on the functor category. As a consequence\, we obtain that every inte
gral rank function decomposes uniquely as a sum of irreducible ones. In th
e following\, we focus on compactly generated triangulated categories\, wh
ere basic rank functions on the compacts are length functions with respect
to certain endofinite objects. We show that rank functions in this contex
t are closely related to definable subcategories and smashing localisation
s\, which allows us to extend the aforementioned results by Chuang and Laz
arev. This talk is based on joint work with Teresa Conde\, Mikhail Gorsky
and Alexandra Zvonareva.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lutz Hille (Universität Münster)
DTSTART:20221208T140000Z
DTEND:20221208T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/109
DESCRIPTION:Title: Polynomial Invariants for Triangulated Categories with Excepti
onal Sequences\nby Lutz Hille (Universität Münster) as part of FD Se
minar\n\n\nAbstract\nGiven two triangulated categories\, it is desirable t
o decide\, whether they are equivalent as triangulated categories. Essenti
ally there are two aspects\, a combinatorial aspect and a geometric aspect
. The first one corresponds to an isomorphism on the level of the Grothend
ieck group together with its Euler form. The solution for triangulated cat
egories of finite dimensional (hereditary or even quasi-hereditary) wild a
lgebras with three vertices is known\, the only free parameter is the larg
est eigen value of the Coxeter transformation (for hereditary algebras)\,
or equivalently\, its trace (that works also for quasi-hereditary algebras
). This idea was used also for cluster algebras with three vertices (in a
joint work with Beineke and Brüstle) to decide\, whether it is acyclic or
not (with some exceptions). It is classically known as an equation betwee
n the ranks of eceptional sequences on the projective plane (Drezet\, le P
otier and later also Rudakov).\n\nFor the general problem\, triangulated c
ategories with a full exceptional sequence of length n we determine a fini
te set of polynomials\, called polynomial invariants\, so that we can gene
rically solve this problem (there are some exceptions one should consider
in more detail) in terms of the values of these polynomials\, they general
ize the Markov equation for n=3.\n\nIn this talk we review some of the his
tory\, formulate the problem over arbitrary fields and solve it using so-c
alled polynomial invariants. We also discuss\, what can be decided using p
olynomial invariants and what is the remaining open problem\, in particula
r\, what to expect for the geometric aspects of the question.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala University)
DTSTART:20221215T140000Z
DTEND:20221215T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/110
DESCRIPTION:Title: Graded extensions of Verma modules\nby Volodymyr Mazorchuk
(Uppsala University) as part of FD Seminar\n\n\nAbstract\nThe aim of this
talk is to report on some recent progress related to the classical proble
m of description of extensions of Verma modules in BGG category O. In part
icular\, looking at the refined picture provided by graded extensions and
using some classical results of Delorme\, we determine the role the R-poly
nomials play in this theory. Consequently\, we determine many cases in whi
ch extensions can be described by the Gabber-Joseph formula and construct
explicit examples where this formula fails.\n\nBased on a joint work with
Hankyung Ko.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laertis Vaso (Norges teknisk-naturvitenskapelige universitet\, NTN
U)
DTSTART:20230119T140000Z
DTEND:20230119T150000Z
DTSTAMP:20260404T131145Z
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://stable.researchseminars.org/talk/fd-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuya Mizuno (Osaka Metropolitan University)
DTSTART:20230126T140000Z
DTEND:20230126T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/112
DESCRIPTION:Title: Complete $g$-fans of rank 2\nby Yuya Mizuno (Osaka Metropo
litan University) as part of FD Seminar\n\n\nAbstract\n$g$-fan of a finite
dimensional algebra is a fan in its real Grothendieck group defined by ti
lting theory. We give a classification of complete $g$-fans of rank 2. Mor
e explicitly\, our main result asserts that every complete sign-coherent f
an of rank 2 is a $g$-fan of some finite dimensional algebra. Our proof is
based on three fundamental results\, Gluing Theorem\, Rotation Theorem an
d Subdivision Theorem\, which realize basic operations on fans in the leve
l of finite dimensional algebras. This is a joint work with T. Aoki\, A. H
igashitani\, O. Iyama and R. Kase.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongxing Chen (Capital Normal University)
DTSTART:20230202T140000Z
DTEND:20230202T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/113
DESCRIPTION:Title: Homological theory of orthogonal modules\nby Hongxing Chen
(Capital Normal University) as part of FD Seminar\n\n\nAbstract\nTachikaw
a’s second conjecture predicts that a finitely generated\, orthogonal mo
dule over a finite-dimensional self-injective algebra is projective. This
conjecture is an important part of the Nakayama conjecture. In the talk\,
we introduce a systematic study of finitely generated\, orthogonal generat
ors over a self-injective Artin algebra from the view point of stable modu
le categories. For an orthogonal generator $M$\, we establish a recollemen
t of the $M$-relative stable categories\, describe compact objects of the
right term of the recollement\, and give equivalent characterizations of T
achikawa’s second conjecture in terms of $M$-Gorenstein categories. Furt
her\, we introduce Gorenstein-Morita algebras and show that the Nakayama c
onjecture holds true for them. This is joint work with Changchang Xi.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (Universität zu Köln)
DTSTART:20230209T140000Z
DTEND:20230209T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/114
DESCRIPTION:Title: $A_\\infty$ deformations of extended Khovanov arc algebras and
Stroppel’s Conjecture\nby Severin Barmeier (Universität zu Köln)
as part of FD Seminar\n\n\nAbstract\nExtended Khovanov arc algebras are gr
aded finite-dimensional algebras which appear at the confluence of represe
ntation theory\, link homology and symplectic geometry. In this talk I wil
l explain how to obtain explicit $A_\\infty$ deformations of these algebra
s by presenting their Koszul duals as path algebras of quivers with relati
ons and using a combinatorial method via reduction systems to determine th
eir deformations. This settles a conjecture by Catharina Stroppel (ICM 201
0) on the bigraded Hochschild cohomology groups of extended Khovanov arc a
lgebras and produces explicit $A_\\infty$ deformations of Fukaya-Seidel ca
tegories associated to Hilbert schemes of points on nilpotent slices of ty
pe $A$ singularities constructed recently by Cheuk Yu Mak and Ivan Smith.
