BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Theo Raedschelders (VUB (Brussels))
DTSTART:20200420T120000Z
DTEND:20200420T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/1
DESCRIPTION:Title: Proper connective differential graded algebras and their geo
metric realizations\nby Theo Raedschelders (VUB (Brussels)) as part of
Paris algebra seminar\n\nLecture held in Zoom.\n\nAbstract\nA dg algebra
A admits a geometric realization if the category of perfect dg A-modules c
an be embedded into the bounded derived category of a smooth projective va
riety. In this talk\, I will first give an overview of Orlov's results on
geometric realizations of dg algebras\, and then explain how all dg algebr
as with finite dimensional cohomology\, which are moreover concentrated in
non-positive degrees\, admit such realizations. The proof is based on a g
eneralization of the Auslander algebra of a finite dimensional algebra to
the setting of finite-dimensional A-infinity algebras. If time allows\, I
will discuss several corollaries related to finite-dimensional models\, no
ncommutative motives\, and non-Fourier-Mukai functors. This is based on jo
int work with Alice Rizzardo\, Greg Stevenson\, and Michel Van den Bergh.\
n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Orsay)
DTSTART:20200427T120000Z
DTEND:20200427T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/2
DESCRIPTION:Title: Associahedra and the Grothendieck group of an extriangulated
structure on the cluster category\nby Pierre-Guy Plamondon (Orsay) as
part of Paris algebra seminar\n\nLecture held in Zoom.\n\nAbstract\nThe a
ssociahedron is a polytope that encodes Catalan families. One of its many
avatars is as a polytopal realization of the g-vector fan of a cluster alg
ebra of type A. Given a cluster algebra with fixed initial seed\, the spa
ce of all polytopal realizations of its g-vector fan has been of interest
to physicists\, appearing for instance in the work of Arkani-Hamed\, Bai\,
He and Yan.\n\nIn this talk\, we will see how a description of the set of
all polytopal realizations of the g-vector fan of any cluster algebra of
finite type with any initial seed can be described by looking for a minima
l set of relations between its g-vectors. To find such a set\, we will se
e how a sub-extriangulated structure of the triangulated structure of the
cluster category allows for a categorification of g-vectors\, and find all
relations in its Grothendieck group.\n\nThis is a report on a joint work
with Arnau Padrol\, Yann Palu and Vincent Pilaud.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Cuntz (Hannover)
DTSTART:20200504T120000Z
DTEND:20200504T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/3
DESCRIPTION:Title: Frieze patterns with coefficients\nby Michael Cuntz (Han
nover) as part of Paris algebra seminar\n\nLecture held in Zoom.\n\nAbstra
ct\nFriezes with coefficients are maps assigning numbers to the edges and
diagonals of a regular polygon such that all Ptolemy relations for crossin
g diagonals are satisfied. These are relevant for example for the study of
cluster algebras\, in a special case they may also be viewed as root syst
ems of certain quantum groups. \nIn this talk I will report on recent resu
lts on subpolygons of friezes. Depending on the domain of the entries of t
he friezes\, these subpolygons satisfy interesting arithmetic obstructions
.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (覃㠶) (Shanghai Jiao Tong)
DTSTART:20200518T120000Z
DTEND:20200518T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/4
DESCRIPTION:Title: Dual canonical bases and quantum cluster algebras\nby Fa
n Qin (覃㠶) (Shanghai Jiao Tong) as part of Paris algebra seminar\n\nLe
cture held in Zoom.\n\nAbstract\nFomin and Zelevinsky invented cluster alg
ebras\, which are algebras with distinguished generators called cluster va
riables. For any symmetrizable Kac-Moody algebra and Weyl group element\,
the corresponding quantum unipotent subgroup possesses the dual canonical
basis\, and it can be viewed as a (quantum) cluster algebra. As a main mot
ivation by Fomin and Zelevinsky\, it has been long conjectured that the qu
antum cluster monomials (certain monomials of cluster variables) belong to
the dual canonical basis up to scalar multiples. We sketch a proof of thi
s conjecture in full generality.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hironori Oya (Shibaura Inst. of Technology)
DTSTART:20200525T120000Z
DTEND:20200525T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/5
DESCRIPTION:Title: Newton-Okounkov polytopes of Schubert varieties arising from
cluster structures and representation-theoretic polytopes\nby Hirono
ri Oya (Shibaura Inst. of Technology) as part of Paris algebra seminar\n\n
\nAbstract\nThe theory of Newton-Okounkov bodies is a generalization of \n
that of Newton polytopes for toric varieties. One of the ingredients for \
nthe definition of a Newton-Okounkov body is a valuation on the function \
nfield of a given projective variety. In this talk\, we consider Newton-\n
Okounkov bodies of Schubert varieties defined from specific valuations \nw
hich generalize extended g-vectors in cluster theory. We show that they \n
provide polytopes unimodularly equivalent to string polytopes and \nNakash
ima-Zelevinsky polytopes\, both of which are well-known polytopes \nin rep
resentation theory. Indeed\, this framework allows us to connect \nstring
polytopes with Nakashima-Zelevinsky polytopes by tropicalized \ncluster mu
tations. \nThis talk is based on a joint work with Naoki Fujita.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrien Brochier (University of Paris)
DTSTART:20200511T120000Z
DTEND:20200511T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/6
DESCRIPTION:Title: On invertible braided tensor categories\nby Adrien Broch
ier (University of Paris) as part of Paris algebra seminar\n\n\nAbstract\n
Dualizability and invertibility are two natural properties one can ask for
objects in (possibly\nhigher) symmetric monoidal categories. On the one h
and\, it recovers as special cases various\nimportant notions in geometry
and representation theory. On the other hand\, it connects those\nnotions
to topology via the cobordism hypothesis. I will explain various examples
of this philosophy\, with an emphasis on applications to finite braided te
nsor categories. This is based on joint work with D. Jordan\, P. Safronov
and N. Snyder.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustavo Jasso (Bonn)
DTSTART:20200601T120000Z
DTEND:20200601T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/7
DESCRIPTION:Title: The symplectic geometry of higher Auslander algebras\nby
Gustavo Jasso (Bonn) as part of Paris algebra seminar\n\n\nAbstract\nIt i
s well known that the partially wrapped Fukaya category of a marked\ndisk
is equivalent to the perfect derived category of a Dynkin quiver of\ntype
A. In this talk I will present a higher-dimensional generalisation\nof thi
s equivalence which reveals a connection between three a\npriori unrelated
subjects:\n\n* Floer theory of symmetric products of marked surfaces
\
n* Higher Auslander-Reiten theory in the sense of Iyama
\n* Waldhausen
K-theory of differential graded categories\n\nIf time permits\, as a first
application of the above relationship\, I\nwill outline a symplecto-geome
tric proof of a recent result of Beckert\nconcerning the derived equivalen
ce between higher Auslander algebras of\ndifferent dimensions. This is a r
eport on joint work with Tobias\nDyckerhoff and Yankı Lekili.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Rognerud (University of Paris)
DTSTART:20200608T120000Z
DTEND:20200608T123000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/8
DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, I\nby Bap
tiste Rognerud (University of Paris) as part of Paris algebra seminar\n\n\
nAbstract\nQuasi-hereditary algebras were introduced by Cline\, Parshall a
nd Scott as a tool to study highest weight theories which arise in the rep
resentation theories of semi-simple complex Lie algebras and reductive gro
ups. Surprisingly\, there are now many examples of such algebras\, such as
Schur algebras\, algebras of global dimension at most two\, incidence alg
ebras and many more.\n\nA quasi-hereditary algebra is an Artin algebra tog
ether with a partial order on its set of isomorphism classes of simple mod
ules which satisfies certain conditions. In the early examples the partial
order predated (and motivated) the theory\, so the choice was clear. Howe
ver\, there are instances of quasi-hereditary algebras where there is no n
atural choice for the partial ordering and even if there is such a natural
choice\, one may wonder about all the possible orderings.\nIn this talk w
e will explain that all these choices for an algebra $A$ can be organized
in a finite partial order which is in relation with the tilting theory of
$A$. In a second part of the talk we will focus on the case where $A$ is t
he path algebra of a Dynkin quiver.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (Bielefeld)
DTSTART:20200608T123000Z
DTEND:20200608T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/9
DESCRIPTION:Title: Combinatorics of quasi-hereditary structures\, II\nby Yu
ta Kimura (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nQuas
i-hereditary algebras were introduced by Cline\, Parshall and Scott as a t
ool to study highest weight theories which arise in the representation the
ories of semi-simple complex Lie algebras and reductive groups. Surprising
ly\, there are now many examples of such algebras\, such as Schur algebras
\, algebras of global dimension at most two\, incidence algebras and many
more.\n\nA quasi-hereditary algebra is an Artin algebra together with a pa
rtial order on its set of isomorphism classes of simple modules which sati
sfies certain conditions. In the early examples the partial order predated
(and motivated) the theory\, so the choice was clear. However\, there are
instances of quasi-hereditary algebras where there is no natural choice f
or the partial ordering and even if there is such a natural choice\, one m
ay wonder about all the possible orderings.\nIn this talk we will explain
that all these choices for an algebra $A$ can be organized in a finite par
tial order which is in relation with the tilting theory of $A$. In a secon
d part of the talk we will focus on the case where $A$ is the path algebra
of a Dynkin quiver.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss (UNAM)
DTSTART:20200615T120000Z
DTEND:20200615T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/10
DESCRIPTION:Title: Generic bases for surface cluster algebras\nby Christof
Geiss (UNAM) as part of Paris algebra seminar\n\n\nAbstract\nThis is a re
port on joint work with D. Labardini-Fragoso and J. Schröer. We show that
for most marked surfaces with non-empty boundary\, possibly with puncture
s\, the generic Caldero-Chapoton functions form a basis of the correspondi
ng cluster algebras for any choice of geometric coefficients. For surfaces
without punctures the $\\tau$-reduced components of the corresponding gen
tle Jacobian algebra are naturally parametrized by X-laminations of the su
rface\, and it is easy to see that for principal coefficients\, the generi
c basis coincides with the bangle basis introduced by Musiker-Schiffler-Wi
lliams.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myungho Kim (Kyung Hee University\, Seoul)
DTSTART:20200622T120000Z
DTEND:20200622T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/11
DESCRIPTION:Title: Braid group action on the module category of quantum affine
algebras\nby Myungho Kim (Kyung Hee University\, Seoul) as part of Pa
ris algebra seminar\n\n\nAbstract\nLet $g_0$ be a simple Lie algebra of ty
pe $ADE$ and let $U′_q(g)$ be the corresponding untwisted quantum affine
algebra. We found an action of the braid group $B(g_0)$ on the quantum Gr
othendieck ring $K_t(g)$ of Hernandez-Leclerc's category $C^0_g$. In the c
ase of $g_0=A_{N−1}$\, we construct a monoidal autofunctor $S_i$ for eac
h integer $i$ on a category $T_N$ arising from the quiver Hecke algebra o
f type $A_\\infty$. \nSince there is an isomorphism between the Grothendie
ck ring $K(T_N)$ of $T_N$ and the quantum Grothendieck ring $K_t(A^(1)_{N
−1})$\, the functors $S_i$\, $(i=1\, ...\, N-1)$\, recover the action of
the braid group $B(A_{N−1})$. \nThis is a joint work with Masaki Kashiw
ara\, Euiyong Park and Se-jin Oh.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Iyama (Nagoya)
DTSTART:20200713T120000Z
DTEND:20200713T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/13
DESCRIPTION:Title: Tilting theory of contracted preprojective algebras and cDV
singularities\nby Osamu Iyama (Nagoya) as part of Paris algebra semin
ar\n\n\nAbstract\nA preprojective algebra of non-Dynkin type has a family
of tilting modules associated with the elements in the corresponding Coxet
er group W. This family is useful to study the representation theory of th
e preprojective algebra and also to categorify cluster algebras.\nIn this
talk\, I will discuss tilting theory of a contracted preprojective algebra
\, which is a subalgebra eAe of a preprojective algebra A given by an idem
potent e of A. It has a family of tilting modules associated with the cham
bers in the contracted Tits cone. They correspond bijectively with certain
double cosets in W modulo parabolic subgroups. \nI will apply these resul
ts to classify a certain family of reflexive modules over a cDV singularit
ies R\, called maximal modifying (=MM) modules. We construct an injective
map from MM R-modules to tilting modules over a contracted preprojective a
lgebra of extended Dynkin type. This is bijective if R has at worst an iso
lated singularity. We can recover previous results (Burban-I-Keller-Reiten
\, I-Wemyss) as a very special case.\nThis is joint work with Michael Wemy
ss.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linyuan Liu (刘琳媛) (Sydney)
DTSTART:20200629T120000Z
DTEND:20200629T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/14
DESCRIPTION:Title: Modular Brylinski-Kostant filtration of tilting modules
\nby Linyuan Liu (刘琳媛) (Sydney) as part of Paris algebra seminar\n\n
\nAbstract\nLet $G$ be a reductive algebraic group over a field $k$. When
$k=\\mathbb{C}$\, R. K. Brylinski constructed a filtration of weight space
s of a $G$-module\, using the action of a principal nilpotent element of t
he Lie algebra\, and proved that this filtration corresponds to Lusztig's
$q$-analogue of the weight multiplicity. Later\, Ginzburg discovered that
this filtration has an interesting geometric interpretation via the geomet
ric Satake correspondence. Recently\, we managed to generalise this result
to the case where $k$ is a field of good positive characteristics. I will
give a brief introduction to both historical results and our new result i
n the talk.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Fang (房欣) (Cologne)
DTSTART:20200706T120000Z
DTEND:20200706T123000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/15
DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\, I
\nby Xin Fang (房欣) (Cologne) as part of Paris algebra seminar\n\n\nAbs
tract\nIn this talk\, we will explain relations between exact structures o
n an additively finite additive category and degenerations of the associat
ed Hall algebras. The first part of the talk will be devoted to the main m
otivation provided by concrete examples of degenerations of negative parts
of quantum groups arising as Hall algebras of quiver representations. We
will then turn to Lie theory in order to establish a link from these examp
les to tropical flag varieties and certain quiver Grassmannians. In the se
cond part of the talk we will present results in the general case and sket
ch their proofs based on Auslander-Reiten theory. If time permits\, we wil
l briefly discuss further conjectural examples and generalizations.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Stuttgart)
DTSTART:20200706T123000Z
DTEND:20200706T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/16
DESCRIPTION:Title: Exact structures and degenerations of Hall algebras\, II\nby Mikhail Gorsky (Stuttgart) as part of Paris algebra seminar\n\n\nAbs
tract\nIn this talk\, we will explain relations between exact structures o
n an additively finite additive category and degenerations of the associat
ed Hall algebras. The first part of the talk will be devoted to the main m
otivation provided by concrete examples of degenerations of negative parts
of quantum groups arising as Hall algebras of quiver representations. We
will then turn to Lie theory in order to establish a link from these examp
les to tropical flag varieties and certain quiver Grassmannians. In the se
cond part of the talk we will present results in the general case and sket
ch their proofs based on Auslander-Reiten theory. If time permits\, we wil
l briefly discuss further conjectural examples and generalizations.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Prague)
DTSTART:20200914T120000Z
DTEND:20200914T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/17
DESCRIPTION:Title: The Cohen–Macaulay property in derived algebraic geometry
\nby Liran Shaul (Prague) as part of Paris algebra seminar\n\n\nAbstra
ct\nIn this talk\, we explain how to extend the theory of Cohen-Macaulay\n
rings to the setting of commutative non-positive DG-rings. By studying\nlo
cal cohomology in the DG-setting\, one obtains certain amplitude\ninequali
ties about certain DG-modules of finite injective dimension.\nWhen these i
nequalities are equalities\, we arrive at the notion of a\nCohen-Macaulay
DG-ring.\n\nWe then show that these arise naturally in many situations\, a
nd\nexplain their basic theory. We explain that any derived quotient of a
\nCohen-Macaulay ring is Cohen-Macaulay\,\nand show that Cohen-Macaulaynes
s is the generic local situation in\nderived algebraic geometry: under mil
d hypothesis\, every eventually\ncoconnective locally noetherian derived s
cheme is Cohen-Macaulay on a\ndense open set.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengfang Wang (Stuttgart)
DTSTART:20200928T120000Z
DTEND:20200928T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/18
DESCRIPTION:Title: $B_\\infty$-algebras and Keller’s conjecture for singular
Hochschild cohomology\nby Zhengfang Wang (Stuttgart) as part of Paris
algebra seminar\n\n\nAbstract\nWe first give a basic introduction to $B_\
\infty$-algebras. Then from a $B_\\infty$-algebra A\, we contruct two new
$B_\\infty$-algebras by using two different swapping maps: the opposite $
B_\\infty$-algebra and the transpose $B_\\infty$-algebra. Quite surprising
ly\, we show that under a certain condition on A (satisfied\, for instance
\, by brace $B_\\infty$-algebras or Gerstenhaber-Voronov algebras) these t
wo $B_\\infty$-algebras are naturally isomorphic\, which is motivated from
Kontsevich-Soibelman's minimal operad. \n\nWe also explain the role of th
e above result in the proof of Keller's conjecture for singular Hochschild
cohomology in the case of radical square zero algebras. This is joint wor
k with Xiaowu Chen and Huanhuan Li.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Julia Redondo (Bahia Blanca)
DTSTART:20200921T120000Z
DTEND:20200921T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/19
DESCRIPTION:Title: $L_\\infty$-structure on Barzdell's complex for monomial al
gebras\nby Maria Julia Redondo (Bahia Blanca) as part of Paris algebra
seminar\n\n\nAbstract\nWhen dealing with a monomial algebra $A$\, Bardzel
l’s complex $B(A)$ has shown to be more efficient for computing Hochschi
ld cohomology groups of $A$ than the Hochschild complex $C(A)$.\nSince $C(
A)[1]$ is a dg Lie algebra\, it is natural to ask if the comparison morphi
sms between these complexes allows us to transfer the dg Lie structure to
$B(A)[1]$. This is true for radical square zero algebras\, but it is not
true in general for monomial algebras.\nIn this talk\, I will describe an
explicit $L_\\infty$-structure on $B(A)$ that induces a weak equivalence o
f $L_\\infty$-algebras between $B(A)$ and $C(A)$. This allows us to descr
ibe the Maurer-Cartan equation in terms of elements of degree 2 in $B(A)$
and make concrete computations when $A$ is a truncated monomial algebra.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (UBC Vancouver)
DTSTART:20201005T120000Z
DTEND:20201005T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/20
DESCRIPTION:Title: Wall-crossing and differential equations\nby Dylan Alle
gretti (UBC Vancouver) as part of Paris algebra seminar\n\n\nAbstract\nThe
Kontsevich-Soibelman wall-crossing formula describes the wall-crossing be
havior of BPS invariants in Donaldson-Thomas theory. It can be formulated
as an identity between (possibly infinite) products of automorphisms of a
formal power series ring. In this talk\, I will explain how these same pro
ducts also appear in the exact WKB analysis of Schrödinger's equation. In
this context\, they describe the Stokes phenomenon for objects known as V
oros symbols.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Fujita (Paris\, IMJ-PRG)
DTSTART:20201012T120000Z
DTEND:20201012T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/22
DESCRIPTION:Title: Twisted Auslander-Reiten quivers\, quantum Cartan matrix an
d representation theory of quantum affine algebras\nby Ryo Fujita (Par
is\, IMJ-PRG) as part of Paris algebra seminar\n\n\nAbstract\nFor a comple
x simple Lie algebra $g$\, its quantum Cartan matrix plays an important ro
le in the representation theory of the quantum affine algebra of $g$. When
$g$ is of type ADE\, Hernandez-Leclerc (2015) related its quantum Cartan
matrix with the representation theory of Dynkin quivers and hence with the
combinatorics of adapted words in the Weyl group of the corresponding ADE
type. In this talk\, we introduce the notion of Q-data\, which can be reg
arded as a combinatorial generalization of a Dynkin quiver with height fun
ction\, and its twisted Auslander-Reiten quiver. Using them\, we relate th
e quantum Cartan matrix of type BCFG with the combinatorics of twisted ada
pted words in the Weyl group of the corresponding unfolded ADE type introd
uced by Oh-Suh (2019). Also\, we see their relation to the representation
theory of quantum affine algebras. For example\, we present a (partially c
onjectural) unified expression of the denominators of R-matrices between t
he Kirillov-Reshetikhin modules in terms of the quantum Cartan matrices. T
his is a joint work with Se-jin Oh.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norihiro Hanihara (Nagoya)
DTSTART:20201019T120000Z
DTEND:20201019T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/23
DESCRIPTION:Title: Cluster categories of formal dg algebras\nby Norihiro H
anihara (Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nCluster c
ategories are Calabi-Yau triangulated categories endowed with cluster tilt
ing objects. They have played an important role in the (additive) categori
fication of cluster algebras. We study the version developed by Amiot-Guo-
Keller\, which is defined in terms of CY dg algebras. Given a negatively g
raded (non-dg) CY algebra\, we view it as a dg algebra with trivial differ
ential. We give a description of the cluster category of such a formal dg
algebra as the triangulated hull of an orbit category of a derived categor
y\, and also as the singularity category of a finite dimensional algebra.
Furthermore\, if time permits\, we will talk about a certain converse of t
his construction\, giving a \nMorita-type theorem for CY triangulated cate
gories arising from hereditary algebras\, partially generalizing that of K
eller-Reiten.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Launois (Kent)
DTSTART:20201109T130000Z
DTEND:20201109T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/24
DESCRIPTION:Title: Catenarity and Tauvel’s height formula for quantum nilpot
ent algebras\nby Stéphane Launois (Kent) as part of Paris algebra sem
inar\n\n\nAbstract\nThis talk is based on joint work with Ken Goodearl and
Tom Lenagan. \nI will explain why quantum nilpotent algebras are catenar
y\, that is\, why all saturated chains of inclusions of prime ideals in a
quantum nilpotent algebra have the same length. As a corollary\, we obtain
that Tauvel’s height formula holds for quantum nilpotent algebras. Time
permitting\, \nI will present a different strategy to prove the latter re
sult.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wai-kit Yeung (Tokyo\, IPMU)
DTSTART:20201026T130000Z
DTEND:20201026T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/25
DESCRIPTION:Title: Pre-Calabi-Yau algebras\nby Wai-kit Yeung (Tokyo\, IPMU
) as part of Paris algebra seminar\n\n\nAbstract\nPre-Calabi-Yau categorie
s are algebraic structures first studied by Kontsevich and Vlassopoulos. T
hey can be viewed as a noncommutative analogue of Poisson structures\, jus
t like Calabi-Yau structures can be viewed as a noncommutative analogue of
symplectic structures. In this talk\, we discuss several aspects of this
notion.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleonore Faber (Leeds)
DTSTART:20201116T130000Z
DTEND:20201116T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/26
DESCRIPTION:Title: McKay quivers of complex reflection groups and the McKay co
rrespondence\nby Eleonore Faber (Leeds) as part of Paris algebra semin
ar\n\n\nAbstract\nFinite complex reflection groups were classified by Shep
herd\nand Todd: up to finitely many exceptions they are the groups G(r\,p\
,n).\nIn this talk we give a combinatorial description of the McKay quiver
s of\nthese groups. Further we will comment on a McKay correspondence for\
ncomplex reflection groups. This is joint work with R.-O. Buchweitz\, C.\n
Ingalls\, and M. Lewis.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Scherotzke (Luxembourg)
DTSTART:20201123T130000Z
DTEND:20201123T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/27
DESCRIPTION:Title: Cotangent complexes of moduli spaces and Ginzburg dg algebr
as\nby Sarah Scherotzke (Luxembourg) as part of Paris algebra seminar\
n\n\nAbstract\nWe start by giving an introduction to the notion of moduli
stack of a dg category. Then we will explain what shifted symplectic struc
tures are and how they are connected to Calabi-Yau structures on dg catego
ries. More concretely\, we will show that the cotangent complex of the mod
uli stack of a dg category A is isomorphic to the moduli stack of the *Cal
abi-Yau completion* of A. This answers a conjecture of Keller-Yeung. This
is joint work with Damien Calaque and Tristan Bozec available on the arXiv.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elie Casbi (MPI Bonn)
DTSTART:20201102T130000Z
DTEND:20201102T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/28
DESCRIPTION:Title: Equivariant multiplicities of simply-laced type flag minors
\nby Elie Casbi (MPI Bonn) as part of Paris algebra seminar\n\n\nAbstr
act\nThe study of remarkable bases of (quantum) coordinate rings has been
an area of\nintensive research since the early 90's. For instance\, the mu
ltiplicative properties of \nthese bases (in particular the dual canonical
basis) was one of the main motivations for\nthe introduction of cluster a
lgebras by Fomin and Zelevinsky around 2000. \nIn recent work\, Baumann-Ka
mnitzer-Knutson introduced an algebra morphism \n$\\overline{D}$ from the
coordinate algebra $\\mathbb{C}[N]$ of a maximal unipotent subgroup $N$\n
to the function field of a maximal torus. It is related to the geometry of
\nMirkovic-Vilonen cycles via the notion of equivariant multiplicity. Thi
s morphism \nturns out to be useful for comparing good bases of the coordi
nate algebra \n$\\mathbb{C}[N]$. We will focus on comparing the values ta
ken by $\\overline{D}$ on several distinguished elements of the Mirkovic-V
ilonen basis and the dual canonical basis. For the latter one\,\nwe will u
se Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster\nstruc
ture of the cluster structure of $\\mathbb{C}[N]$ via quiver Hecke algebra
s as well as\nrecent results by Kashiwara-Kim. This will lead us to an exp
licit description of\nthe images under $\\overline{D}$ of the flag minors
of $\\mathbb{C}[N]$ as well as remarkable\nidentities between them.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Bochum)
DTSTART:20201130T130000Z
DTEND:20201130T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/29
DESCRIPTION:Title: Wild quantum dilogarithm identities\nby Markus Reineke
(Bochum) as part of Paris algebra seminar\n\n\nAbstract\nWe formulate and
discuss "wild" analogues of the Fadeev-Kashaev identity for quantum diloga
rithms. We review a general quiver setup\nfor such identities\, resulting
from wall-crossing formulas\, motivic Donaldson-Thomas invariants\, and th
e geometry of quiver moduli spaces. The quantum dilogarithm identities are
then derived from special properties of representations of generalized Kr
onecker quivers.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manon Defosseux (Université de Paris)
DTSTART:20210111T130000Z
DTEND:20210111T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/30
DESCRIPTION:Title: Brownian motion in the unit interval and the Littelmann pat
h model\nby Manon Defosseux (Université de Paris) as part of Paris al
gebra seminar\n\n\nAbstract\nWe will present for a Brownian motion in the
unit interval a Pitman type\ntheorem obtained recently in joint work with
Philippe Bougerol. We will focus\non algebraic aspects and will explain ho
w it is related to the Littelmann path\nmodel for an affine Kac–Moody al
gebra of extended type $A_1$.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Estanislao Herscovich (Grenoble)
DTSTART:20210118T130000Z
DTEND:20210118T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/31
DESCRIPTION:Title: Double quasi-Poisson algebras are pre-Calabi-Yau\nby Es
tanislao Herscovich (Grenoble) as part of Paris algebra seminar\n\n\nAbstr
act\nDouble Poisson and double quasi-Poisson algebras were introduced by M
. Van den Bergh in his study of noncommutative quasi-Poisson geometry. Nam
ely\, they satisfy the so-called Kontsevich-Rosenberg principle\, since th
e representation scheme of a double (quasi-)Poisson algebra has a natural
(quasi-)Poisson structure. On the other hand\, N. Iyudu and M. Kontsevich
found a link between double Poisson algebras and pre-Calabi-Yau algebras\,
a notion introduced by Kontsevich and Y. Vlassopoulos. The aim of this ta
lk will be to explain how such a connection can be extended to double quas
i-Poisson algebras\, which thus give rise to pre-Calabi-Yau algebras. This
pre-Calabi-Yau structure is however more involved in the case of double q
uasi-Poisson algebras since\, in particular\, we get an infinite number of
nonvanishing higher multiplications for the associated pre-Calabi-Yau alg
ebra\, which involve the Bernoulli numbers. \n\nThis is joint work with D.
Fernández from the Universität Bielefeld.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Letellier (Université de Paris)
DTSTART:20201214T130000Z
DTEND:20201214T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/32
DESCRIPTION:Title: E-series of character varieties associated with non orienta
ble surfaces\nby Emmanuel Letellier (Université de Paris) as part of
Paris algebra seminar\n\n\nAbstract\nIn this talk we will be interested in
two kinds of character varieties associated to a compact non-orientable s
urface S. The first one is just the quotient stack of all representations
of the fundamental group of S in GL(n\,C). For the second one\, we conside
r k punctures of S as well as k semisimple conjugacy classes of GL(n\,C).
We then consider the stack of anti-invariant local systems on the orienta
tion covering of S with local monodromies around the punctures in the pres
cribed conjugacy classes. We compute the number of points of these spaces
over finite fields and we give a cohomological interpretation of our count
ing formulas. For the second kind of character varieties\, we give a conje
ctural formula for the mixed Poincaré series in terms of Macdonald symmet
ric functions.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruslan Maksimau (Montpellier)
DTSTART:20201207T130000Z
DTEND:20201207T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/33
DESCRIPTION:Title: KLR algebras for curves and semi-cuspidal representations\nby Ruslan Maksimau (Montpellier) as part of Paris algebra seminar\n\n\
nAbstract\nThe talk is based on the preprint arXiv:2010.01419. This is joi
nt work with Alexandre Minets.\n\nThe KLR algebras (also called quiver Hec
ke algebras) are known to have the following geometric construction: they
are isomorphic to the (equivariant) Borel-Moore homology of the Steinberg
variety. A point of this variety is given by a representation of a quiver
and two full flags of subrepresentations.\n\nWe define and study analogues
of KLR algebras for curves (curve Hecke algebras). We define these algebr
as geometrically\, similarly to usual KLR algebras. But we replace represe
ntations of a quiver by torsion sheaves on a smooth curve C. In particular
\, for C=P1\, we get a geometric realization of the affine zigzag algebra
of type A1. The case C=P1 is particularly interesting because it allows us
to describe the imaginary semi-cuspidal category for the KLR algebra for
affine sl2.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Lebed (Caen)
DTSTART:20210125T130000Z
DTEND:20210125T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/34
DESCRIPTION:Title: Homotopical tools for computing rack homology\nby Victo
ria Lebed (Caen) as part of Paris algebra seminar\n\n\nAbstract\nRacks are
certain algebraic structures yielding powerful tools for knot theory\, Ho
pf algebra classification and other areas. Rack homology plays a crucial r
ole in these applications. The homology of a rack is very easy to define (
via an explicit chain complex)\, but extremely difficult to compute. Until
recently\, the full homology was known only for three families of racks.
Together with Markus Szymik\, we added a forth family to this list\, the f
amily of permutation racks. More importantly\, our work unexpectedly broug
ht homotopical methods into the area\, and showed that in spite of their a
bstract flavour they can yield concrete computations. The necessary backgr
ound on racks and their homology\, as well as an overview of the tools pre
viously used for its computation\, will be given.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Yekutieli (Ben Gurion University)
DTSTART:20210301T130000Z
DTEND:20210301T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/35
DESCRIPTION:Title: Rigidity\, Residues and Duality: Overview and Recent Progre
ss\nby Amnon Yekutieli (Ben Gurion University) as part of Paris algebr
a seminar\n\n\nAbstract\nIn this lecture\, we explain the theory of rigid
residue complexes in commutative algebra and algebraic geometry. Unlike al
l previous approaches to Grothendieck Duality\, the rigid approach concent
rates on rigid residue complexes over rings\, and their intricate yet robu
st properties. Most of the lecture will about the results for rings. The g
eometrization\, i.e. the passage to rigid residue complexes on schemes and
Deligne-Mumford (DM) stacks\, by gluing\, is fairly easy. In the geometri
c part of the theory\, the main results are the Rigid Residue Theorem and
the Rigid Duality Theorem for proper maps between schemes\, and for tame p
roper maps between DM stacks. These results will only be outlined briefly.
\n\nMore details are available in the eprint with the same title at\nhttp
s://arxiv.org/abs/2102.00255\n\nThe lecture notes can be downloaded from
\nhttp://www.math.bgu.ac.il/~amyekut/lectures/RRD-2021/notes.pdf\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Tamaroff (Dublin)
DTSTART:20210201T130000Z
DTEND:20210201T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/36
DESCRIPTION:Title: Poincaré--Birkhoff--Witt theorems: homotopical and effecti
ve computational methods for universal envelopes\nby Pedro Tamaroff (D
ublin) as part of Paris algebra seminar\n\n\nAbstract\nIn joint work with
V. Dotsenko\, we developed a categorical framework for Poincaré-Birkhoff-
Witt type theorems about universal enveloping algebras of various algebrai
c structures\, and used methods of term rewriting for operads to obtain ne
w PBW theorems\, in particular answering an open question of J.-L. Loday.