This talk is based on https://arxiv.org/abs/2211.03354 joint with Zhengfan
g Wang.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicja Jaworska-Pastuszak (Nicolaus Copernicus University)
DTSTART:20230223T140000Z
DTEND:20230223T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/115
DESCRIPTION:Title: On Krull-Gabriel dimension of cluster repetitive categories an
d cluster-tilted algebras\nby Alicja Jaworska-Pastuszak (Nicolaus Cope
rnicus University) as part of FD Seminar\n\n\nAbstract\nLet $K$ be an alge
braically closed field\, $R$ a locally support-finite locally bounded $K$-
category and $G$ a torsion-free admissible group of $K$-linear automorphis
ms of $R$. Recently Pastuszak showed that the induced Galois covering $R\\
rightarrow R/ G$\, where $R/ G$ denotes the orbit category\, preserves the
Krull-Gabriel dimension\, i.e. $\\mathrm{KG}(R)=\\mathrm{KG}(R/ G)$. Ther
efore\, in order to determine Krull-Gabriel dimensions of tame standard se
lf-injective algebras it was sufficient to determine Krull-Gabriel dimensi
ons of repetitive categories of tilted algebras of\nDynkin type\, tilted o
f Euclidean 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
categories and cluster-tilted algebras which are their orbit categories.
We will also give some background on the Galois coverings of functor categ
ories\, since it is the main tool used in these results\, as well as prese
nt some related problems and applications. This is a report of a joint wor
k with Grzegorz Pastuszak.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHÉS)
DTSTART:20230302T140000Z
DTEND:20230302T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/116
DESCRIPTION:Title: Pre-Calabi-Yau structures and string topology\nby Alex Tak
eda (IHÉS) as part of FD Seminar\n\n\nAbstract\nPre-Calabi-Yau structures
are noncommutative versions of Poisson structures appearing in homologica
l mirror symmetry\, and can be used to describe certain types of TQFT oper
ations on Hochschild homology. In this talk\, I will recall the definition
s and applications of these structures\, and then describe how to use thes
e structures to give a certain algebraic model for the string topology of
non-simply connected manifolds. This talk is based on a current joint proj
ect with Manuel Rivera and Zhengfang Wang.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alastair King (University of Bath)
DTSTART:20230309T140000Z
DTEND:20230309T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/117
DESCRIPTION:Title: Twisted surfaces and clusters of curves\nby Alastair King
(University of Bath) as part of FD Seminar\n\n\nAbstract\nI will describe
a combinatorial way to associate to a (tagged) triangulation of a surface
with marked points and punctures a “twisted surface” together with a
“cluster of curves” whose intersection matrix is the corresponding exc
hange matrix. The twisted surface roughly models the spectral curve associ
ated to quadratic differentials\, as in [Bridgeland-Smith]\, but the combi
natorial construction has some subtle differences. This is joint work with
Qiu-Yu.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/118
DESCRIPTION:Title: Symmetric quivers and symmetric varieties\nby Martina Lani
ni (Università degli Studi di Roma Tor Vergata) as part of FD Seminar\n\n
\nAbstract\nIn this talk I will report on ongoing joint work with Ryan Kin
ser and Jenna Rajchgot on varieties of symmetric quiver representations. T
hese varieties are acted upon by a reductive group via change of basis\, a
nd it is natural to ask for a parametrisation of the orbits\, for the clos
ure inclusion relation among them\, for information about the singularitie
s arising in orbit closures. Since the Eighties\, same (and further) quest
ions about representation varieties for type A quivers have been attached
by relating such varieties to Schubert varieties in type A flag varieties
(Zelevinsky\, Bobinski-Zwara\, ...). I will explain that in the symmetric
setting it is possible to interpret the above questions in terms of certai
n symmetric varieties. More precisely\, we show that singularities of an o
rbit closure of a symmetric quiver representation variety are smoothly equ
ivalent to singularities of an appropriate Borel orbit closure in a symmet
ric variety.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Julia Redondo (Universidad Nacional del Sur)
DTSTART:20230420T130000Z
DTEND:20230420T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/119
DESCRIPTION:Title: The Ext-Algebra for infinitesimal deformations\nby Maria J
ulia Redondo (Universidad Nacional del Sur) as part of FD Seminar\n\n\nAbs
tract\nLet $f$ be a Hochschild $2$-cocycle and $A_f$ an infinitesimal d
eformation of a finite-dimensional associative $k$-algebra $A$. We describ
e\, under some conditions on $f$\, the algebra structure of the Ext-algebr
a of $A_f$ in terms of the Ext-algebra of $A$. We achieve this descript
ion by getting an explicit construction of minimal projective resolutions.