Later\, in joint work with A. Khoroshkin\, we developed a formalism to stu
dy Poincaré–Birkhoff–Witt type theorems for universal envelopes of al
gebras over differential graded operads\, motivated by the problem of comp
uting the universal enveloping algebra functor on dg Lie algebras in the h
omotopy category. Our formalism allows us\, among other things\, to obtain
a homotopy invariant version of the classical Poincaré–Birkhoff–Witt
theorem for universal envelopes of Lie algebras\, and extend Quillen's qu
asi-isomorphism C(g) ---> BU(g) to homotopy Lie algebras. I will survey an
d explain the role homological algebra\, homotopical algebra\, and effecti
ve computational methods play in the main results obtained with both V. Do
tsenko (1804.06485) and A. Khoroshikin (2003.06055) and\, if time allows\,
explain a new direction in which these methods can be used to study certa
in operads as universal envelopes of pre-Lie algebras.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Kus (Bochum)
DTSTART:20210315T130000Z
DTEND:20210315T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/37
DESCRIPTION:Title: Prime representations in the Hernandez-Leclerc category
\nby Deniz Kus (Bochum) as part of Paris algebra seminar\n\n\nAbstract\nGe
nerators and relations of graded limits of certain finite dimensional irre
ducible representations of quantum affine algebras have been determined in
recent years. For example\, the representations in the Hernandez-Leclerc
category corresponding to cluster variables appear to be certain truncatio
ns of representations for current algebras and tensor products are related
to the notion of fusion products. In this talk we will discuss some known
results on this topic and study the classical and graded characters of pr
ime representations in the HL category.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern)
DTSTART:20210215T130000Z
DTEND:20210215T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/38
DESCRIPTION:Title: Root of unity quantum cluster algebras\nby Milen Yakimo
v (Northeastern) as part of Paris algebra seminar\n\n\nAbstract\nWe will d
escribe a theory of root of unity quantum cluster algebras\, which are not
necessarily specializations of quantum cluster algebras. All such algebra
s are shown to be polynomial identity (PI) algebras. Inside each of them\,
we construct a canonical central subalgebra which is proved to be isomorp
hic to the underlying cluster algebra. (In turn\, this is used to show tha
t two exchange graphs are canonically isomorphic). This setting generalize
s the De Concini-Kac-Procesi central subalgebras in big quantum groups and
presents a general framework for studying the representation theory of qu
antum algebras at roots of unity by means of cluster algebras as the relev
ant data becomes (PI algebra\, canonical central subalgebra)=(root of unit
y quantum cluster algebra\, underlying cluster algebra). We also obtain a
formula for the corresponding discriminant in this general setting that ca
n be applied in many concrete situations of interest\, such as the discrim
inants of all root of unity quantum unipotent cells for symmetrizable Kac-
Moody algebras\, defined integrally over Z[root of unity]. This is a joint
work with Bach Nguyen (Xavier Univ) and Kurt Trampel (Notre Dame Univ).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sondre Kvamme (Uppsala)
DTSTART:20210208T130000Z
DTEND:20210208T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/39
DESCRIPTION:Title: Admissibly finitely presented functors for exact categories
\nby Sondre Kvamme (Uppsala) as part of Paris algebra seminar\n\n\nAbs
tract\nIn this talk we introduce the category of admissibly finitely prese
nted functors mod_{adm}(E) for an exact category E. In particular\, we ch
aracterize exact categories of the form mod_{adm}(E)\, and show that they
have properties similar to module categories of Auslander algebras. For a
fixed idempotent complete category C\, we also use this construction to sh
ow that exact structures on C correspond to certain resolving subcategorie
s in mod(C). This is joint work with Ruben Henrard and Adam-Christiaan van
Roosmalen.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Fujita (University of Paris)
DTSTART:20210308T130000Z
DTEND:20210308T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/40
DESCRIPTION:Title: Isomorphisms among quantum Grothendieck rings and propagati
on of positivity\nby Ryo Fujita (University of Paris) as part of Paris
algebra seminar\n\n\nAbstract\nFor a complex simple Lie algebra $\\mathfr
ak{g}$\, finite-dimensional representations of its quantum loop algebra fo
rm an interesting monoidal abelian category\, which has been studied from
various perspectives. Related to the fundamental problem of determining th
e characters of irreducible representations\, we consider its quantum Grot
hendieck ring\, a 1-parameter deformation of the usual Grothendieck ring.
When $\\mathfrak{g}$ is of simply-laced type\, Nakajima and Varagnolo-Vass
erot proved that it enjoys some positivity properties based on the geometr
y of quiver varieties. In this talk\, we show that the same positivities h
old also for non-simply-laced type by establishing an isomorphism between
the quantum Grothendieck ring of non-simply-laced type and that of ''unfol
ded'' simply-laced type. In addition\, we find that an analog of Kazhdan-L
usztig conjecture holds for several new cases in non-simply-laced type. Th
is is a joint work with David Hernandez\, Se-jin Oh\, and Hironori Oya.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander P. Veselov (Loughborough (UK) and Moscow (Russia))
DTSTART:20210322T130000Z
DTEND:20210322T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/42
DESCRIPTION:Title: Automorphic Lie algebras and modular forms\nby Alexande
r P. Veselov (Loughborough (UK) and Moscow (Russia)) as part of Paris alge
bra seminar\n\n\nAbstract\nThe automorphic Lie algebras can be viewed as g
eneralisations of twisted loop Lie algebras\, when a group $G$ acts holomo
rphically and discretely on a Riemann surface and by automorphisms on the
chosen Lie algebra. \n \nIn the talk we will discuss the automorphic Lie a
lgebras of modular type\, when $G$ is a finite index subgroup of the modul
ar group $\\Gamma=SL(2\, \\mathbb Z)$ acting on the upper half plane. In
the case when the action of $G$ can be extended to $SL(2\,\\mathbb C)$ we
prove analogues of Kac’s isomorphism theorem for the twisted loop Lie al
gebras.\nFor the modular group and some of its principal congruence subgro
ups we provide an explicit description of such isomorphisms using the clas
sical theory of modular forms.\n \nThe talk is based on the ongoing joint
work with Vincent Knibbeler and Sara Lombardo.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Ovsienko (Reims)
DTSTART:20210222T130000Z
DTEND:20210222T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/43
DESCRIPTION:Title: Combinatorial and analytic properties of q-deformed real n
umbers\nby Valentin Ovsienko (Reims) as part of Paris algebra seminar\
n\n\nAbstract\nI will explain a recent notion of \nq-deformed real numbers
\, and discuss its various combinatorial and analytic properties. A "\nq-d
eformed real" is a Laurent series in one variable\, \nq\, with integer coe
fficients. The subject is connected to different theories\, such as knot i
nvariants\, continued fractions\, and cluster algebras. I will formulate a
challenging conjecture about the convergence of the series arising as \nq
-deformed real numbers. (Here we understand \nq as a complex variable.) Th
e conjecture is proved in particular cases and concrete examples. In the m
ost simple examples of q-Fibonacci and q-Pell numbers\, the explicit formu
las for the radius of convergence are very similar to certain formulas of
Ramanujan. \nThe talk is based on a joint work with Ludivine Leclere\, Sop
hie Morier-Genoud and Alexander Veselov.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksandr Tsymbaliuk (Purdue)
DTSTART:20210503T120000Z
DTEND:20210503T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/44
DESCRIPTION:Title: Quantum loop groups and shuffle algebras via Lyndon words\nby Oleksandr Tsymbaliuk (Purdue) as part of Paris algebra seminar\n\n\
nAbstract\nClassical q-shuffle algebras provide combinatorial models for t
he positive half U_q(n) of a finite quantum group. We define a loop versio
n of this construction\, yielding a combinatorial model for the positive h
alf U_q(Ln) of a quantum loop group. In particular\, we construct a PBW ba
sis of U_q(Ln) indexed by standard Lyndon words\, generalizing the work of
Lalonde-Ram\, Leclerc and Rosso in the U_q(n) case. We also connect this
to Enriquez' degeneration A of the elliptic algebras of Feigin-Odesskii\,
proving a conjecture that describes the image of the embedding U_q(Ln) ---
> A in terms of pole and wheel conditions. Joint work with Andrei Negut.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregg Musiker (Minnesota)
DTSTART:20210426T120000Z
DTEND:20210426T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/45
DESCRIPTION:Title: Combinatorial Expansion Formulas for Decorated Super-Teichm
üller Spaces\nby Gregg Musiker (Minnesota) as part of Paris algebra s
eminar\n\n\nAbstract\nMotivated by the definition of super Teichmuller spa
ces\, and Penner-Zeitlin's recent extension of this definition to decorate
d super Teichmuller space\, as examples of super Riemann surfaces\, we use
the super Ptolemy relations to obtain formulas for super lambda-lengths a
ssociated to arcs in a bordered surface. In the special case of a disk\, w
e are able to give combinatorial expansion formulas for the super lambda-l
engths associated to diagonals of a polygon in the spirit of Ralf Schiffle
r's T-path formulas for type A cluster algebras. We further connect our fo
rmulas to the super-friezes of Morier-Genoud\, Ovsienko\, and Tabachnikov\
, and obtain partial progress towards defining super cluster algebras of t
ype A. In particular\, following Penner-Zeitlin\, we are able to get formu
las (up to signs) for the mu-invariants associated to triangles in a trian
gulated polygon\, and explain how these provide a step towards understandi
ng odd variables of a super cluster algebra. This is joint work with Nich
olas Ovenhouse and Sylvester Zhang.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Mozgovoy (Trinity College Dublin)
DTSTART:20210329T120000Z
DTEND:20210329T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/47
DESCRIPTION:Title: Operadic approach to wall-crossing and attractor invariants
\nby Sergey Mozgovoy (Trinity College Dublin) as part of Paris algebra
seminar\n\n\nAbstract\nWall-crossing describes how various invariants in
algebraic geometry and theoretical physics transform under the variation o
f parameters. In this talk I will discuss a framework\, reminiscent of col
lections and plethysms in the theory of operads\, that concenptualizes tho
se transformation rules. I will describe how some new and existing wall-cr
ossing formulas can be proved using this approach. In particular\, I will
discuss applications to attractor invariants (also called initial data in
the theory of scattering diagrams).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Darpoe (Nagoya)
DTSTART:20210412T120000Z
DTEND:20210412T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/48
DESCRIPTION:Title: Periodic trivial extension algebras and fractionally Calabi
–Yau algebras\nby Erik Darpoe (Nagoya) as part of Paris algebra semi
nar\n\n\nAbstract\nAn important open problem in the homological algebra of
self-injective algebras is to characterise periodic algebras. An algebra
B is said to be periodic if if has a periodic projective resolution as a B
-B-bimodule.\n\nIn this talk\, I will present a solution to this problem f
or trivial extension algebras: the trivial extension algebra T(A) of a fin
ite-dimensional algebra A is periodic if and only if A has finite global d
imension and is fractionally Calabi-Yau.\n\nThis is based on joint work wi
th Chan\, Iyama and Marczinzik.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Baumann (Strasbourg)
DTSTART:20210510T120000Z
DTEND:20210510T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/49
DESCRIPTION:Title: Explicit calculations in the geometric Satake equivalence\nby Pierre Baumann (Strasbourg) as part of Paris algebra seminar\n\n\nA
bstract\nLet $G$ be a complex connected reductive group. As shown by Mirko
vić and Vilonen\, the geometric Satake equivalence yields a basis in each
irreducible rational representation of $G$\, defined out of algebraic cyc
les in the affine Grassmannian of the Langlands dual of $G$. Goncharov and
Shen extended this construction to each tensor product of irreducible rep
resentations. We will investigate the properties of all these bases and ex
plain a method to compute them. Based on a joint work with Peter Littelman
n and Stéphane Gaussent.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Damien Calaque (Montpellier)
DTSTART:20210531T120000Z
DTEND:20210531T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/50
DESCRIPTION:Title: Calabi-Yau structures for multiplicative preprojective alge
bras\nby Damien Calaque (Montpellier) as part of Paris algebra seminar
\n\n\nAbstract\nI will start by motivating and recalling Calabi-Yau struct
ures and relative versions thereof. \nI will then provide several examples
of Calabi-Yau structures occurring in the context of (dg-versions of) mul
tiplicative preprojective algebras. The A_2 case\, that we will describe i
n detail\, will be used as a building block for general quivers. At the en
d of the talk\, I will describe a strategy for a comparison with other con
structions\, for instance Van den Bergh's quasi-bi-hamiltonian structures.
\nThis is a report on joint work with Tristan Bozec and Sarah Scherotzke.
\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Leicester)
DTSTART:20210419T120000Z
DTEND:20210419T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/51
DESCRIPTION:Title: The higher Stasheff–Tamari orders in representation theor
y\nby Nicholas Williams (Leicester) as part of Paris algebra seminar\n
\n\nAbstract\nOppermann and Thomas show that tilting modules over Iyama's
higher Auslander algebras of type A are in bijection with triangulations o
f even-dimensional cyclic polytopes. Triangulations of cyclic polytopes ar
e partially ordered in two natural ways known as the higher Stasheff–Tam
ari orders\, which were introduced in the 1990s by Kapranov\, Voevodsky\,
Edelman\, and Reiner as higher-dimensional generalisations of the Tamari l
attice. These two partial orders were conjectured to be equal in 1996 by E
delman and Reiner\, but this is still an open problem. We show how the hig
her Stasheff–Tamari orders correspond in even dimensions to natural orde
rs on tilting modules which were studied by Riedtmann\, Schofield\, Happel
\, and Unger. This then allows us to complete the picture of Oppermann and
Thomas by showing that triangulations of odd-dimensional cyclic polytopes
correspond to equivalence classes of d-maximal green sequences\, which we
introduce as higher-dimensional analogues of Keller’s maximal green seq
uences. We show that the higher Stasheff–Tamari orders correspond to nat
ural orders on equivalence classes of d-maximal green sequences\, which re
late to the no-gap conjecture of Brüstle\, Dupont\, and Perotin. If time
permits\, we will also briefly discuss more recent work concerning the rel
ation between the first higher Stasheff–Tamari orders and the higher Bru
hat orders\, which are higher-dimensional analogues of the weak Bruhat ord
er on the symmetric group.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Gautam (Ohio State)
DTSTART:20210517T120000Z
DTEND:20210517T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/52
DESCRIPTION:Title: Poles of finite-dimensional representations of Yangians
\nby Sachin Gautam (Ohio State) as part of Paris algebra seminar\n\n\nAbst
ract\nThe Yangian associated to a simple Lie algebra g is a Hopf algebra w
hich quantizes the Lie algebra of polynomials g[t]. Its finite-dimensional
representation theory has remarkable connections with equivariant cohomol
ogy\, combinatorics\, integrable systems and mathematical physics. Concret
ely\, a finite-dimensional representation of the Yangian is prescribed by
a finite collection of operators whose coefficients are rational functions
\, satisfying a list of commutation relations.\n\nIn this talk I will give
an explicit combinatorial description of the sets of poles of the rationa
l currents of the Yangian\, acting on an irreducible finite-dimensional re
presentation. This result uses the generalization of Baxter's Q-operators
obtained by Frenkel-Hernandez. Based on a joint work with Curtis Wendlandt
(arxiv:2009.06427).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justine Fasquel (Lille)
DTSTART:20210614T120000Z
DTEND:20210614T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/53
DESCRIPTION:Title: Rationality at admissible levels of the simple W-algebras a
ssociated with subregular nilpotent elements in sp_4\nby Justine Fasqu
el (Lille) as part of Paris algebra seminar\n\n\nAbstract\nW-algebras are
certain vertex algebras obtained from the quantized Drinfeld-Sokolov reduc
tion of universal affine vertex algebras associated with a complex paramet
er k and a simple complex Lie algebra g. Their simple quotients are believ
ed to be rational for specific values of k\, called admissible\, which dep
end on the choice of a nilpotent orbit in g. Here\, by rationality\, one m
eans the complete reducibility of their positively graded modules.\n\nThis
conjecture was partially proved by Arakawa-van Ekeren and Creutzig-Linsha
w. In this talk\, I will discuss some consequences of the rationality for
a very concrete example\, namely the W-algebra associated with a subregula
r nilpotent element of the symplectic Lie algebra sp_4. In particular\, we
will be interested in certain actions on the W-algebra and the set of its
simple modules.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Kaplan (Birmingham)
DTSTART:20210524T120000Z
DTEND:20210524T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/54
DESCRIPTION:Title: Multiplicative preprojective algebras for Dynkin quivers\nby Dan Kaplan (Birmingham) as part of Paris algebra seminar\n\n\nAbstra
ct\nCrawley-Boevey and Shaw defined the multiplicative preprojective algeb
ra to understand Kac’s middle convolution and to solve the Deligne-Simps
on problem. In Shaw’s thesis he noticed a curious phenomenon: for the D_
4 quiver the multiplicative preprojective algebra (with parameter q=1) is
isomorphic to the (additive) preprojective algebra if and only if the unde
rlying field has characteristic not two. Later\, Crawley-Boevey proved the
multiplicative and additive preprojective algebras are isomorphic for all
Dynkin quivers over the complex numbers. Recent work of Etgü-Lekili and
Lekili-Ueda\, in the dg-setting\, sharpens the result to hold over fields
of good characteristic\, meaning characteristic not 2 in type D\, not 2 or
3 in type E and not 2\, 3\, or 5 for E_8. Neither work produces an isomor
phism. \n\nIn this talk\, I will explain how to construct these isomorphis
ms and prove their non-existence in the bad (i.e.\, not good) characterist
ics. For each bad characteristic\, a single class in zeroth Hochschild hom
ology obstructs the existence of an isomorphism. Time permitting\, I’ll
explain how to interpret these results in the dg-setting where the 2-Calab
i-Yau property allows us to recast these obstructions as non-trivial defor
mations\, using Van den Bergh duality.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (Orsay)
DTSTART:20210607T120000Z
DTEND:20210607T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/55
DESCRIPTION:Title: The flow tree formula for Donaldson-Thomas invariants of qu
ivers with potentials\nby Pierrick Bousseau (Orsay) as part of Paris a
lgebra seminar\n\n\nAbstract\nVery generally\, Donaldson-Thomas invariants
are counts of stable objects in Calabi-Yau triangulated categories of dim
ension 3. A natural source of examples is provided by the representation t
heory of quivers with potentials. I will present a proof of a formula\, co
njectured by Alexandrov-Pioline from string-theory arguments\, which compu
tes Donaldson-Thomas invariants of a quiver with potential in terms of a m
uch smaller set of "attractor invariants". The proof uses the framework of
scattering diagrams to reorganize sequences of iterated applications of t
he Kontsevich-Soibelman wall-crossing formula. This is joint work with Hü
lya Argüz.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Tōhoku)
DTSTART:20210621T120000Z
DTEND:20210621T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/56
DESCRIPTION:Title: Categorical dynamical systems arising from sign-stable muta
tion loops\nby Shunsuke Kano (Tōhoku) as part of Paris algebra semina
r\n\n\nAbstract\nA pair formed by a triangulated category and an autoequiv
alence is called a \ncategorical dynamical system. Its complexity is measu
red by the so-called categorical entropy. \nIn this talk\, I will present
a computation of the categorical entropies of categorical dynamical system
s obtained by lifting a sign-stable mutation loop of a quiver to an autoeq
uivalence of the derived category of the corresponding Ginzburg dg algebra
.\nThe notion of sign-stability is introduced as a generalization of the p
seudo-Anosov property of mapping classes of surfaces. If time permits\, we
will discuss the pseudo-Anosovness of the autoequivalences constructed.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Amiens)
DTSTART:20210628T120000Z
DTEND:20210628T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/57
DESCRIPTION:Title: Braid varieties\, positroids\, and Legendrian links\nby
Mikhail Gorsky (Amiens) as part of Paris algebra seminar\n\n\nAbstract\nI
will discuss a class of affine algebraic varieties associated with positi
ve braids\, their cluster structures and their relation to open Bott-Samel
son varieties. First\, I will explain our motivation which comes both from
symplectic topology and from the study of HOMFLY-PT polynomials. Then we
will discuss how the study of DG algebras associated with certain Legendri
an links may help us to better understand the algebraic geometry of Richar
dson varieties in type A. I will illustrate our results and conjectures co
ncerning this interplay between topology and algebraic geometry with the e
xample of open positroid varieties in Grassmannians. If time permits\, I w
ill briefly explain conjectural relations between certain stratifications
of braid varieties and cluster structures on their coordinate rings. This
is joint work with Roger Casals\, Eugene Gorsky\, and José Simental.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ehud Meir (Aberdeen)
DTSTART:20210705T120000Z
DTEND:20210705T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/58
DESCRIPTION:Title: Interpolations of monoidal categories by invariant theory\nby Ehud Meir (Aberdeen) as part of Paris algebra seminar\n\n\nAbstract
\nIn this talk\, I will present a recent construction that enables one to\
ninterpolate symmetric monoidal categories by interpolating algebraic\nstr
uctures and their automorphism groups.\nI will explain how one can recover
the constructions of Deligne for\ncategories such as Rep(S_t)\, Rep(O_t)
and Rep(Sp_t)\, the constructions\nof Knop for wreath products with S_t an
d GL_t(O_r)\, where O_r is a\nfinite quotient of a discrete valuation ring
\, and also the TQFT\ncategories recently constructed from a rational func
tion by Khovanov\, Ostrik\, and Kononov.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Cerulli Irelli (Rome La Sapienza)
DTSTART:20211004T120000Z
DTEND:20211004T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/59
DESCRIPTION:Title: On degeneration and extensions of symplectic and orthogonal
quiver representations\nby Giovanni Cerulli Irelli (Rome La Sapienza)
as part of Paris algebra seminar\n\n\nAbstract\nMotivated by linear degen
erations of flag varieties\, and the study of 2-nilpotent B-orbits for cla
ssical groups\, I will review the representation theory of symmetric quive
rs\, initiated by Derksen and Weyman in 2002. I will then focus on the pro
blem of describing the orbit closures in this context and how to relate it
to the orbit closures for the underlying quivers. In collaboration with M
. Boos we have recently given an answer to this problem for symmetric quiv
ers of finite type. I believe that this result is a very special case of a
much deeper and general result that I will mention in the form of conject
ures and open problems. The talk is based on the preprint version of my pa
per with Boos available on the arXiv as 2106.08666.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Gurevich (Technion\, Haifa)
DTSTART:20211011T120000Z
DTEND:20211011T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/60
DESCRIPTION:Title: RSK-transform for L-parameters\nby Maxim Gurevich (Tech
nion\, Haifa) as part of Paris algebra seminar\n\nAbstract: TBA\n\nWhat is
common between the Specht construction for modules over\npermutation grou
ps\, normal sequences of quiver Hecke algebra modules à\nla Kashiwara-Kim
\, and the local Langlands classification for GL_n ?\nI would like to show
how these themes fit well together under a\nframework of a representation
-theoretic Robinson-Schensted-Knuth\ntransform\, devised recently in my wo
rk with Erez Lapid on\nrepresentations of p-adic groups.\n\nOn one hand\,
RSK-standard modules are curious models for all smooth\nirreducible GL_n-r
epresentations. Yet\, going through Bernstein-Rouquier\ncategorical equiva
lences this notion is quantized into its natural\nexistence in the realm o
f type A quiver Hecke algebras. A convenient\nbridge is thus portrayed bet
ween the cyclotomic approach of classifying\nsimple modules through a gene
ralized Specht construction\, and the\nPBW-basis approach from Lusztig's w
ork on quantum groups.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (Leeds)
DTSTART:20211018T120000Z
DTEND:20211018T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/63
DESCRIPTION:Title: A cluster character for y-variables\nby Matthew Pressla
nd (Leeds) as part of Paris algebra seminar\n\n\nAbstract\nGiven a (Froben
ius or triangulated) cluster category\, I will explain how to categorify v
arious cluster algebraic identities via lattice maps associated to pairs o
f cluster-tilting objects. For example\, one such map is the index\, well-
known to categorify g-vectors. Using this formalism\, I will recall the cl
uster character for x-variables developed by Caldero–Chapoton\, Palu\, F
u–Keller and others\, and give a similar categorical expression for y-va
riables. This is joint work with Jan E. Grabowski.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haicheng Zhang (Nanjing Normal University)
DTSTART:20211108T130000Z
DTEND:20211108T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/66
DESCRIPTION:Title: Hall algebras of extriangulated categories and quantum clus
ter algebras\nby Haicheng Zhang (Nanjing Normal University) as part of
Paris algebra seminar\n\n\nAbstract\nFirstly\, we define the Hall algebra
of an extriangulated category\, a notion introduced by Nakaoka and Palu.
Then for a finite acyclic valued quiver Q\, we consider the Hall algebras
of certain subcategories of the bounded derived category of the represent
ation category of Q over a finite field\, which are extriangulated categor
ies. We recover the quantum Caldero-Chapoton formula via the Hall algebra
approach and give the higher-dimensional (cluster) multiplication formulas
in the quantum cluster algebra of Q with arbitrary coefficients\, which c
an be viewed as the quantum version of the Caldero-Keller multiplication f
ormula in the cluster algebra. This talk is based on the joint preprints a
rXiv:2005.10617\, 2107.05883 and 2108.03558.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryo Fujita (University of Paris)
DTSTART:20211122T130000Z
DTEND:20211122T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/67
DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojective alge
bras\, II\nby Ryo Fujita (University of Paris) as part of Paris algebr
a seminar\n\n\nAbstract\nIn their study of deformed W-algebras associated
with complex simple Lie algebras\, E. Frenkel-Reshetikhin (1998) introduce
d certain two parameter deformations of the Cartan matrices. They play an
important role in the representation theory of quantum affine algebras. In
the former half of this talk\, we explain a representation-theoretic inte
rpretation of these deformed Cartan matrices and their inverses in terms o
f the generalized preprojective algebras recently introduced by Geiss-Lecl
erc-Schröer (2017). In the latter half of the talk\, we discuss its appli
cation to the representation theory of quantum affine algebras in connecti
on with the theory of cluster algebras.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kota Murakami (Kyoto)
DTSTART:20211122T130000Z
DTEND:20211122T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/68
DESCRIPTION:Title: Deformed Cartan matrices and generalized preprojective alge
bras\, I\nby Kota Murakami (Kyoto) as part of Paris algebra seminar\n\
n\nAbstract\nIn their study of deformed W-algebras associated with complex
simple Lie algebras\, E. Frenkel-Reshetikhin (1998) introduced certain tw
o parameter deformations of the Cartan matrices. They play an important ro
le in the representation theory of quantum affine algebras. In the former
half of this talk\, we explain a representation-theoretic interpretation o
f these deformed Cartan matrices and their inverses in terms of the genera
lized preprojective algebras recently introduced by Geiss-Leclerc-Schröer
(2017). In the latter half of the talk\, we discuss its application to th
e representation theory of quantum affine algebras in connection with the
theory of cluster algebras.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (Edinburgh)
DTSTART:20211025T120000Z
DTEND:20211025T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/69
DESCRIPTION:Title: (Canonical) bases of the elliptic Hall algebra\nby Luci
en Hennecart (Edinburgh) as part of Paris algebra seminar\n\n\nAbstract\nT
he global nilpotent cone is a closed substack of the stack of Higgs sheave
s on a smooth projective curve whose geometry has been studied in depth an
d is also an essential object in the geometric Langlands program. It is a
highly singular stack and in particular it has several irreducible compone
nts which were rather recently explicitly described by Bozec. In this talk
\, we will concentrate on elliptic curves. We will recall Bozec's parametr
ization of the set of irreducible components of the global nilpotent cone
and present another parametrization of the same set using (a refinement of
) the Harder-Narasimhan stratification of the stack of coherent sheaves on
the elliptic curve. Then\, we raise the question of the comparison of the
se two bases\, showing the emergence piecewise linear structures. We will
also see how the second description can be useful to understand a part of
the cohomological Hall algebra of an elliptic curve.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (Edinburgh)
DTSTART:20220131T130000Z
DTEND:20220131T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/70
DESCRIPTION:Title: Local Normal Forms of Noncommutative Functions\nby Mich
ael Wemyss (Edinburgh) as part of Paris algebra seminar\n\n\nAbstract\nThi
s talk will explain how to generalise Arnold's results classifying commuta
tive singularities into the noncommutative setting\, and will classify fin
ite dimensional Jacobi algebras arising on the d-loop quiver. The surpris
ing thing is that a classification should exist at all\, and it is even mo
re surprising that ADE enters. I will spend most of my time explaining wh
at the algebras are\, why they classify\, and how to intrinsically extract
ADE information from them. At the end\, I'll briefly explain why I'm real
ly interested in this problem\, the connection with different quivers\, an
d the applications of the above classification to curve counting and birat
ional geometry. This is all joint work with Gavin Brown.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (Cambridge)
DTSTART:20211115T130000Z
DTEND:20211115T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/71
DESCRIPTION:Title: Generalized cluster dualities\nby Lang Mou (Cambridge)
as part of Paris algebra seminar\n\n\nAbstract\nFock and Goncharov introdu
ced dualities between cluster varieties. I will explain how this duality u
nder the framework of Gross-Hacking-Keel-Kontsevich can be naturally exten
ded to generalized cluster varieties in the sense of Chekhov-Shapiro. In p
articular\, I will construct generalized cluster scattering diagrams which
are used to construct bases of functions on the dual varieties. As a gene
ralized A-cluster variety yields a generalized cluster algebra\, certain p
ositivity property of the cluster monomials will be derived as a result of
the positivity of the corresponding scattering diagram. This talk is main
ly based on arXiv: 2110.02416.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Fraser (Minnesota)
DTSTART:20211129T130000Z
DTEND:20211129T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/72
DESCRIPTION:Title: Automorphisms of open positroid varieties from braids\n
by Chris Fraser (Minnesota) as part of Paris algebra seminar\n\n\nAbstract
\nPositroid varieties are distinguished subvarieties of Grassmannians whic
h have cluster structure(s). I will give some reminders on the combinatori
cs underlying these cluster structures\, partially based on a joint work w
ith Melissa Sherman-Bennett. In a previous work\, I described an action of
a certain braid group on the top-dimensional positroid subvariety by "qua
si" cluster automorphisms. I will explain how a similar statement can be e
xtended to arbitrary open positroid varieties. This is joint with Bernhard
Keller.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abel Lacabanne (Clermont-Ferrand)
DTSTART:20211213T130000Z
DTEND:20211213T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/73
DESCRIPTION:Title: Higher rank Askey-Wilson algebras as skein algebras\nby
Abel Lacabanne (Clermont-Ferrand) as part of Paris algebra seminar\n\n\nA
bstract\nThe skein algebra of a surface is built from the framed unoriente
d links in the thickened surface\, modulo the Kauffman bracket relations.
If the surface is the $4$-punctured sphere\, it turns out that the skein a
lgebra is a central extension of the universal Askey-Wilson algebra. De Bi
e\, De Clercq and Van de Vijver proposed a definition of higher rank Askey
-Wilson algebras\, as a subalgebra of an $n$-fold tensor product of $U_q(\
\mathfrak{sl}_2)$. The aim of this talk is to explain an isomorphism betwe
en these higher rank Askey-Wilson algebras\, and the skein algebras of pun
ctured spheres. The diagrammatic flavour of the skein algebra provides the
n an efficient way to compute some relations between some elements of the
Askey-Wilson algebra\, notably the $q$-commutation relations discovered by
De Clercq. This is joint work with J. Cooke.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Ovenhouse (Minnesota)
DTSTART:20211206T130000Z
DTEND:20211206T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/74
DESCRIPTION:Title: q-Rational Numbers and Finite Schubert Varieties\nby Ni
cholas Ovenhouse (Minnesota) as part of Paris algebra seminar\n\n\nAbstrac
t\nRecently\, Morier-Genoud and Ovsienko generalized the notion of q-integ
ers to include rational numbers. The q-analogue of a rational number is so
me rational function with integer coefficients. There are some known combi
natorial interpretations of the numerators as rank generating functions of
certain posets. I will review this interpretation\, and re-phrase it in t
erms of lattice paths on "snake graphs". Using this snake graph interpreta
tion\, I will explain how the numerators count the number of points in som
e variety over a finite field. This variety is a union of Schubert cells i
n some Grassmannian.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfredo Nájera Chávez (Oaxaca)
DTSTART:20220117T130000Z
DTEND:20220117T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/75
DESCRIPTION:Title: Deformation theory for finite cluster complexes\nby Alf
redo Nájera Chávez (Oaxaca) as part of Paris algebra seminar\n\n\nAbstra
ct\nCluster complexes are a certain class of simplicial complexes that nat
urally arise in the theory of cluster algebras. They codify a wealth of fu
ndamental information about cluster algebras. The purpose of this talk is
to elaborate on a geometric relationship between cluster algebras and clus
ter complexes. In vague words\, this relationship is the following: cluste
r algebras of finite cluster type with universal coefficients may be obtai
ned via a torus action on a Hilbert scheme. In particular\, we will discus
s the deformation theory of the Stanley-Reisner ring associated to a finit
e cluster complex and present some applications related to the Gröbner th
eory of the ideal of relations among cluster and frozen variables of a clu
ster algebra of finite cluster type. Time permitting I will elaborate on h
ow to generalize this approach to the context of tau-tilting finite algebr
as.\n\nThis is based on a joint project with Nathan Ilten and Hipolito Tre
ffinger whose first outcome is the preprint arXiv:2111.02566.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Hamburg)
DTSTART:20220124T130000Z
DTEND:20220124T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/76
DESCRIPTION:Title: Gluing constructions of Ginzburg algebras and cluster categ
ories\nby Merlin Christ (Hamburg) as part of Paris algebra seminar\n\n
\nAbstract\nGinzburg algebras are a class of 3-CY dg algebras\, which have
attracted attention for their use in the categorification of cluster alge
bras. Given a marked surface with a triangulation\, there is an associated
Ginzburg algebra G. I will begin by describing how its derived category D
^perf(G) can be glued from the derived categories of the relative Ginzburg
algebras of the ideal triangles of the triangulation. We will see that th
e passage to Amiot's cluster category\, defined as the quotient D^perf(G)/
D^fin(G)\, does not commute with this gluing. As we will discuss\, this ca
n fixed by instead starting with the relative Ginzburg algebra of the tria
ngulation and again applying Amiot's quotient formula. Remarkably\, this r
esulting relative version of cluster category turns out to be equivalent t
o the 1-periodic topological Fukaya category of the surface.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Brav (HSE Moscow)
DTSTART:20220110T130000Z
DTEND:20220110T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/77
DESCRIPTION:Title: Non-commutative string topology\nby Chris Brav (HSE Mos
cow) as part of Paris algebra seminar\n\n\nAbstract\nWe explain how relati
ve Calabi-Yau structures on dg functors\, more generally relative orientat
ions\, give a non-commutative generalisation of oriented manifolds with bo
undary. We then construct genus zero string topology operations on the rel
ative Hochschild homology HH_*(C\,D) of a dg functor D —> C equipped wit
h a relative orientation. More precisely\, we prove a relative version of
the cyclic Deligne conjecture\, stating that this shifted relative Hochsch
ild homology carries a natural structure of framed E_2-algebra. Examples i
nclude 1) the functor of induction of local systems for the inclusion of t
he boundary into an oriented manifold with boundary\, in which case the re
lative Hochschild homology is identified with the relative loop homology 2
) the functor of pushforward of coherent sheaves for the inclusion of the
anti-canonical divisor into a variety\, in which case relative Hochschild
homology can be related to differential forms\, and 3) various examples co
ming from representation theory.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Cologne)
DTSTART:20220207T130000Z
DTEND:20220207T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/78
DESCRIPTION:Title: Equivalence of maximal green sequences\nby Nicholas Wil
liams (Cologne) as part of Paris algebra seminar\n\n\nAbstract\nIt is natu
ral to study the set of maximal green sequences of an algebra under an equ
ivalence relation. The resulting set of equivalence classes has the struct
ure of a poset\; it is a lattice in type A\, where the equivalence classes
are in bijection with triangulations of three-dimensional cyclic polytope
s. There are at least four appealing ways of defining an equivalence relat
ion on maximal green sequences: commutation\, exchange pairs\, tau-rigid s
ummands\, and bricks. The main result of my talk will be that the first th
ree methods define the same equivalence relation\, while the fourth does n
ot. This gives a surprising lack of duality between bricks\, which corresp
ond to simples\, and tau-rigid summands\, which correspond to projectives.