This is based on joint work with L. Román and F. Rossi Bertone.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Cipriani (Università degli Studi di Verona)
DTSTART:20230427T130000Z
DTEND:20230427T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/120
DESCRIPTION:Title: Highest weight perverse sheaves\nby Alessio Cipriani (Univ
ersità degli Studi di Verona) as part of FD Seminar\n\n\nAbstract\nGiven
a topologically stratified space $X$ and a perversity function $p$ on it\,
one can build the category of $p$-perverse sheaves on $X$ by considering
the heart of a certain t-structure. Under suitable topological assumptions
on $X$ perverse sheaves are finite dimensional modules over a finite dime
nsional algebra independently on the chosen perversity function. It is the
n natural to ask under which further assumptions on the topology of the co
nsidered space perverse sheaves are highest weight. In this talk\, based o
n ongoing joint work with Jon Woolf\, I will explain some sufficient (topo
logical) conditions on $X$ which ensure that perverse sheaves are highest
weight.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karin Marie Jacobsen (Aarhus University)
DTSTART:20230504T130000Z
DTEND:20230504T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/121
DESCRIPTION:Title: Correspondences from tilting theory in higher homological alge
bra\nby Karin Marie Jacobsen (Aarhus University) as part of FD Seminar
\n\n\nAbstract\nAdachi\, Iyama and Reiten developed $\\tau$-tilting theory
to mirror the properties of mutation seen in cluster algebras. The theory
gives a generalisation of classical tilting modules using the Auslander-R
eiten translation $\\tau$\, and one studies distinguished pairs of objects
in the module category of a finite-dimensional algebra known as $\\tau$-r
igid pairs. An important result from the theory is the correspondence betw
een functorially finite torsion classes\, maximal $\\tau$-rigid pairs and
2-term silting complexes\, amongst others.\n\nMeanwhile\, higher homologic
al algebra has since its introduction by Iyama become a very active field
of research\, and many authors have generalised notions to the higher homo
logical setting\, including both torsion classes and $\\tau$-rigid pairs.
This talk is a report on work in progress investigating the relationship b
etween higher torsion classes\, silting objects and maximal $\\tau_d$-rigi
d pairs. We describe explicit correspondences\, and also show computationa
l results.\n\nThe talk is based on joint work with August\, Haugland\, Kva
mme\, Palu and Treffinger\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sondre Kvamme (Norges teknisk-naturvitenskapelige universitet\, NT
NU)
DTSTART:20230511T130000Z
DTEND:20230511T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/122
DESCRIPTION:Title: Indecomposables in the monomorphism category\nby Sondre Kv
amme (Norges teknisk-naturvitenskapelige universitet\, NTNU) as part of FD
Seminar\n\n\nAbstract\nThe study of submodule categories is an old subjec
t in representation theory going all the way back to beginning of the 20th
century by work of Miller and Hilton. It has connections to\, for example
\, Littlewood—Richardson tableaux\, valuated p-groups and metabelian gro
ups. In 2004 Ringel and Schmidmeier studied such categories using modern t
ools like Auslander—Reiten theory and covering theory.\n\nA generalizati
on of submodule categories\, called (separated) monomorphism categories\,
has also been actively studied by several authors. They have found connect
ions to for example cotorsion pairs\, Gorenstein homological algebra\, sin
gularity theory and topological data analysis.\n\nIn this talk I will defi
ne submodule and monomorphism categories\, and mention some of the known r
esults about them. Then I will explain how they can be related to represen
tations over stable categories via epivalences (also called representation
equivalences)\, and how this can often be used to determine their indecom
posables. I will also say something about our proof\, which uses free mona
ds on abelian categories. If time permits\, I will discuss analogues of mo
nomorphism categories for species. In particular\, I will explain how our
result can be used to give a characterization of Cohen-Macaulay finiteness
for the algebras H associated to symmetrizable Cartan matrices introduced
by Geiss-Leclerc-Schröer\, assuming the terms in the symmetrizer are les
s than or equal to 2.\n\nThis is joint work with Nan Gao\, Julian Külsham
mer and Chrysostomos Psaroudakis.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhou (Tsinghua University)
DTSTART:20230518T130000Z
DTEND:20230518T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/123
DESCRIPTION:Title: Surfaces with binary and skew-gentle algebras\nby Yu Zhou
(Tsinghua University) as part of FD Seminar\n\n\nAbstract\nIndecomposable
objects in the bounded derived category of a skew-gentle algebra have been
classified by many authors in an algebraic\, combinatorial or geometric w
ay\, while a description of morphisms has not been given. In this talk\, w
e use a new geometric model\, namely a graded marked surface with binary\,
to investigate a non-positive graded skew-gentle algebra. For any graded
unknotted curve on the surface\, we associate an object in the perfect der
ived category of the algebra\, and for any oriented intersection between u
nknotted curves\, we construct a morphism\, which form a basis of the corr
esponding morphism space. This is based on joint work with Yu Qiu and Chao
Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Haiden (Syddansk University)
DTSTART:20230525T130000Z
DTEND:20230525T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/124
DESCRIPTION:Title: Algebras from surfaces: deformation\, duality\, quotients\
nby Fabian Haiden (Syddansk University) as part of FD Seminar\n\n\nAbstrac