This is a report on joint work in progress with Mikhail Gorsky.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Véronique Bazier-Matte (Connecticut)
DTSTART:20220214T130000Z
DTEND:20220214T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/79
DESCRIPTION:Title: Connection between knot theory and Jacobian algebras\nb
y Véronique Bazier-Matte (Connecticut) as part of Paris algebra seminar\n
\n\nAbstract\nThis is joint work with Ralf Schiffler.\nIn knot theory\, it
is known that we can compute the Alexander polynomial of a knot from the
lattice of Kauffman states of a knot diagram. Recently\, my collaborator a
nd I associated a quiver with a knot diagram. From this quiver\, one can o
btain a Jacobian algebra. It appears that the lattice of submodules of ind
ecomposable modules over this algebra is in bijection with the lattice of
Kauffman states. This bijection allows us to compute the Alexander polynom
ial of a knot with a specialization of the F-polynomial of any indecomposa
ble module over this algebra.\nAfter a brief introduction to knot theory\,
I will explain how to compute an Alexander polynomial from a F-polynomial
.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonçalo Tabuada (Warwick)
DTSTART:20220221T130000Z
DTEND:20220221T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/80
DESCRIPTION:Title: Jacques Tits motivic measure\nby Gonçalo Tabuada (Warw
ick) as part of Paris algebra seminar\n\n\nAbstract\nThe Grothendieck ring
of varieties\, introduced in a letter from Alexander Grothendieck to Jean
-Pierre Serre (August 16th 1964)\, plays an important role in algebraic ge
ometry. However\, despite the efforts of several mathematicians\, the stru
cture of this ring still remains poorly understood. In order to capture so
me of the flavor of Grothendieck’s ring of varieties\, a few motivic mea
sures have been built throughout the years. In this talk I will present a
new motivic measure\, called the Jacques Tits motivic measure\, and descri
be some of its numerous applications.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Guy Plamondon (Versailles)
DTSTART:20220228T130000Z
DTEND:20220228T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/81
DESCRIPTION:Title: Cluster algebras\, categorification\, and some configuratio
n spaces\nby Pierre-Guy Plamondon (Versailles) as part of Paris algebr
a seminar\n\n\nAbstract\nThe real part of the configuration space M_{0\,n}
of n points on a projective line has a connected component which is close
ly related to the associahedron. As an affine variety\, it is defined by
explicit equations which are in close connection with exchange relations f
or cluster variables in type A. This has been generalized to all Dynkin t
ypes.\n\nIn this talk\, we will construct an affine variety associated to
any representation-finite finite-dimensional algebra over an algebraically
closed field. The equations defining the variety will be obtained from t
he F-polynomials of indecomposable modules over the algebra. This general
izes previous results\, which can be recovered by applying our constructio
n to Jacobian algebras in Dynkin types.\n\nThis talk is based on an ongoin
g project with Nima Arkani-Hamed\, Hadleigh Frost\, Giulio Salvatori and H
ugh Thomas.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Léa Bittmann (Edinburgh)
DTSTART:20220425T120000Z
DTEND:20220425T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/82
DESCRIPTION:Title: A Schur-Weyl duality between Double Affine Hecke Algebras a
nd quantum groups\nby Léa Bittmann (Edinburgh) as part of Paris algeb
ra seminar\n\nLecture held in hybrid.\n\nAbstract\nSchur-Weyl duality is o
ften used to relate type A Lie groups (or quantum groups) to symmetric gro
ups (or Hecke algebras). In this talk\, I will use ribbon calculus and ske
in modules to describe an instance of this Schur-Weyl duality between repr
esentations of the type A quantum group at roots of unity and representati
ons of the Double Affine Hecke Algebra. This is based on joint work with A
. Chandler\, A. Mellit and C. Novarini.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bitoun (Calgary)
DTSTART:20220516T120000Z
DTEND:20220516T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/83
DESCRIPTION:Title: On centralizers in Azumaya domains\nby Thomas Bitoun (C
algary) as part of Paris algebra seminar\n\nLecture held in hybrid.\n\nAbs
tract\nWe prove a positive characteristic analogue of the classical result
that the centralizer of a nonconstant differential operator in one variab
le is commutative. This leads to a new\, short proof of that classical cha
racteristic zero result\, by reduction modulo p. This is joint work with J
ustin Desrochers available at https://arxiv.org/abs/2201.04606.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Takeda (IHES)
DTSTART:20220307T130000Z
DTEND:20220307T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/84
DESCRIPTION:Title: The ribbon quiver complex and the noncommutative Legendre t
ransform\nby Alex Takeda (IHES) as part of Paris algebra seminar\n\n\n
Abstract\nThe structure of a fully extended oriented 2d TQFT is given by a
Frobenius algebra. If one wants to lift this structure to a cohomological
field theory\, the correct notion is that of a Calabi-Yau algebra or cate
gory\; the CohFT operations can be described by a certain graph complex. T
here are two different notions of Calabi-Yau structure on categories\, bot
h requiring some type of finiteness or dualizability. In this talk I will
discuss a variation that works in non-dualizable cases as well\; in this c
ase the graphs get replaced by quivers. The resulting complex calculates t
he homology of certain moduli spaces of open-closed surfaces\, and can be
used to give a fully explicit description of these operations. In the seco
nd half of the talk\, I will describe some of these constructions\, includ
ing how to produce operations from smooth and/or relative Calabi-Yau struc
tures\, and explain how\, in the smooth case\, this can be thought of as a
noncommutative version of the Legendre transform. This is joint work with
M. Kontsevich and Y. Vlassopoulos.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norihiro Hanihara (Nagoya)
DTSTART:20220321T130000Z
DTEND:20220321T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/85
DESCRIPTION:Title: Tilting theory via enhancements\nby Norihiro Hanihara (
Nagoya) as part of Paris algebra seminar\n\n\nAbstract\nTilting theory aim
s at giving equivalences among various triangulated categories\, such as d
erived categories\, cluster categories\, and singularity categories. Const
ructing such an equivalence provides a mutual understanding of these categ
ories. In this talk\, we study tilting theory for singularity categories a
nd cluster categories from the viewpoint of dg enhancements. We will first
review their construction in terms of their enhancements\, and then based
on this we explain a general method of giving equivalences between singul
arity categories and cluster categories. Our main steps are existence of (
weak) right Calabi-Yau structure on the dg singularity category of commuta
tive Gorenstein rings\, and a characterization of dg orbit categories amon
g bigraded dg categories. This is a joint work with Osamu Iyama.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jie Pan (Zhejiang U.)
DTSTART:20220314T130000Z
DTEND:20220314T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/86
DESCRIPTION:Title: Positivity and polytope basis in cluster algebras via Newto
n polytopes\nby Jie Pan (Zhejiang U.) as part of Paris algebra seminar
\n\n\nAbstract\nWe work in the generality of a totally sign-skew-symmetric
(e.g. skew-symmetrizable) \ncluster algebra of rank $n$. We study the New
ton polytopes of $F$-polynomials and\, more generally\, a\nfamily of polyt
opes $N_h$ indexed by vectors $h$ in $Z^n$. We use it to give a new proof
of Laurent \npositivity and to construct what we call the polytope basis o
f the upper cluster algebra. The polytope \nbasis consists of certain univ
ersally indecomposable Laurent polynomials. It is strongly positive\nand g
eneralizes the greedy basis constructed by Lee-Li-Zelevinsky in rank 2.\nT
his is a report on joint work with Fang Li\, cf. arXiv:2201.01440.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asilata Bapat (Australian National U.)
DTSTART:20220328T120000Z
DTEND:20220328T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/87
DESCRIPTION:Title: Categorical q-deformed rational numbers via Bridgeland stab
ility conditions\nby Asilata Bapat (Australian National U.) as part of
Paris algebra seminar\n\n\nAbstract\nWe will discuss new categorical inte
rpretations of two distinct q-deformations of the rational numbers. The fi
rst one\, introduced by Morier-Genoud and Ovsienko in a different context\
, enjoys fascinating combinatorial\, topological\, and algebraic propertie
s. The second one is a natural partner to the first\, and is new. We obtai
n these deformations via boundary points of a compactification of the spac
e of Bridgeland stability conditions on the 2-Calabi-Yau category of the A
2 quiver. The talk is based on joint work with Louis Becker\, Anand Deopur
kar\, and Anthony Licata.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hipolito Treffinger (City University of Paris)
DTSTART:20220404T120000Z
DTEND:20220404T123000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/88
DESCRIPTION:Title: Torsion classes and tau-tilting in higher homological algeb
ra\, I\nby Hipolito Treffinger (City University of Paris) as part of P
aris algebra seminar\n\nLecture held in hybrid.\n\nAbstract\nHigher homolo
gical algebra was introduced by Iyama in the late \n2000's. His point of v
iew was that some classical results by Auslander \nand Auslander--Reiten w
ere somehow 2-dimensional and should have \nn-dimensional equivalents. Thi
s new theory quickly attracted a lot of \nattention\, with many authors ge
neralising classical notions to the \nsetting of higher homological algebr
a. Examples of such generalisations \nare the introduction of n-abelian ca
tegories by Jasso\, n-angulated \ncategories by Geiss--Keller--Oppermann\,
and n-torsion classes by Jørgensen.\n\nRecently\, it was shown by Kvamme
and\, independently\, by Ebrahimi and \nNasr-Isfahani\, that every small
n-abelian category is the \nn-cluster-tilting subcategory of an abelian ca
tegory. In this talk\, we \nwill focus on the relation between n-torsion c
lasses in an n-abelian \ncategory $\\mathcal{M}$ and (classical) torsion c
lasses of the abelian \ncategory $\\mathcal{A}$ in which $\\mathcal{M}$ is
embedded. By \nconsidering functorially finite torsion classes\, this wil
l allow us to \nrelate n-torsion classes with maximal tau_n-rigid objects
in $\\mathcal{M}$.\n\nSome of the results presented in this talk are part
of a joint work by \nJ. Asadollahi\, P. Jørgensen\, S. Schroll\, H. Treff
inger. The rest \ncorresponds to an ongoing project by J. August\, J. Haug
land\, \nK. Jacobsen\, S. Kvamme\,Y. Palu and H. Treffinger.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Palu (Amiens)
DTSTART:20220404T123000Z
DTEND:20220404T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/89
DESCRIPTION:Title: Torsion classes and tau-tilting in higher homological algeb
ra\, II\nby Yann Palu (Amiens) as part of Paris algebra seminar\n\nLec
ture held in hybrid.\n\nAbstract\nHigher homological algebra was introduce
d by Iyama in the late \n2000's. His point of view was that some classical
results by Auslander \nand Auslander--Reiten were somehow 2-dimensional a
nd should have \nn-dimensional equivalents. This new theory quickly attrac
ted a lot of \nattention\, with many authors generalising classical notion
s to the \nsetting of higher homological algebra. Examples of such general
isations \nare the introduction of n-abelian categories by Jasso\, n-angul
ated \ncategories by Geiss--Keller--Oppermann\, and n-torsion classes by J
ørgensen.\n\nRecently\, it was shown by Kvamme and\, independently\, by E
brahimi and \nNasr-Isfahani\, that every small n-abelian category is the \
nn-cluster-tilting subcategory of an abelian category. In this talk\, we \
nwill focus on the relation between n-torsion classes in an n-abelian \nca
tegory $\\mathcal{M}$ and (classical) torsion classes of the abelian \ncat
egory $\\mathcal{A}$ in which $\\mathcal{M}$ is embedded. By \nconsidering
functorially finite torsion classes\, this will allow us to \nrelate n-to
rsion classes with maximal tau_n-rigid objects in $\\mathcal{M}$.\n\nSome
of the results presented in this talk are part of a joint work by \nJ. Asa
dollahi\, P. Jørgensen\, S. Schroll\, H. Treffinger. The rest \ncorrespon
ds to an ongoing project by J. August\, J. Haugland\, \nK. Jacobsen\, S. K
vamme\,Y. Palu and H. Treffinger.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (Hebrew University)
DTSTART:20220411T120000Z
DTEND:20220411T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/90
DESCRIPTION:Title: On exchange matrices from string diagrams\nby Peigen Ca
o (Hebrew University) as part of Paris algebra seminar\n\nLecture held in
Zoom.\n\nAbstract\nIn this talk\, we will first recall the constructions o
f triangular extension and of source-sink extensio for skew-symmetrizable
matrices and some invariants under these constructions. Secondly\, we will
recall the string diagrams introduced by Shen-Weng\, which are very usefu
l to describe many interesting skew-symmetrizable matrices closely related
with Lie theory. Thirdly\, we will sketch the proof of our main result: t
he skew-symmetrizable matrices from string diagrams are in the smallest cl
ass of skew-symmetrizable matrices containing the (1 times 1) zero matrix
and closed under mutations and source-sink extensions. This result applies
to the exchange matrices of cluster algebras from double Bruhat cells\, u
nipotent cells\, double Bott-Samelson cells among others. Finally\, some i
mmediate applications regarding reddening sequences and non-degenerate pot
entials for many quivers from Lie theory are given.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Sorbonne Paris Nord)
DTSTART:20220523T120000Z
DTEND:20220523T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/91
DESCRIPTION:Title: Pre-Calabi-Yau algebras and homotopy double Poisson gebras<
/a>\nby Bruno Vallette (Sorbonne Paris Nord) as part of Paris algebra semi
nar\n\n\nAbstract\nWe prove that the notion of a curved pre-Calabi–Yau a
lgebra is equivalent to the notion of a curved homotopy double Poisson geb
ra\, thereby settling the equivalence between the two ways to define deriv
ed noncommutative Poisson structures. We actually prove that the respectiv
e differential graded Lie algebras controlling both deformation theories a
re isomorphic. This allows us to apply the recent developments of the prop
eradic calculus in order to establish the homotopical properties of curved
pre-Calabi–Yau algebras: infini-morphisms\, homotopy transfer theorem\,
formality\, Koszul hierarchy\, and twisting procedure. (Joint work with J
ohan Leray available at arxiv.org/abs/2203.05062).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasuki Kinjo (IPMU)
DTSTART:20220502T120000Z
DTEND:20220502T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/92
DESCRIPTION:Title: Deformed Calabi--Yau completion and its application to DT t
heory\nby Tasuki Kinjo (IPMU) as part of Paris algebra seminar\n\n\nAb
stract\nIn this talk\, we investigate an application of the theory of defo
rmed Calabi--Yau completion to enumerative geometry. The notion of Calabi-
-Yau completion was first introduced by Keller as a non-commutative analog
ue of the canonical bundle. In the same paper\, he also introduced a defor
med version of the Calabi--Yau completion.\nWe will explain that the defor
med Calabi--Yau completion is a non-commutative analogue of an affine bund
le modeled on the canonical bundle. Combining this observation with a rece
nt work of Bozec--Calaque--Scherotzke\, we prove that the moduli space of
coherent sheaves on a certain non-compact Calabi--Yau threefold is describ
ed as the critical locus inside a smooth moduli space. This description ha
s several applications in Donaldson--Thomas theory including Toda's \\chi-
independence conjecture of Gopakumar--Vafa invariants for arbitrary local
curves. By dimensional reduction\, it implies (and extends) Hausel--Thadde
us's cohomological \\chi-independence conjecture for Higgs bundles.\n\nThi
s talk is based on a joint work with Naruki Masuda and another joint work
with Naoki Koseki.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Naef
DTSTART:20220509T120000Z
DTEND:20220509T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/93
DESCRIPTION:Title: The (non-)homotopy invariance of the string coproduct\n
by Florian Naef as part of Paris algebra seminar\n\n\nAbstract\nA Calabi-Y
au structure on a smooth algebra allows one to identify Hochschild homolog
y with Hochschild cohomology. With this identification Hochschild homology
acquires an additional Gerstenhaber algebra structure. One way to formula
te the amount of structure one has on Hochschild homology is to encode it
into a 2d TFT. This explains some of the string topology operations on the
free loop space of a manifold\, but not the string coproduct. If the alge
bra has additional structure (trivialization of its Hattori-Stalling Euler
characteristic) one obtains an extra secondary operation on Hochschild ho
mology\, which recovers the string coproduct. Finally\, in the free loop s
pace setting\, this additional structure can either be recovered from inte
rsection theory of the manifold or from its underlying simple homotopy typ
e\, thus relating the two. Using this last relation one can express the di
fference between the string coproduct of two homotopic but not necessarily
homeomorphic manifolds in terms of Whitehead torsion.\nThis is joint work
with Pavel Safronov\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Rickard (Bristol)
DTSTART:20220606T120000Z
DTEND:20220606T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/94
DESCRIPTION:Title: Generating the derived category\nby Jeremy Rickard (Bri
stol) as part of Paris algebra seminar\n\n\nAbstract\nThe unbounded derive
d category of (right) modules over a ring is a triangulated category with
infinite products and coproducts. As a triangulated category with coproduc
ts it is easy to see that it is generated by the projective modules\, and
similarly it is generated as a triangulated category with products by the
injective modules.\n\nI will discuss the question of whether it is generat
ed as a triangulated category with coproducts by the injective modules\, o
r as a triangulated category with products by the projective (or flat) mod