t\nThere are a number of constructions which start with a (suitably decora
ted) surface together with a triangulation or more general system of arcs
and produce an algebra\, possibly differential-graded or A-infinity. Examp
les include: gentle algebras\, Jacobian and Ginzburg algebras of surfaces\
, Brauer graph algebras\, as well as generalizations of these. I will revi
ew some of these constructions and discuss recently discovered connections
between them\, involving deformation\, Koszul duality\, and cyclic group
quotients. Based on joint work with Merlin Christ and Yu Qiu (arXiv:2303.1
8249).\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Garcia (Université Paris-Saclay)
DTSTART:20230601T130000Z
DTEND:20230601T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/125
DESCRIPTION:Title: Thick subcategories and semistability for projective presentat
ions\nby Monica Garcia (Université Paris-Saclay) as part of FD Semina
r\n\n\nAbstract\nFor every finite dimensional algebra\, there are correspo
ndences between support $\\tau$-tilting modules\, functorially finite tors
ion pairs\, and left finite wide subcategories of the module category. The
first two classes of objects have “mirror” versions in the category o
f projective presentations\, namely\, 2-term silting complexes and cotorsi
on pairs. 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 thi
ck subcategory of the category of projective presentations and show that t
hose with enough injectives are in bijection with left finite wide subcate
gories. We will explain how thick subcategories arise from an attempt to d
efine semistability for projective presentations.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erlend D. Børve (Norges teknisk-naturvitenskapelige universitet\,
NTNU)
DTSTART:20230608T130000Z
DTEND:20230608T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/126
DESCRIPTION:Title: Two-term silting and τ-cluster morphism categories\nby Er
lend D. Børve (Norges teknisk-naturvitenskapelige universitet\, NTNU) as
part of FD Seminar\n\n\nAbstract\nWe explain how Iyama—Yang’s silting
reduction is compatible with Buan—Marsh’s reduction of $\\tau$-rigid p
airs. Then\, we reconstruct the $\\tau$-cluster morphism category of a fin
ite-dimensional algebra\, or more generally of a non-positive proper diffe
rential graded algebra. Approaching $\\tau$-cluster morphism categories in
terms of silting theory\, as opposed to $\\tau$-tilting theory\, has the
advantage that the associativity of composition is proved more neatly. Tim
e permitting\, we explore the cubical structure of $\\tau$-cluster morphis
m categories and discuss alternative ways of defining them.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiarui Fei (Shanghai Jiao Tong University)
DTSTART:20230615T130000Z
DTEND:20230615T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/127
DESCRIPTION:Title: Crystal Structure of Upper Cluster Algebras\nby Jiarui Fei
(Shanghai Jiao Tong University) as part of FD Seminar\n\n\nAbstract\nWe d
escribe the (weaker) upper seminormal crystal structure for the $\\mu$-sup
ported $\\delta$-vectors for any ice quiver with potential\, or equivalent
ly for the tropical points of the corresponding cluster $\\mathcal{X}$-var
iety. We show that the crystal structure can be algebraically lifted to a
biperfect basis of the upper cluster algebra. This can be viewed as an add
itive categorification of the crystal structure arising from cluster algeb
ras. All such biperfect bases are parametrized by lattice points in a prod
uct of polytopes. We find that the requirement for upgrading to a (semi)no
rmal crystal is almost minimal in some sense. We illustrate this theory fr
om classical examples and new examples.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Burban (Universität Paderborn)
DTSTART:20230622T130000Z
DTEND:20230622T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/128
DESCRIPTION:Title: Derived-tame algebras\nby Igor Burban (Universität Paderb
orn) as part of FD Seminar\n\n\nAbstract\nI shall first give a survey of k
nown classes of derived-tame finite dimensional algebras (gentle\, skew-ge
ntle) explaing the origin of the corresponding combinatorics of indecompos
able objects from the point of view of matrix problems (representations of
bunches of (semi-)chains). Then I discuss another class of derived-tame a
lgebras which can be approached by a similar method. This is a joint work
in progress with Yuriy Drozd.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yadira Valdivieso (University of the Americas Puebla)
DTSTART:20230914T130000Z
DTEND:20230914T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/129
DESCRIPTION:Title: Skew-Brauer algebras and admissible cuts\nby Yadira Valdiv
ieso (University of the Americas Puebla) as part of FD Seminar\n\n\nAbstra
ct\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 Brauer 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-gentle algebra is a skew-Brauer graph algebra. Finally\, we present
a geometric interpretation of the notion of admissible cuts of a trivial e
xtension of skew-gentle algebras using dissections of orbifild surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Gunawan (University of Massachusetts Lowell)
DTSTART:20230921T130000Z
DTEND:20230921T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/130
DESCRIPTION:Title: Triangulations and maximal almost rigid modules over gentle al
gebras\nby Emily Gunawan (University of Massachusetts Lowell) as part
of FD Seminar\n\n\nAbstract\nA type $A$ path algebra is an algebra whose b
asis is the set of all paths in an orientation of a type $A$ Dynkin diagra
m. We introduce a new class of modules over a type $A$ path algebra and ca
ll them maximal almost rigid (MAR). They are counted by the Catalan number
s and are naturally modeled by triangulations of a polygon. The endomorphi
sm algebras of the MAR modules are classical tilted algebras of type $A$.