ules. I will describe the relationship with the finitistic dimension conje
cture\, as well as some more recent results.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuya Mizuno (Osaka Metropolitan University)
DTSTART:20220613T120000Z
DTEND:20220613T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/95
DESCRIPTION:Title: g-simplicial complex and silting theory\nby Yuya Mizuno
(Osaka Metropolitan University) as part of Paris algebra seminar\n\n\nAbs
tract\nFor a finite dimensional algebra $A$\, the 2-term silting complexes
of $A$ give a simplicial complex $\\Delta(A)$\, which is called the g-sim
plicial complex.\nWe study several properties of $\\Delta(A)$ and\, in par
ticular\, we give tilting theoretic interpretations of the $h$-vectors and
the Dehn-Sommerville equations of $\\Delta(A)$.\nConsequently\, we can e
xplain a close correspondence between torsion classes and wide subcategori
es\, which can be regarded as a refinement of the Koenig-Yang corresponden
ce.\nThis is joint work with Aoki-Higashitani-Iyama-Kase\, cf. https://arx
iv.org/pdf/2203.15213.pdf\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Niklas Eberhardt (Bonn)
DTSTART:20220530T120000Z
DTEND:20220530T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/96
DESCRIPTION:Title: Motivic Springer Theory\nby Jens Niklas Eberhardt (Bonn
) as part of Paris algebra seminar\n\n\nAbstract\nAlgebras and their repre
sentations can often be constructed geometrically in terms of convolution
of cycles. \nFor example\, the Springer correspondence describes how irred
ucible representations of a Weyl group can be realised in terms of a convo
lution action on the vector spaces of irreducible components of Springer f
ibers. Similar situations yield the affine Hecke algebra\, quiver Hecke al
gebra (KLR algebra)\, quiver Schur algebra or Soergel bimodules.\nIn this
spirit\, we show that these algebras and their representations can be real
ised in terms of certain equivariant motivic sheaves called Springer motiv
es.\nOn our way\, we will discuss weight structures and their applications
to motives.\nThis is joint work with Catharina Stroppel.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Shapiro (Edinburgh)
DTSTART:20220620T120000Z
DTEND:20220620T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/97
DESCRIPTION:Title: Positive representation theory\nby Alexander Shapiro (E
dinburgh) as part of Paris algebra seminar\n\n\nAbstract\nThe notions of a
modular tensor category\, 2d topological modular functor\, and 3d topolog
ical quantum field theory are essentially equivalent. Fock and Goncharov c
onjectured that the quantised higher Teichmüller theory gives rise to an
analogue of a modular functor. Their construction in turn yields a family
of "positive" representations of quantum groups. I will argue that these r
epresentations provide a compelling first step towards constructing an ana
logue of a modular tensor category. This talk will be based on joint works
with Gus Schrader.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daping Weng (UC Davis)
DTSTART:20220627T120000Z
DTEND:20220627T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/98
DESCRIPTION:Title: Grid plabic graphs\, Legendrian weaves\, and (quasi-)cluste
r structures\nby Daping Weng (UC Davis) as part of Paris algebra semin
ar\n\n\nAbstract\nGiven a plabic graph on R^2\, we can choose a conormal l
ift of its zig-zag strands to the unit cotangent bundle of R^2\, obtaining
a Legendrian link. If the plabic graph satisfies a “grid” condition\,
its Legendrian link admits a natural embedding into the standard contact
R^3. We study the Kashiwara-Schapira moduli space of microlocal rank 1 she
aves associated with the Legendrian link\, and construct a natural (quasi-
)cluster structure on this moduli space using Legendrian weaves. In partic
ular\, we prove that any braid variety associated with (beta Delta) for a
3-strand braid beta admits cluster structures with an explicit constructio
n of initial seeds. We also construct Donaldson-Thomas transformations for
these moduli spaces and prove that the upper cluster algebra equals its c
luster algebra. In this talk\, I will introduce the theoretical background
and describe the basic combinatorics for constructing Legendrian weaves a
nd the (quasi-)cluster structures from a grid plabic graph. This is based
on joint work with Roger Casals\, cf. https://arxiv.org/abs/2204.13244.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sibylle Schroll (Cologne)
DTSTART:20220704T120000Z
DTEND:20220704T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/99
DESCRIPTION:Title: Recollements of derived categories of graded gentle algebra
s\nby Sibylle Schroll (Cologne) as part of Paris algebra seminar\n\n\n
Abstract\nGraded gentle algebras are classical objects in representation t
heory. They are quadratic monomial algebras making them particularly amena
ble to study and they appear in many different areas of mathematics such a
s in cluster theory\, in N=2 gauge theories and in homological mirror symm
etry of surfaces. \nIn this talk\, we give a construction of a partial cof
ibrant dg algebra resolution of a graded quadratic monomial algebra induci
ng an explicit recollement of their derived categories. We show that for g
raded gentle algebras\, both the left and the right side of such a recolle
ment corresponds to cutting the underlying surface which can be associated
to a graded gentle algebra. In the case of homologically smooth and prope
r graded gentle algebras this recollement can be restricted to the derived
categories with finite total cohomology\, thus inducing a recollement of
the corresponding partially wrapped Fukaya categories. We give some conseq
uences of this construction such as the existence of full exceptional sequ
ences\, silting objects and simple minded collections. This is joint work
with Wen Chang and Haibo Jin https://arxiv.org/abs/2206.11196.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Labardini-Fragoso (UNAM)
DTSTART:20221107T130000Z
DTEND:20221107T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/100
DESCRIPTION:Title: Revisiting Derksen-Weyman-Zelevinsky's mutations\nby D
aniel Labardini-Fragoso (UNAM) as part of Paris algebra seminar\n\nLecture
held in room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbst
ract\nThe mutation theory of quivers with potential and their representati
ons\, developed around 15 years ago by Derksen-Weyman-Zelevinsky\, has had
a profound impact both inside and outside the theory of cluster algebras.
In this talk I will present results obtained in joint works with Geiss an
d Schröer\, and with de Laporte\, about some interesting behaviors of DWZ
's mutations of representations. Namely\, despite needing several non-cano
nical choices of linear-algebraic data in order to be performed\, they can
always be arranged so as to become regular maps on dense open subsets of
representation spaces rep(Q\,S\,d). As a consequence\, one obtains the inv
ariance of Geiss-Leclerc-Schröer's 'generic basis' under mutations even i
n the Jacobi-infinite case\, thus generalizing a result of Plamondon. Furt
hermore\, given two distinct vertices k\, \\ell of a quiver with potential
(Q\,S)\, the k-th mutation of representations takes the \\ell-th indecomp
osable projective over (Q\,S) to the \\ell-th indecomposable projective ov
er \\mu_k(Q\,S). When a certain 'optimization' condition is satisfied by \
\ell\, this allows to compute certain 'Landau-Ginzburg potentials' as F-po
lynomials of projective representations.\n\nIn-person talk at the room 01
of the Institut Henri Poincaré\, Paris\, France\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greg Muller (Oklahoma)
DTSTART:20221010T120000Z
DTEND:20221010T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/101
DESCRIPTION:Title: Juggler's friezes\nby Greg Muller (Oklahoma) as part o
f Paris algebra seminar\n\n\nAbstract\nFrieze patterns are infinite strips
of numbers satisfying certain determinantal identities. Originally motiva
ted by Gauss’ “miraculous pentagram” identities\, these patterns hav
e since been connected to triangulations\, integrable systems\, representa
tion theory\, and cluster algebras. In this talk\, we will review a few ch
aracterizations and constructions of frieze patterns\, as well as a genera
lization which allows friezes with a “ragged edge” described by a jugg
ling function. These “juggler’s friezes” correspond to special point
s in positroid varieties\, in direct analogy with how classical friezes co
rrespond to special points in Grassmannians.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhui Shen (Michigan State)
DTSTART:20221017T120000Z
DTEND:20221017T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/102
DESCRIPTION:Title: Cluster Nature of Quantum Groups\nby Linhui Shen (Mich
igan State) as part of Paris algebra seminar\n\n\nAbstract\nWe present a r
igid cluster model to realize the quantum group $U_q(g)$ for $g$ of type A
DE. That is\, we prove that there is a natural Hopf algebra isomorphism fr
om the quantum group to a quotient algebra of the Weyl group invariants of
a Fock-Goncharov quantum cluster algebra. By applying the quantum duality
of cluster algebras\, we show that the quantum group admits a cluster can
onical basis $\\Theta$ whose structural coefficients are in $\\mathbb{N}[q
^{\\frac{1}{2}}\, q^{-\\frac{1}{2}}]$. The basis $\\Theta$ satisfies an in
variance property under Lusztig's braid group action\, the Dynkin automorp
hisms\, and the star anti-involution.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slava Pimenov (Nottingham)
DTSTART:20221003T120000Z
DTEND:20221003T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/103
DESCRIPTION:Title: Planar Prop of Differential Operators of Associative Algeb
ras\nby Slava Pimenov (Nottingham) as part of Paris algebra seminar\n\
nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eleven speakers
DTSTART:20220905T120000Z
DTEND:20220905T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/104
DESCRIPTION:Title: Algebra days in Paris\nby Eleven speakers as part of P
aris algebra seminar\n\n\nAbstract\nYou may be interested in the eleven ta
lks delivered on September 5 and 6 at the Algebra days in Paris.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kapranov (Yale and IPMU)
DTSTART:20220912T120000Z
DTEND:20220912T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/105
DESCRIPTION:Title: Perverse sheaves and schobers on symmetric products\nb
y Mikhail Kapranov (Yale and IPMU) as part of Paris algebra seminar\n\n\nA
bstract\nThe talk\, based on joint work in progress with V. Schechtman\, w
ill first recall our description of perverse sheaves on $Sym^n(\\mathbb{C}
)$\, the symmetric product of the complex line with its natural stratifica
tion by multiplicities. This description proceeds in terms of contingency
matrices\, which are certain integer matrices appearing (besides their ori
gin in statistics) in three different contexts:\n\n- A natural cell decomp
osition of $Sym^n(\\mathbb{C})$.\n\n- Compatibility of multiplication and
comultiplication in $\\mathbb{Z}_+$-graded Hopf algebras.\n\n- Parabolic B
ruhat decomposition for $GL_n$.\n\nPerverse sheaves on $Sym^n(\\mathbb{C})
$ are described in terms of certain data of mixed functoriality on conting
ency matrices which we call Janus sheaves. I will then explain our approac
h to categorifying the concept of Janus sheaves\, in which sums are replac
ed by filtrations with respect to the Bruhat order. Such data can be calle
d Janus schobers. Examples can be obtained from $\\mathbb{Z}_+$-graded Hop
f categories\, a concept going back to Crane-Frenkel\, of which we conside
r two examples related to representations of groups $GL_n$ over finite fie
lds (Joyal-Street) and $p$-adic fields (Bernstein-Zelevinsky). [This talk
is kindly shared by Noncommutative shape
s.]\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Neeman (Australian National University)
DTSTART:20220926T120000Z
DTEND:20220926T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/106
DESCRIPTION:Title: Two results\, both developments of a 2015 article by Kraus
e\nby Amnon Neeman (Australian National University) as part of Paris a
lgebra seminar\n\n\nAbstract\nIn 2020\, the pandemic hit\, and all around
the globe we went into lockdowns of various description. During the first
lockdown I carefully read Krause's 2015 article "Deriving Auslander's form
ula".\n\nIn this talk\, I will outline how the ideas of Krause's paper und
erpin two articles written in 2020 in collaboration with Canonaco and Stel
lari. One is about the uniqueness of enhancements of large classes of tria
ngulated categories\, while the second offers a counterexample to certain
vanishing conjectures in negative K-theory. [This talk is kindly shared by
Representation theory and triangulated categories.]\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liran Shaul (Prague)
DTSTART:20220919T120000Z
DTEND:20220919T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/107
DESCRIPTION:Title: The finitistic dimension conjecture via DG-rings\nby L
iran Shaul (Prague) as part of Paris algebra seminar\n\n\nAbstract\nThe fi
nitistic dimension of a ring A is defined to be the supremum of projective
dimensions among all A-modules of finite projective dimension. It is an o
pen problem whether this quantity is finite for finite dimensional algebra
s over a field and for artin algebras.\n\nIn this talk\, I will explain a
new approach for studying the finiteness of the finitistic dimension by em
bedding the ring A inside a nicely behaved differential graded algebra\, a
nd using relation between this DG-algebra and A to deduce results about th
e finitistic dimension.\nAs an application of these methods\, I will expla
in how to generalize a recent sufficient condition of Rickard\, for FPD(A)
<∞ in terms of generation of D(A) from finite dimensional algebras over
a field to all left perfect rings which admit a dualizing complex.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Sauter (Bielefeld)
DTSTART:20221024T120000Z
DTEND:20221024T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/108
DESCRIPTION:Title: Tilting theory in exact categories\nby Julia Sauter (B
ielefeld) as part of Paris algebra seminar\n\n\nAbstract\nWe define tiltin
g subcategories in arbitrary exact categories to archieve the following. F
irstly: Unify existing definitions of tilting subcategories to arbitrary e
xact categories. Discuss standard results for tilting subcategories: Ausla
nder correspondence\, Bazzoni description of the perpendicular category. S
econdly: We treat the question of induced derived equivalences separately
- given a tilting subcategory T\, we ask if a functor on the perpendicular
category induces a derived equivalence to a (certain) functor category ov
er T. If this is the case\, we call the tilting subcategory ideq tilting.
We prove a generalization of Miyashita's theorem (which is itself a genera
lization of a well-known theorem of Brenner-Butler) and characterize exact
categories with enough projectives allowing ideq tilting subcategories. I
n particular\, this is always fulfilled if the exact category is abelian w
ith enough projectives.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sota Asai (Osaka)
DTSTART:20221031T130000Z
DTEND:20221031T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/109
DESCRIPTION:Title: TF equivalence classes and canonical decompositions for E-
tame algebras\nby Sota Asai (Osaka) as part of Paris algebra seminar\n
\n\nAbstract\nThis is joint work with Osamu Iyama. Let $A$ be a finite dim
ensional algebra over an algebraically closed field. Then the numerical to
rsion pairs of Baumann-Kamnitzer-Tingley give an equivalence relation on t
he real Grothendieck group of finitely generated projective $A$-modules\,
which is called TF equivalence. By results of Yurikusa and Bruestle-Smith-
Treffinger\, we have that the g-vector cone of each 2-term presilting comp
lex is a TF equivalence class. To get more TF equivalence classes\, we can
use canonical decompositions of elements in the (integral) Grothendieck g
roup of finitely generated projectives introduced by Derksen-Fei. We have
showed that the cone defined by the canonical decomposition of each elemen
t is contained in some single TF equivalence class. Moreover\, we have als
o obtained that\, if $A$ is an E-tame algebra\, then this cone is precisel
y a TF equivalence class. In this talk\, I will explain these results and
some important steps to prove them.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Marin (Amiens and CNRS)
DTSTART:20221114T130000Z
DTEND:20221114T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/110
DESCRIPTION:Title: Geometric realization via random variables\nby Ivan Ma
rin (Amiens and CNRS) as part of Paris algebra seminar\n\nLecture held in
room 01 of the Institut Henri Poincaré\, Paris\, France.\n\nAbstract\nTop
ological spaces up to (weak) equivalences are\nfaithfully represented by s
implicial combinatorial\nstructures. Through an identification of the\n$n$
-dimensional simplex with the space of probability\nmeasures on a finite s
et of size $n+1$\, we investigate\nwhat happens when it is replaced by the
\nspace of random variables that naturally lies 'above' it.\nBy this proce
dure\, we obtain in particular a simple description\nof the classifying se
t of a (discrete) group\, and also\na new concept of geometric realization
. This new one\nalso induces an equivalence of categories up to homotopy\n
with simplicial sets and topological spaces. The 'probability-law'\nmap th
en defines a natural transformation between the\ntwo corresponding Quillen
equivalences.\n\nIn-person talk at the room 01 of the Institut Henri Poin
caré\, Paris\, France\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euiyong Park (Seoul)
DTSTART:20221205T130000Z
DTEND:20221205T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/111
DESCRIPTION:Title: Extended crystal structures of Hernandez-Leclerc categorie
s\nby Euiyong Park (Seoul) as part of Paris algebra seminar\n\n\nAbstr
act\nIn this talk\, we will discuss the categorical crystal structure on t
he Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. We define ex
tended crystals for quantum groups and show that there is a braid group ac
tion on extended crystals. We then explain how the set of the isomorphism
classes of simple modules in $\\mathscr{C}_\\mathfrak{g}^0$ has an extend
ed crystal structure\, and discuss the braid group action from the viewpoi
nt of the Hernandez-Leclerc category $\\mathscr{C}_\\mathfrak{g}^0$. This
talk is based on joint work with M. Kashiwara (arXiv: 2111.07255 and 2207.