Furthermore\, their oriented flip graph is the oriented exchange graph of
a smaller type $A$ cluster algebra which is known to define a Tamari or Ca
mbrian poset.\n\nThe type $A$ path algebras are special cases of gentle al
gebras\, a family of finite-dimensional algebras whose indecomposable modu
les are classified by certain walks called strings and bands. We generaliz
e the notion of MAR to this setting. First\, we use the surface models stu
died by Opper\, Plamondon\, and Schroll and by Baur and Coelho Simões to
show that the MAR modules correspond bijectively to triangulations of a ma
rked surface. We then show that the endomorphism algebra of a MAR module i
s the endomorphism algebra of a tilting module over a bigger gentle algebr
a. Finally\, we define an oriented flip graph of the MAR modules and conje
cture that it is acyclic.\n\nThis talk is based on joint projects with Emi
ly Barnard\, Raquel Coelho Simões\, Emily Meehan\, and Ralf Schiffler.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (University of Glasgow)
DTSTART:20230928T130000Z
DTEND:20230928T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/131
DESCRIPTION:Title: Positroid varieties via representation theory\nby Matthew
Pressland (University of Glasgow) as part of FD Seminar\n\n\nAbstract\nTot
al positivity is by now a classical subject in linear algebra\, having beg
un in earnest with the work of Gantmacher and Krein from 1937. Recent resu
lts of Postnikov and others have emphasised the importance of positivity i
n flag varieties\, particularly the Grassmannian. A key tool in this area
is Postnikov’s positroid stratification of the Grassmannian\, and the cl
uster algebra structures on its various (open) cells\, recently confirmed
to exist by Galashin and Lam.\n\nIn this talk\, I will explain this story
in the language of representation theory\, with the positroid varieties an
d their cluster algebra structures being encoded by the representation the
ory of various non-commutative orders over the power series ring in one va
riable. Except for the top-dimensional stratum\, Galashin and Lam’s cons
truction produces two different cluster algebra structures on each open po
sitroid\, and an application of this representation theoretic approach is
a proof that these two structures quasi-coincide\, as conjectured by Mulle
r and Speyer in 2017. In particular\, this means that these structures are
equivalent from the point of view of total positivity.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tobias Dyckerhoff (Universität Hamburg)
DTSTART:20230907T130000Z
DTEND:20230907T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/132
DESCRIPTION:Title: Complexes of stable infinity-categories\nby Tobias Dyckerh
off (Universität Hamburg) as part of FD Seminar\n\n\nAbstract\nDerived ca
tegories have come to play a decisive role in a wide range of topics. Seve
ral recent developments\, in particular in the context of topological Fuka
ya categories\, arouse the desire to study not just single categories\, bu
t rather complexes of categories. In this talk\, we will discuss examples
of such complexes in algebra\, topology\, algebraic geometry\, and symplec
tic geometry\, along with some results and conjectures involving them.\n\n
Based on joint work with Merlin Christ and Tashi Walde.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calvin Pfeifer (University of Southern Denmark)
DTSTART:20231005T130000Z
DTEND:20231005T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/133
DESCRIPTION:Title: On $\\tau$-representation types with examples from the represe
ntation theory of valued quivers\nby Calvin Pfeifer (University of Sou
thern Denmark) as part of FD Seminar\n\n\nAbstract\nIn this talk\, we prop
ose a stable and a τ-reduced version of the second Brauer-Thrall conjectu
re. The former is a slight strengthening of a brick version of the second
Brauer-Thrall conjecture introduced by Mousavand and Schroll-Treffinger-Va
ldivieso. The latter is stated in terms of Geiß-Leclerc-Schröer’s gene
rically τ-reduced components and provides a geometric interpretation of a
question raised by Demonet. We outline implications among these conjectur
es and relate them to recent variations of tameness in stability and τ-ti
lting theory. It follows from Schroll-Treffinger-Valdivieso’s work that
the conjectures are true for special biserial algebras\, and we confirm th
em for Geiß-Leclerc-Schröer’s (GLS) algebras associated to valued quiv
ers. If time permits\, we demonstrate that the in general representation w
ild GLS algebras of affine type are still „tame“ from a $\\tau$-tiltin
g perspective.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/134
DESCRIPTION:Title: Relative cluster categories and Higgs categories with infinite
-dimensional morphism spaces\nby Yilin Wu (University of Science and T
echnology of China) as part of FD Seminar\n\n\nAbstract\nCluster categorie
s were introduced in 2006 by Buan–Marsh–Reineke–Reiten–Todorov in
order to categorify acyclic cluster algebras without coefficients. Their c
onstruction was generalized by Amiot to Jacobi-finite quivers with potenti
al (2009). Later\, Plamondon generalized it to arbitrary cluster algebras
associated with quivers (2009 and 2011). Cluster algebras with coefficient
s are important since they appear in nature as coordinate algebras of vari
eties like Grassmannians\, double Bruhat cells\, unipotent cells\, … The
work of Geiss-Leclerc-Schröer often yields Frobenius exact categories wh
ich allow to categorify such cluster algebras.\n\nIn previous work\, we ha
ve constructed Higgs categories and relative cluster categories in the rel
ative Jacobi-finite setting (arXiv:2109.03707). Higgs categories generaliz
e the Frobenius categories used by Geiss-Leclerc-Schröer. In this talk\,
we give the construction of the Higgs category and of the relative cluster
category in the relative Jacobi-infinite setting under suitable hypothese
s. As in the relative Jacobi-finite case\, the Higgs category is no longer
exact but still extriangulated in the sense of Nakaoka-Palu (2019). We al
so give the construction of a cluster character in this setting.\n\nThis i
s a joint work with Chris Fraser and Bernhard Keller (arXiv:2307.12279).\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanna Le Gros (Universitat Autónoma de Barcelona)
DTSTART:20231019T130000Z
DTEND:20231019T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/135
DESCRIPTION:Title: Serre’s conditions and the finite type of classes of modules
of bounded projective dimension\nby Giovanna Le Gros (Universitat Aut
ónoma de Barcelona) as part of FD Seminar\n\n\nAbstract\nThe class of mod
ules of projective dimension at most $n$\, denoted $\\mathcal{P}_n$\, is s
aid to be of finite type when its right $\\mathsf{Ext}$-orthogonal is exac
tly the right $\\mathsf{Ext}$-orthogonal of the subclass of strongly finit
ely presented modules in $\\mathcal{P}_n$ (recall that the strongly finite
ly presented modules are the modules with a projective resolution consisti
ng of finitely generated modules). In particular\, the finite type of $\\m
athcal{P}_n$ is equivalent to the right $\\mathsf{Ext}$-orthogonal of $\\m
athcal{P}_n$ being an $n$-tilting class.\n\nThe classes $\\mathcal{P}_n$ w
hich are of finite type enjoy many additional properties with respect to t
hose which are not\, so a next aim is to characterise the rings over which
$\\mathcal{P}_n$ is of finite type for some $n$. In this talk\, we plan t
o address this question for commutative noetherian rings\, and relate this
question to a classical criterion of Serre. Explicitly\, over a commutati
ve noetherian ring\, the class $\\mathcal{P}_n$ is of finite type if and o
nly if Serre’s condition $(S_n)$ holds. Additionally\, we will also cons
ider the slightly weaker condition of when the class of modules of flat di
mension at most $n$ coincides with the direct limit closure of the strongl
y finitely presented modules in $\\mathcal{P}_n$ over commutative noetheri
an rings\, or\, in other words\, when a ``higher’’ Govorov-Lazard Theo
rem holds over these rings.\n\nThis talk is based on joint work with Micha
l Hrbek.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Booth (Lancaster University)
DTSTART:20231026T130000Z
DTEND:20231026T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/136
DESCRIPTION:Title: Singularity categories via the derived quotient\nby Matt B
ooth (Lancaster University) as part of FD Seminar\n\n\nAbstract\nGiven a r
easonable commutative ring R and a noncommutative partial resolution A of
R\, the singularity category of A relative to R is controlled by a connect
ive dg algebra\, the derived exceptional locus\, which can be obtained as
a derived quotient of A. In fact\, one can identify the derived exceptiona
l 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 categ
ory of R\, which - by a result of Hua and Keller - recovers the isomorphis
m type of R itself. I’ll talk about the above before giving an applicati
on: the classification of singular threefold flops via their derived contr
action algebras. Derived methods must come into play here since\, in the s
ingular setting\, the usual contraction algebra does not classify\, in con
trast to a recent theorem of Jasso\, Keller\, and Muro in the smooth setti
ng.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Bird (Charles University)
DTSTART:20231102T140000Z
DTEND:20231102T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/137
DESCRIPTION:Title: Coherent and definable functors for triangulated categories\nby Isaac Bird (Charles University) as part of FD Seminar\n\n\nAbstract\
nIn this talk\, I shall introduce coherent and definable functors for tria
ngulated categories. The former are the purity preserving functors into fi
nitely accessible categories with products\, and generalise their namesake
s as introduced by Krause. It will be shown that the restricted Yoneda emb
edding is the universal coherent functor. I will then introduce definable
functors between triangulated categories\, which will be shown to be those
which preserve the pure structure. Their properties will be discussed and
examples given. I will then give some applications to representation theo
ry. This is based on joint work with Jordan Williamson.\n
LOCATION:https://stable.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:20260404T131145Z
UID:fd-seminar/138
DESCRIPTION:Title: On exact dg categories\nby Xiaofa Chen (University of Scie
nce 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
explore their application to various correspondences in representation th
eory. We will generalize the Auslander–Iyama correspondence\, the Iyama
–Solberg correspondence\, and a correspondence considered in a paper by
Iyama in 2005 to the setting of exact dg categories. The slogan is that so
lving correspondence-type problems becomes easier using dg categories\, an
d interesting phenomena emerge when the dg category is concentrated in deg
ree zero or is abelian.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University)
DTSTART:20231109T140000Z
DTEND:20231109T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/139
DESCRIPTION:Title: Derived Picard groups of graded gentle algebras and integratio
n of Hochschild classes\nby Sebastian Opper (Charles University) as pa
rt of FD Seminar\n\n\nAbstract\nThe talk is based on my ongoing project co
ncerning the derived Picard groups of graded gentle algebras\, or equivale
ntly\, partially wrapped Fukaya categories of surfaces in the sense of Hai
den-Katzarkov-Kontsevich. After recalling some previous results in the ung
raded case\, I will explain the structure of these groups and the main ing
redients of this result. As such\, we discuss a projection map from the de
rived Picard group to the mapping class group and mapping class group acti
ons on these categories. The last ingredient is the use of exponential map
s to determine the kernel of the projection map. I will explain how they a
llow 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://stable.researchseminars.org/talk/fd-seminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Gallauer (University of Warwick)
DTSTART:20231123T140000Z
DTEND:20231123T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/140
DESCRIPTION:Title: On dense cohomological invariants\nby Martin Gallauer (Uni
versity of Warwick) as part of FD Seminar\n\n\nAbstract\nA classical theor
em of Quillen expresses the mod-p cohomology of a finite group in terms of
its elementary abelian p-subgroups\, up to inseparable isogeny. In this t
alk I will discuss variations on this theme: “going pro-finite” and
“going Mackey”. I will then explain how these are all linked to “den
se invariants” in tensor-triangular geometry. Based on joint work with P
aul Balmer.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Barbieri (Università degli Studi di Verona)
DTSTART:20231207T140000Z
DTEND:20231207T150000Z
DTSTAMP:20260404T131145Z
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 Sem
inar\n\n\nAbstract\nI will introduce a notion of “multi-scale stability
conditions” that\, under some finiteness assumptions\, generalise the no
tion of Bridgeland stability for a triangulated category. For Ginzburg cat
egories of type A_n\, multi-scale stability conditions can be used to cons
truct a smooth compactification of an appropriate quotient of the usual st
ability manifold. Based on joint work with M.Moeller and J.So.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss (Universidad Nacional Autónoma de México\, UNAM)
DTSTART:20231214T140000Z
DTEND:20231214T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/143
DESCRIPTION:Title: MSW-bangle functions are generic bases for marked surfaces
\nby Christof 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 wi
th Daniel Labardini and Jan Schröer from unpunctured surfaces to puncture
d surfaces with non-empty boundaries. Let T be a tagged triangulation of s
uch a marked surface and A(T) the corresponding Jacobian algebra for the L
abardini potential. A(T) is finite-dimensional and tame\, however it is on
ly gentle if the surface has no punctures. More precisely\, A(T) is skewed
-gentle if T is of signature 0\, otherwise there is no explicit classifica
tion of the indecomposable representations known. Moreover\, the correspon
dence between curves and indecomposable representations is complicated by
the presence of kinks. We sketch briefly\, how to deal with these difficul
ties.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bethany Marsh (University of Leeds)
DTSTART:20240125T140000Z
DTEND:20240125T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/144
DESCRIPTION:Title: An introduction to tau-exceptional sequences\nby Bethany M
arsh (University of Leeds) as part of FD Seminar\n\n\nAbstract\nJoint work
with Aslak Bakke Buan.\n\nExceptional sequences in module categories over
hereditary algebras (e.g. path algebras of quivers) were introduced and s
tudied by W. Crawley-Boevey and C. M. Ringel in the early 1990s\, as a way
of understanding the structure of such categories. They were motivated by
the consideration of exceptional sequences in algebraic geometry by A. I.