11644).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gustavo Jasso and Fernando Muro (Lund and Sevilla)
DTSTART:20221121T130000Z
DTEND:20221121T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/112
DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, I\nb
y Gustavo Jasso and Fernando Muro (Lund and Sevilla) as part of Paris alge
bra seminar\n\n\nAbstract\nIn these two talks\, we will start by introduci
ng a result which establishes the existence and uniqueness of (DG) enhance
ments for triangulated categories which admit an additive generator whose
endomorphism algebra is finite-dimensional (over a perfect field). We will
then present a generalisation of this result that allows us to treat a la
rger class of triangulated categories\, which instead admit a generator wi
th a strong regularity property (a so-called dZ-cluster tilting object). W
e will also explain how our result\, combined with crucial theorems of Aug
ust and Hua-Keller\, leads to a positive solution of the Donovan-Wemyss Co
njecture for contraction algebras as observed by Keller. We will also comm
ent on some details about the proof.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Muro and Gustavo Jasso (Sevilla and Lund)
DTSTART:20221128T130000Z
DTEND:20221128T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/113
DESCRIPTION:Title: The triangulated Auslander-Iyama correspondence\, II\n
by Fernando Muro and Gustavo Jasso (Sevilla and Lund) as part of Paris alg
ebra seminar\n\n\nAbstract\nIn these two talks\, we will start by introduc
ing a result which establishes the existence and uniqueness of (DG) enhanc
ements for triangulated categories which admit an additive generator whose
endomorphism algebra is finite-dimensional (over a perfect field). We wil
l then present a generalisation of this result that allows us to treat a l
arger class of triangulated categories\, which instead admit a generator w
ith a strong regularity property (a so-called dZ-cluster tilting object).
We will also explain how our result\, combined with crucial theorems of Au
gust and Hua-Keller\, leads to a positive solution of the Donovan-Wemyss C
onjecture for contraction algebras as observed by Keller. We will also com
ment on some details about the proof.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphaël Rouquier (UCLA)
DTSTART:20221212T130000Z
DTEND:20221212T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/114
DESCRIPTION:Title: Coherent realizations of 2-representations\nby Raphaë
l Rouquier (UCLA) as part of Paris algebra seminar\n\n\nAbstract\n2-repres
entations of Kac-Moody algebras arise algebraically and as categories of c
onstructible sheaves. We will discuss two settings involving coherent shea
ves: derived cotangent bundles to spaces of quiver representations and spa
ces of quasi-maps in flag varieties.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alireza Nasr-Isfahani (IPM Isfahan)
DTSTART:20230116T130000Z
DTEND:20230116T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/115
DESCRIPTION:Title: Lower bound cluster algebras generated by projective clust
er variables\nby Alireza Nasr-Isfahani (IPM Isfahan) as part of Paris
algebra seminar\n\n\nAbstract\nWe introduce the notion of a lower (upper)
bound cluster algebra generated by projective cluster variables. Projectiv
e cluster variables are often categorified\nby projective modules of the c
orresponding quiver with relations.\nWe show that under an acyclicity assu
mption\, the cluster algebra and the lower bound cluster\nalgebra generate
d by projective cluster variables coincide.\nIn this case\, we use our res
ults to construct a basis for the cluster algebra.\nWe also show that the
coincidence between cluster algebra and the lower bound cluster\nalgebra g
enerated by projective cluster variables holds beyond acyclic seeds. Part
of this talk is based on joint work with Karin Baur. - This talk will be o
n Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (University at Albany)
DTSTART:20230123T130000Z
DTEND:20230123T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/116
DESCRIPTION:Title: A generalization of the Murnaghan-Nakayama rule for $K$-$k
$-Schur and $k$-Schur functions\nby Duc-Khanh Nguyen (University at Al
bany) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce a gener
alization of $K$-$k$-Schur functions and k-Schur functions via the Pieri r
ule. Then we obtain the Murnaghan-Nakayama rule for the generalized functi
ons. The rule is described explicitly in the cases of $K$-$k$-Schur functi
ons and $k$-Schur functions\, with concrete descriptions and algorithms fo
r coefficients. Our work recovers the result of Bandlow\, Schilling\, and
Zabrocki for $k$-Schur functions\, and explains it as a degeneration of th
e rule for $K$-$k$-Schur functions. In particular\, many other special cas
es promise to be detailed in the future. - This talk will be on Zoom only.
\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauren Williams (Harvard)
DTSTART:20230605T120000Z
DTEND:20230605T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/117
DESCRIPTION:Title: The amplituhedron and cluster algebras\nby Lauren Will
iams (Harvard) as part of Paris algebra seminar\n\n\nAbstract\nI will give
a gentle introduction to the amplituhedron\, a geometric object that was
introduced in the context of scattering amplitudes in N=4 super Yang Mills
. I'll then explain some of the connections of the amplituhedron to clust
er algebras.\n\nThis talk will take place in hybrid mode at the Institut H
enri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (IHES)
DTSTART:20230130T130000Z
DTEND:20230130T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/118
DESCRIPTION:Title: Coxeter quiver representations in fusion categories and Ga
briel’s theorem\nby Edmund Heng (IHES) as part of Paris algebra semi
nar\n\n\nAbstract\nOne of the most celebrated theorems in the theory of qu
iver representations is undoubtedly Gabriel’s theorem\, which reveals a
deep connection between quiver representations and root systems arising fr
om Lie algebras. In particular\, Gabriel’s theorem shows that the finite
-type quivers are classified by the ADE Dynkin diagrams and the indecompos
able representations are in bijection with the underlying positive roots.
Following the works of Dlab—Ringel\, the classification can be generalis
ed to include all the other Dynkin diagrams (including BCFG) if one consid
ers the more general notion of valued quivers (K-species) representations
instead.\n\nWhile the theories above relate (valued) quiver representation
s to root systems arising from Lie algebras\, the aim of this talk is to g
eneralise Gabriel’s theorem in a slightly different direction using root
systems arising in Coxeter theory. Namely\, we shall introduce a new noti
on of Coxeter quivers and their representations built in (other) fusion ca
tegories\, where we have a generalised Gabriel’s theorem as follows: a C
oxeter quiver has finitely many indecomposable representations if and only
if its underlying graph is a Coxeter-Dynkin diagram — including the non
-crystallographic types H and I. Using a similar notion of reflection func
tors as introduced by Bernstein—Gelfand—Ponomarev\, we shall also show
that the isomorphism classes of indecomposable representations of a Coxet
er quiver are in bijection with the positive roots associated to the root
system of the underlying Coxeter graph. --\nThis talk will take place in h
ybrid mode at the IHP.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Shanghai Jiao Tong)
DTSTART:20230220T130000Z
DTEND:20230220T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/119
DESCRIPTION:Title: Bracelets are theta functions for surface cluster algebras
\nby Fan Qin (Shanghai Jiao Tong) as part of Paris algebra seminar\n\n
\nAbstract\nThe skein algebra of a marked surface admits the basis of brac
elet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams
. As a cluster algebra\, it also admits the theta basis from the cluster s
cattering diagram by Gross-Hacking-Keel-Kontsevich. In a joint work with T
ravis Mandel\, we show that the two bases coincide except for the once-pun
ctured torus. Our results extend to quantum cluster algebras with coeffici
ents arising from the surface even in punctured cases. Long-standing conje
ctures on strong positivity and atomicity follow as corollaries.\n\nExcept
ionally\, this talk will take place in hybrid mode in room 1013 of the Sop
hie Germain building (8\, place Aurélie Nemours\, 75013 Paris).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wille Liu (Taipei)
DTSTART:20230213T130000Z
DTEND:20230213T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/120
DESCRIPTION:Title: Translation functors for trigonometric double affine Hecke
algebras\nby Wille Liu (Taipei) as part of Paris algebra seminar\n\n\
nAbstract\nThe double affine Hecke algebra was introduced by Cherednik aro
und 1995 as a tool in his study of Macdonald polynomials. Its degenerate v
ersion\, called trigonometric double affine Hecke algebra (TDAHA)\, has al
so turned out to be linked to different areas\, notably to the representat
ion theory of $p$-adic groups.\n\nGiven a root system\, the TDAHA $H_c$ de
pends on a family of complex parameters $c$. Given two families of paramet
ers $c$ and $c'$ whose difference takes integer values\, there exists a tr
iangle equivalence between the bounded derived categories of the correspon
ding TDAHAs\, which we call translation functor. The objective of this tal
k is to explain the construction of this functor. \n\nThis talk will be on
Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haruhisa Enomoto (Osaka Metropolitan)
DTSTART:20230227T130000Z
DTEND:20230227T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/121
DESCRIPTION:Title: Maximal self-orthogonal modules and a new generalization o
f tilting modules\nby Haruhisa Enomoto (Osaka Metropolitan) as part of
Paris algebra seminar\n\n\nAbstract\nWe study self-orthogonal modules\, i
.e.\, modules T such that Ext^i(T\, T) = 0 for all i > 0. We introduce pro
jectively Wakamatsu-tilting modules (pW-tilting modules) as a generalizati
on of tilting modules. If A is a representation-finite algebra\, every sel
f-orthogonal A-module can be completed to a pW-tilting module\, and the fo
llowing classes coincide: pW-tilting modules\, Wakamatsu tilting modules\,
maximal self-orthogonal modules\, and self-orthogonal modules T with |T|
= |A|. We also prove that every self-orthogonal module over a representati
on-finite Iwanaga-Gorenstein algebra has finite projective dimension. We f
inally explain some open conjectures on self-orthogonal modules.\n\nThis t
alk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keyu Wang (Paris Cité)
DTSTART:20230206T130000Z
DTEND:20230206T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/122
DESCRIPTION:Title: QQ˜ -systems for twisted quantum affine algebras\nby
Keyu Wang (Paris Cité) as part of Paris algebra seminar\n\n\nAbstract\nAs
a part of Langlands duality\, certain equations were found in two differe
nt areas of mathematics. They are known as Baxter’s TQ systems and the Q
Q type systems\, as they trace back to Baxter’s study on integrable mode
ls in the 1970s. During the same decade\, similar systems of equations wer
e discovered in the area of ordinary differential equations (ODE) by Sibuy
a\, Voros and others. Today\, this remarkable correspondence is realized a
s a duality between representation theory of nontwisted quantum affine alg
ebras (QAA) and the theory of opers for their Langlands dual Lie algebras.
\n\nWe are interested in this duality when the roles of the affine Lie alg
ebra and its dual are exchanged. When the nontwisted QAA is of type BCFG\,
its dual will be a twisted QAA. To exchange their roles amounts to studyi
ng representations of twisted QAAs.\n\nIn this talk\, we will begin by rev
iewing this story. We will explain the representation theory of twisted QA
As and their Borel algebras. We will explain the expected relationship bet
ween twisted and nontwisted types\, and we will establish TQ systems and Q
Q^{~} systems for twisted QAAs.\n\nThis talk will take place in hybrid mod
e at the IHP.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amnon Yekutieli (Ben Gurion University)
DTSTART:20230403T120000Z
DTEND:20230403T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/123
DESCRIPTION:Title: An Algebraic Approach to the Cotangent Complex\nby Amn
on Yekutieli (Ben Gurion University) as part of Paris algebra seminar\n\n\
nAbstract\nLet $B/A$ be a pair of commutative rings. We propose an algebra
ic approach to the cotangent complex $L_{B/A}$. Using commutative semi-fre
e DG ring resolutions of B relative to A\, we construct a complex of $B$-m
odules $LCot_{B/A}$. This construction works more generally for a pair $B/
A$ of commutative DG rings.\n\nIn the talk\, we will explain all these con
cepts. Then we will discuss the important properties of the DG $B$-module
$LCot_{B/A}$. It time permits\, we'll outline some of the proofs.\n\nIt is
conjectured that for a pair of rings $B/A$\, our $LCot_{B/A}$ coincides w
ith the usual cotangent complex $L_{B/A}$\, which is constructed by simpli
cial methods. We shall also relate $LCot_{B/A}$ to modern homotopical vers
ions of the cotangent complex.\n\n\nSlides: https://sites.google.com/view/
amyekut-math/home/lectures/cotangent\n\n(updated 18 March 2023)\n\n\nThis
talk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luc Pirio (Versailles)
DTSTART:20230306T130000Z
DTEND:20230306T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/124
DESCRIPTION:Title: Hyperlogarithmic functional identities on del Pezzo surfac
es\nby Luc Pirio (Versailles) as part of Paris algebra seminar\n\n\nAb
stract\nFor any d in {1\,…\,6}\, we prove that the web of conics on a de
l Pezzo surface of degree d carries a functional identity HLog(7-d) whose
components are antisymmetric hyperlogarithms of weight 7-d. Our approach i
s uniform with respect to d and relies on classical results about the acti
on of the Weyl group on the set of lines on the del Pezzo surface. These
hyperlogarithmic functional identities HLog(7-d) are natural generalizatio
ns of the classical 3-term and (Abel's) 5-term identities of the logarith
m and the dilogarithm\, which are the identities HLog(1) and HLog(2) corre
sponding to the cases d=6 and d=5 respectively.\n\nIf time allows\, I will
give a list of many nice properties enjoyed by the 5-term identity of the
dilogarithm and will explain that most of these properties (such as being
of cluster type) have natural generalizations which are satisfied by the
weight 3 hyperlogarithmic identity HLog(3).\n\nThe talk will be mainly bas
ed on the preprint arXiv:2301.06775 written with Ana-Maria Castravet.\n\nE
xceptionally\, this talk will take place in hybrid mode in room 1013 of th
e Sophie Germain building (8\, place Aurélie Nemours\, 75013 Paris).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Holstein (Hamburg)
DTSTART:20230313T130000Z
DTEND:20230313T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/125
DESCRIPTION:Title: Enriched Koszul duality for dg categories\nby Julian H
olstein (Hamburg) as part of Paris algebra seminar\n\n\nAbstract\nThe cate
gory of dg categories is related by Koszul duality to a certain category o
f colagebras\, so-called pointed curved coalgebras. In this talk we wil re
view this Quillen equivalence and observe that it is in fact quasi-monoida
l. By constructing internal homs of pointed curved coalgebras we can then
construct a concrete closed monoidal model for dg categories. In particula
r this gives natural descriptions of mapping spaces and internal homs betw
een dg categories. This is joint work with A. Lazarev.\n\nExceptionally\,
this talk will take place in hybrid mode in room 1013 of the Sophie Germai
n building (8\, place Aurélie Nemours\, 75013 Paris).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Bochum)
DTSTART:20230320T130000Z
DTEND:20230320T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/126
DESCRIPTION:Title: Expander representations\nby Markus Reineke (Bochum) a
s part of Paris algebra seminar\n\n\nAbstract\nDimension expanders\, intro
duced by Wigderson and Lubotzky-Zelmanov\, are a linear algebra analogue o
f the notion of expander graphs. We interpret this notion in terms of quiv
er representations\, as a quantitative variant of stability. We use Schofi
eld’s recursive description of general subrepresentations to re-derive e
xistence of dimension expanders and to determine optimal expansion coeffic
ients.\n\nThe talk will take place in hybrid mode at the IHP.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Koshevoy (IHES)
DTSTART:20230327T120000Z
DTEND:20230327T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/127
DESCRIPTION:Title: Polyhedral parametrization of canonical bases\nby Gleb
Koshevoy (IHES) as part of Paris algebra seminar\n\n\nAbstract\nParametri
zations of the canonical bases\, string basis and theta basis\, can be ob
tained by the tropicalization of the Berenstein-Kazhdan decoration functi
on and the Gross-Hacking-Keel-Kontsevich potential respectively. For a cl
assical Lie algebra and a reduced decomposition $\\mathbf i$\, the decora
ted graphs are constructed algorithmically\, vertices of such graphs are l
abeled by monomials which constitute the set of monomials of the Berenstei
n-Kazhdan potential. Due to this algorithm we obtain a characterization
of $\\mathbf i$-trails introduced by Berenstein and Zelevinsky. Our algori
thm uses multiplication and summations only\, its complexity is linear in
time of writing the monomials of the potential. For SL_n\, there is an al
gorithm due to Gleizer and Postnikov which gets all monomials of the Beren
stein-Kazhdan potential using combinatorics of wiring diagrams. For this c
ase\, our algorithm uses simpler combinatorics and is faster than the Glei
zer-Postnikov algorithm. The cluster algorithm due to Genz\, Schumann and
me is polynomial in time but it uses divisions of polynomials of several v
ariables.\nIf time permits I will report on applications of decorated grap
hs to analysis of the Newton polytopes of F-polynomials related to the Gr
oss-Hacking-Keel-Kontsevich potentials. The talk is based on joint works w