Bondal\, A. L. Gorodontsev and A. N. Rudakov.\n\nExceptional sequences ca
n also be considered over arbitrary finite dimensional algebras\, but thei
r behaviour is not so good in general: for example\, complete exceptional
sequences may not exist. We look at different ways of generalising to the
hereditary case\, with a focus on tau-exceptional sequences\, recently int
roduced in joint work with A. B. Buan (NTNU)\, motivated by the tau-tiltin
g theory of T. Adachi\, O. Iyama and I. Reiten\, and signed exceptional se
quences in the hereditary case defined by K. Igusa and G. Todorov.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jasper van de Kreeke (Universiteit van Amsterdam)
DTSTART:20240201T140000Z
DTEND:20240201T150000Z
DTSTAMP:20260404T131145Z
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\n
Nakajima’s quiver varieties are moduli spaces of quiver representations
which bear an additional symplectic structure. Out of such a symplectic si
ngularity\, Namikawa constructs a “Namikawa-Weyl group” by means of de
formation theory\, but implementing his construction in case of quiver var
ieties remains open until today. In this talk\, I recapitulate how quiver
varieties arise from representation theory\, what is already known about N
amikawa-Weyl groups of other symplectic singularities\, and how Raf Bockla
ndt 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
construct non-affine GIT quotients.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hankyung Ko (Uppsala University)
DTSTART:20240208T140000Z
DTEND:20240208T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/146
DESCRIPTION:Title: Atoms in Singularland\nby Hankyung Ko (Uppsala University)
as part of FD Seminar\n\n\nAbstract\nThe talk explains singular Coxeter c
ombinatorics\, i.e.\, combinatorics of parabolic double cosets in a Coxete
r group. In particular\, we give a generators and relations presentation (
or two) of the double cosets. Here appears a singular analogue of the simp
le reflections\, called atoms. Atoms generate a new combinatorial structur
e which\, by a work of Iyama and Wemyss\, describes the tilting theory of
contracted (i.e. idempotent subalgebras of) preprojective algebras.\n\nBas
ed on a joint project with Ben Elias\, Nico Libedinsky\, Leonardo Patimo.\
n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michal Hrbek (Czech Academy of Sciences)
DTSTART:20240215T140000Z
DTEND:20240215T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/147
DESCRIPTION:Title: Telescope conjecture via homological residue fields with appli
cations to schemes\nby Michal Hrbek (Czech Academy of Sciences) as par
t of FD Seminar\n\n\nAbstract\nIn his landmark ‘00 paper\, Krause gave a
n abstract model theory characterization of when the Telescope Conjecture
(TC) holds in a compactly generated triangulated category. Restricting to
the tensor-triangulated (tt) setting\, the tt version of (TC) can then be
translated as “every definable ideal is the orthogonal to a set of compa
ct objects”\, as explained by R. Wagstaffe. (TC) was originally formulat
ed 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 answ
er last year. Our results are motivated by the case of D(X)\, the derived
category 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 aff
ine-local property on the Balmer spectrum of a big tt-category. In the pre
sent work (arXiv:2311.00601)\, we show that under very mild (and conjectur
ally vacuous) 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 hom
ological residue field objects generates the local tt-category over the co
rresponding stalk as a definable ideal.\n\nIn the case of D(X)\, this ties
(TC) strongly with separation properties of the adic topology of the stal
k rings. We apply this to recover most known examples of validity or failu
re of (TC) in D(X)\, as well as to construct some new ones. Moreover\, we
show that certain restriction of (TC) can be characterized in terms of pse
udoflat ring epimorphisms over R\, yielding a surprising example of a non-
surjective pseudoflat local ring morphism.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorna Gregory (University of East Anglia)
DTSTART:20240222T140000Z
DTEND:20240222T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/148
DESCRIPTION:Title: Representation Type and Pseudofinite-dimensional Modules over
Finite-dimensional Algebras\nby Lorna Gregory (University of East Angl
ia) as part of FD Seminar\n\n\nAbstract\nThe (theory of) a class of module
s is said 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 a
bout modules) answers whether it is true in all modules in that class. A l
ong-standing conjecture of Mike Prest claims that the (theory of) the clas
s of all modules over a finite-dimensional algebra is decidable theory if
and only if it is of tame representation type. The reverse direction of th
is conjecture is often hard to prove even in particular examples. One diff
iculty is that the conjecture talks about all modules rather than just fin
ite-dimensional ones. In this talk I will present work in progress around
and in support of a new conjecture\, inspired by Prest’s conjecture\, wh
ich claims that the (theory of) the class of finite-dimensional modules ov
er a finite-dimensional algebra is decidable if and only if it is of tame
representation type.\n\nNo background knowledge in logic or model theory w
ill be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20240229T140000Z
DTEND:20240229T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/149
DESCRIPTION:Title: Okounkov's conjecture via BPS Lie algebras\nby Ben Davison
(University of Edinburgh) as part of FD Seminar\n\n\nAbstract\nGiven an a
rbitrary finite quiver Q\, Maulik and Okounkov defined a new Yangian-style
quantum group. It is built from the FRT formalism and their construction
of R matrices on the cohomology of Nakajima quiver varieties\, via the sta
ble envelopes that they also defined. Just as in the case of ordinary Yang
ians\, there is a Lie algebra g_Q inside their new algebra\, and the Yangi
an is a deformation of the current algebra of this Lie algebra.\n\nOutside
of extended ADE type\, numerous basic features of g_Q have remained myste
rious since the outset of the subject\, for example\, the dimensions of th
e graded pieces. A conjecture of Okounkov predicts that these dimensions a
re given by the coefficients of Kac’s polynomials\, which count isomorph
ism classes of absolutely indecomposable Q-representations over finite fie
lds. I will explain a recent proof\, with Botta\, of the result that the M
aulik-Okounkov Lie algebra is isomorphic to the “BPS Lie algebra” asso
ciated to the tripled quiver with potential\, defined in joint work with M
einhardt\, following the work of Kontsevich and Soibelman on critical coho
mological Hall algebras\, and then completely described in joint work with
Hennecart and Schlegel-Mejia. A corollary of these results is that Okounk
ov’s conjecture is true.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Broomhead (University of Plymouth)
DTSTART:20240314T140000Z
DTEND:20240314T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/150
DESCRIPTION:Title: Convex geometry for fans of triangulated categories\nby Na
than Broomhead (University of Plymouth) as part of FD Seminar\n\n\nAbstrac
t\nFans and other convex-geometric objects have recently appeared in homol
ogical algebra in several related contexts. For example\, as g-fans in the
silting theory of finite-dimensional algebras and as scattering diagrams
in Bridgeland stability theory. I will discuss joint work with David Pauks
ztello\, David Ploog and Jon Woolf on a general construction which we hope
will provide a natural and unifying framework. Starting with a triangulat
ed category D and a finite rank quotient lattice L of its Grothendieck gro
up\, 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 fo
rward tilts form a heart fan’ in V. If H is `algebraic’\, i.e. is a le
ngth category with finitely many simple objects\, then the heart cone is s
implicial and the heart fan is complete.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Linckelmann (City\, University of London)
DTSTART:20240321T140000Z
DTEND:20240321T150000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/151
DESCRIPTION:Title: Generating functions for the Hochschild cohomology of symmetri
c groups\nby Markus Linckelmann (City\, University of London) as part
of FD Seminar\n\n\nAbstract\nWe start out by reviewing some classical mate
rial on the representation theory of symmetric groups and the Hochschild c
ohomology of finite-dimensional algebras. We describe generating functions
for the dimensions of the Hochschild cohomology of symmetric groups in ea
ch degree.\n\nWhile it is known\, using the classification of finite simpl
e groups\, that the first Hochschild cohomology of a non-semisimple finite
group algebra is non-zero\, it remains an open question whether this is t
rue for non-simple blocks of finite groups.\n\nWe use generating functions
to show that the first Hochschild cohomology of any non-simple block of a
symmetric group algebra is non-zero. This is joint work with Dave Benson
and Radha Kessar.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (Institut des Hautes Études Scientifiques)
DTSTART:20240411T130000Z
DTEND:20240411T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/152
DESCRIPTION:Title: Fusion-equivariant stability conditions and Morita duality
\nby Edmund Heng (Institut des Hautes Études Scientifiques) as part of FD
Seminar\n\n\nAbstract\nClassically\, finite symmetries are captured by th
e action of a finite group. Moving to the quantum world\, one has to allow
for (possibly non-invertible) quantum symmetries — these are instead ca
ptured by the action of a more general algebraic structure\, known as a fu
sion category. Such quantum symmetries are actually ubiquitous in mathemat
ics\; for 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 act
ion of the category of representations rep(G)\, where rep(G) has the struc
ture of a fusion category.\nThe aim of this talk is to study the role of f
usion categories as “quantum symmetries” in relation to (Bridgeland) s
tability conditions. Given a triangulated category equipped an action of a
fusion category C\, we introduce the notion of “C-equivariant stability
conditions”\, a generalisation of “G-invariant stability conditions
”. The first result is that these stability conditions form a closed sub
manifold of the stability manifold\, just as the G-invariant stability con
ditions do. Moreover\, given a triangulated D with a G-action\, so that it
s G-equivariant category D^G has a rep(G)-action\, we will see the followi
ng (Morita) duality result for stability conditions: the complex manifold
of G-invariant stability conditions (associated to D) is homeomorphic to t
he complex 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://stable.researchseminars.org/talk/fd-seminar/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azzurra Ciliberti (University of Rome La Sapienza)
DTSTART:20240502T130000Z
DTEND:20240502T140000Z
DTSTAMP:20260404T131145Z
UID:fd-seminar/153
DESCRIPTION:Title: Categorification of cluster algebras of type B and C through s
ymmetric quivers and their representations\nby Azzurra Ciliberti (Univ
ersity of Rome La Sapienza) as part of FD Seminar\n\n\nAbstract\nAfter rec
alling the combinatorial description of their cluster complex\, we will st
ate a cluster expansion formula for cluster algebras of type B and C in te
rms of cluster variables of type A. Then\, we will explain how to associat
e a symmetric quiver with relations Q to any seed of a cluster algebra of
type B and C. Under this correspondence\, cluster variables of type B (res
p. C) correspond to orthogonal (resp. symplectic) indecomposable represent
ations of Q. Finally\, we will give a categorical interpretation of the cl
uster expansion formula in the case of acyclic quivers.\n
LOCATION:https://stable.researchseminars.org/talk/fd-seminar/153/
END:VEVENT
END:VCALENDAR