ith Volker Genz and Bea Schumann and with Yuki Kanakubo and Toshiki Nakash
ima.\n\nThis talk will take place in hybrid mode at the IHP.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Vasserot (Paris Cité)
DTSTART:20230417T120000Z
DTEND:20230417T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/128
DESCRIPTION:Title: Critical convolution algebras and quantum loop groups\
nby Eric Vasserot (Paris Cité) as part of Paris algebra seminar\n\n\nAbst
ract\nWe introduce a new family of algebras attached to quivers with poten
tials\, using critical K-theory and critical Borel-Moore homology. They ge
neralize the convolution algebras attached to quivers by Nakajima. We give
some applications to cohomological and K-theoretical Hall algebras\, to s
hifted quantum loop groups\, and to Kirillov-Reshetikhin and prefundamenta
l representations. \n\nThis talk will take place in hybrid mode at the Ins
titut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Owen Garnier (Amiens)
DTSTART:20230424T120000Z
DTEND:20230424T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/129
DESCRIPTION:Title: Homology of a category and the Dehornoy-Lafont order compl
ex\nby Owen Garnier (Amiens) as part of Paris algebra seminar\n\n\nAbs
tract\nThe work of Squier and Kobayashi proves that the homology of a mono
id can be computed using a so called complete rewriting system\, which act
s as a convenient presentation of the monoid.\n\nLater\, Dehornoy and Lafo
nt noted that such a convenient presentation arises in particular when con
sidering monoids satisfying combinatorial assumptions regarding existence
of lcms. This gave rise to the so called Dehornoy-Lafont order complex\, w
hich was used to compute the homology of complex braid groups by Callegaro
and Marin.\n\nAfter giving a quick summary of these works\, I will presen
t a generalization of this latter complex to the case of a category which
again satisfies convenient combinatorial assumptions. \n\nOf course\, as m
y "true" goal is to compute the homology of a group using some associated
category\, I will also give a link between the homology of a category\, th
at of its enveloping groupoid\, and that of a group which is equivalent to
the said groupoid.\n\nLastly\, I will explain an application to the case
of the complex braid group $B_{31}$\, which is studied through its associa
ted Garside category\, and which was not directly covered by previous appr
oaches.\n\nThis talk will take place in hybrid mode at the Institut Henri
Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Chapoton (CNRS Strasbourg)
DTSTART:20230619T120000Z
DTEND:20230619T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/130
DESCRIPTION:Title: Posets and fractional Calabi-Yau categories\nby Fréd
éric Chapoton (CNRS Strasbourg) as part of Paris algebra seminar\n\n\nAbs
tract\nIn combinatorics\, several famous enumeration results involve a spe
cial kind of product formula. The very same kind of product formula gives
the Milnor number of an isolated quasi-homogenous singularity. It seems po
ssible that one could relate combinatorics and singularities by means of d
erived categories: on the one hand\, modules over incidence algebras of pa
rtially ordered sets (posets) and on the other hand\, some kind of Fukaya-
like category that should categorify the Milnor fibration. Even if part of
this remains very unprecise and vague\, this implies many concrete conjec
tures about derived equivalences between posets. \n\nThis talk will take p
lace in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Bershtein (Moscow and IPMU)
DTSTART:20230508T120000Z
DTEND:20230508T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/131
DESCRIPTION:Title: Cluster Hamiltonian reductions: examples\nby Mikhail B
ershtein (Moscow and IPMU) as part of Paris algebra seminar\n\n\nAbstract\
nI will talk about an\, in general conjectural\, construction of a X-clust
er structure on certain Hamiltonian reduction of a X-cluster variety. Ther
e are two main classes of examples of such constructions: moduli spaces of
framed local systems with special monodromies and phase spaces of Gonchar
ov-Kenyon integrable systems. The first class includes the phase space of
open XXZ chain and Ruijsenaars integrable systems. The second class includ
es integrable systems corresponding to the q-difference Painleve equations
.\n\nBased on works in progress and discussions with P. Gavrylenko\, A. Ma
rshakov\, M. Semenyakin\, A. Shapiro\, G. Schrader.\n\nThis talk will take
place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haibo Jin (Cologne)
DTSTART:20230515T120000Z
DTEND:20230515T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/132
DESCRIPTION:Title: A complete derived invariant and silting theory for graded
gentle algebras\nby Haibo Jin (Cologne) as part of Paris algebra semi
nar\n\n\nAbstract\nWe show that among the derived equivalent classes of ho
mologically smooth and proper graded gentle algebras there is only one cla
ss whose perfect derived category does not admit silting objects.\n\nAs on
e application we give a sufficient and necessary condition for any homolo
gically smooth and proper graded gentle algebra under which all pre-siltin
g objects in its perfect derived category may be complete into silting obj
ects.\n\nAs another application we confirm a conjecture by Lekili and Poli
shchuk that the geometric invariants which they construct for homologicall
y smooth and proper graded gentle algebras are a complete derived invarian
t. Hence\, we obtain a complete invariant for partially wrapped Fukaya cat
egories of surfaces with stops. \n\nThis is a report on joint work with Si
bylle Schroll and Zhengfang Wang.\n\nThis talk will take place in hybrid m
ode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Positselski (Prague)
DTSTART:20230522T121500Z
DTEND:20230522T131500Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/133
DESCRIPTION:Title: The homomorphism removal and repackaging construction\
nby Leonid Positselski (Prague) as part of Paris algebra seminar\n\n\nAbst
ract\nThis work is an attempt to understand the maximal natural generality
context for\nthe Koenig-Kuelshammer-Ovsienko construction in the theory o
f quasi-hereditary algebras by\nputting it into a category-theoretic conte
xt. Given a field k and a k-linear exact category E \nwith a chosen set of
nonzero objects F_i such that every object of E is a finitely iterated \n
extension of some F_i\, we construct a coalgebra C whose irreducible comod
ules L_i are indexed by the same indexing set\, and an exact functor from
C-comod to E taking L_i to F_i such that the spaces Ext^n between L_i in C
−comod are the same as between F_i in E (for n > 0). Thus\, the abelian
category C−comod is obtained from the exact category E by removing all t
he nontrivial homomorphisms between the chosen objects F_i in E while keep
ing the Ext spaces unchanged. The removed homomorphisms are then repackage
d into a semialgebra S over C such that the exact category E can be recove
red as the category of S-semimodules induced from finite-dimensional C-com
odules. The construction used Koszul duality twice: once as absolute and o
nce as relative Koszul duality.\n\n\nThis talk will take place in hybrid f
ormat at the GAP conference at the Institut Henri Poincaré\, cf. GAP.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine De Saint Germain (Hong Kong U.)
DTSTART:20230612T120000Z
DTEND:20230612T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/134
DESCRIPTION:Title: Cluster additive functions and acyclic cluster algebras\nby Antoine De Saint Germain (Hong Kong U.) as part of Paris algebra sem
inar\n\n\nAbstract\nIn his study of combinatorial features of cluster cate
gories and cluster-tilted algebras\, Ringel introduced an analogue of addi
tive functions of stable translation quivers called cluster-additive funct
ions. \n\nIn this talk\, we will define cluster-additive functions associ
ated to any acyclic mutation matrix\, relate them to tropical points of th
e cluster X-variety\, and realise their values as certain compatibility de
grees between functions on the cluster A-variety associated to the Langlan
ds dual mutation matrix (in accordance with the philosophy of Fock-Gonchar
ov). This is based on joint work with Peigen Cao and Jiang-Hua Lu. \n\nThi
s talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Rivera (Purdue)
DTSTART:20230626T120000Z
DTEND:20230626T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/135
DESCRIPTION:Title: Loop spaces and bialgebras\nby Manuel Rivera (Purdue)
as part of Paris algebra seminar\n\n\nAbstract\nI will discuss several int
erlocked constructions giving rise to bialgebra structures all of which ha
ve parallel algebraic and topological interpretations. The bialgebras cons
idered will be of different flavors depending on the compatibility between
the product and coproduct\; for instance\, we will see examples of Hopf\,
Frobenius\, infinitesimal and Lie bialgebras. These structures appear whe
n analyzing the role of loop spaces in homotopy theory and manifold topolo
gy and reveal new results regarding the algebraic nature of geometric spac
e.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duncan Laurie (Oxford)
DTSTART:20231002T120000Z
DTEND:20231002T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/136
DESCRIPTION:Title: Quantum toroidal algebras: braid group actions\, automorph
isms\, and representation theory\nby Duncan Laurie (Oxford) as part of
Paris algebra seminar\n\n\nAbstract\nQuantum toroidal algebras Uq(g_tor)
occur as the Drinfeld\nquantum affinizations of quantum affine algebras. I
n particular\; they\ncontain (and are generated by) a horizontal and verti
cal copy of the\naffine quantum group. In type A\, Miki obtained an automo
rphism of\nUq(g_tor) exchanging these subalgebras\, which has since played
a\ncrucial role in the investigation of its structure and representation\
ntheory.\n\nIn this talk\; we shall construct an action of the extended do
uble\naffine braid group B on the quantum toroidal algebra in all untwiste
d\ntypes. In the simply laced cases\, using this action and certain\ninvol
utions of B we obtain automorphisms and anti-automorphisms of\nUq(g_tor) w
hich exchange the horizontal and vertical subalgebras\, thus\ngeneralising
the results of Miki. We shall then discuss potential\nextensions of these
results\, and applications to the representation\ntheory of quantum toroi
dal algebras.\n\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bill Crawley-Boevey (Bielefeld)
DTSTART:20230713T120000Z
DTEND:20230713T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/137
DESCRIPTION:Title: Integral representations of quivers\nby Bill Crawley-B
oevey (Bielefeld) as part of Paris algebra seminar\n\n\nAbstract\nIn the 1
990s\, I classified rigid representations of a quiver by finitely generate
d free modules over a principal ideal ring. I shall extend the results to
representations of a quiver by finitely generated projective modules over
an arbitrary commutative ring. \n\nThis talk will kindly be shared by the
organisation of the conference \nHomological algebra and representation theory.
It will take place in hybrid mode at Karlovasi (Samos\, Greece).\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Thomas (Heidelberg)
DTSTART:20231127T130000Z
DTEND:20231127T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/138
DESCRIPTION:Title: A q-deformation of sl2 and the Witt algebra\nby Alexan
der Thomas (Heidelberg) as part of Paris algebra seminar\n\n\nAbstract\nI
will present new q-deformations of Lie algebras linked to the modular grou
p and the q-rational numbers as defined by Morier-Genoud and Ovsienko. In
particular\, I will describe deformations of sl2 and the Witt algebra. The
se deformations are realized as differential operators acting on the hyper
bolic plane\, giving new insights into q-rationals. \n\nThis talk will tak
e place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norihiro Hanihara (IPMU)
DTSTART:20231023T120000Z
DTEND:20231023T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/139
DESCRIPTION:Title: Silting-cluster tilting correspondences\nby Norihiro H
anihara (IPMU) as part of Paris algebra seminar\n\n\nAbstract\nCluster cat
egories are fundamental objects in representation theory\, including such
topics as cluster algebras\, tilting theory\, singularity theory. The theo
ry of Amiot\, Guo\, and Keller shows that tilting/silting objects in deriv
ed categories (of a finite dimensional algebra or of a Calabi-Yau dg algeb
ra) give rise to cluster tilting objects in the cluster category. We study
such correspondences between silting objects and cluster tilting objects.
We propose a conjecture on the liftability of cluster tilting objects in
the cluster category to silting objects\, and discuss some evidence for it
. This is based on a joint work with Osamu Iyama.\n\nThis talk will take p
lace in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Se-jin Oh (Sungkyunkwan U.)
DTSTART:20231016T120000Z
DTEND:20231016T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/140
DESCRIPTION:Title: A noncommutative algebra arising from the $t$-quantized Ca
rtan matrix\nby Se-jin Oh (Sungkyunkwan U.) as part of Paris algebra s
eminar\n\n\nAbstract\nThe quantum Cartan matrix appears ubiquitously as a
key combinatorial ingredient in the representation theory of quantum affin
e algebras. Through the generalized Schur-Weyl duality\, it also plays a c
entral role in the one of quiver Hecke algebras and the quantum unipotent
coordinate ring of (skew-)symmetric finite type. Even though there are qui
ver Hecke algebras and quantum unipotent coordinate rings of non (skew-)sy
mmetric finite type\, there is no counterpart in representation theory as
far as I and my collaborators understand.\nIn this talk\, I introduce a no
n-commutative ring over $\\Q(q^{1/2}$)\, which is expected to be a quantum
Grothendieck ring for a Hernandez-Leclerc category\, if such a representa
tion theory exists\, by using the t-quantized Cartan matrix. When we consi
der its heart subalgebra\, the algebra is isomorphic to the quantum unipo
tent coordinate ring of any finite type.\nThis talk is mainly based on joi
nt work with Kashiwara\, Jang and Lee.\n\nThis talk will take place on Zoo
m only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Shanghai Jiaotong)
DTSTART:20231009T120000Z
DTEND:20231009T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/141
DESCRIPTION:Title: Analogs of dual canonical bases for cluster algebras from
Lie theory\nby Fan Qin (Shanghai Jiaotong) as part of Paris algebra se
minar\n\n\nAbstract\nThe (quantized) coordinate rings of many interesting
varieties from Lie theory are (quantum) cluster algebras. We construct the
common triangular bases for these algebras. Such bases provide analogs of
the dual canonical bases\, whose existence has been long expected in clus
ter theory. For symmetric Cartan matrices\, they are positive and admit mo
noidal categorification after base change. We employ a unified approach ba
sed on cluster algebra operations. Our results apply to algebraic groups\,
double Bott-Samelson cells\, and braid varieties\, etc. Additionally\, we
find applications in representations of quantum affine algebras.\n\nThis
talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (IMJ-PRG)
DTSTART:20231106T130000Z
DTEND:20231106T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/142
DESCRIPTION:Title: Relative Calabi-Yau structures and extriangulated cluster
categories\nby Merlin Christ (IMJ-PRG) as part of Paris algebra semina
r\n\n\nAbstract\nWe will begin with an introduction to relative Calabi-Yau
structures in the sense of Brav-Dyckerhoff\, generalizing the notion of a
Calabi-Yau triangulated (or dg-) category to functors. Via so-called rela
tive theory\, Calabi-Yau functors give rise to extriangulated categories\,
which are Frobenius 2-Calabi-Yau. We apply this to examples of cluster ca
tegories of surfaces\, categorifying the surface cluster algebras with coe
fficients in the boundary arcs. This talk is mostly based on my preprint a
rXiv:2209.06595. \n\nThis talk will take place in hybrid mode at the Insti
tut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Francone (Lyon)
DTSTART:20231113T130000Z
DTEND:20231113T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/143
DESCRIPTION:Title: Minimal monomial lifting of cluster algebras and branching
problems\nby Luca Francone (Lyon) as part of Paris algebra seminar\n\
n\nAbstract\nThe minimal monomial lifting is a sort of homogenisation tech
nique\, whose goal is to identify a cluster algebra structure on certain "
suitable for lifting" schemes\, compatibly with a base cluster structure o
n a distinguished subscheme. This technique allows to recover\, by geometr
ic methods\, some well known cluster structures. In this talk\, we will pr
esent this technique and discuss applications to branching problems in rep
resentation theory of complex reductive groups.\n\nThis talk will take pla
ce in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wahei Hara (IPMU)
DTSTART:20231120T130000Z
DTEND:20231120T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/144
DESCRIPTION:Title: Spherical objects in dimension two and three\nby Wahei
Hara (IPMU) as part of Paris algebra seminar\n\n\nAbstract\nIn this talk\
, we discuss the classification problem of spherical “like” objects in
various geometric settings including the minimal resolution of an ADE sur
face singularity and a 3-fold flopping contraction. The classification of
spherical objects is related to questions about the autoequivalence groups
or Bridgeland stability conditions\, but in 3-fold settings\, this is not
always a correct problem to ask. In the first half of the talk\, we discu
ss what kind of objects should be classified\, and in the second half\, a
sketch of the proof will be explained. Our new technique can also be appli
ed to the heart of a bounded t-structure\, and classifies all t-structures
of the associated null category. As a corollary\, the connectedness of th
e space of stability conditions follows. This is all joint work with Micha
el Wemyss.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonah Berggren (Kentucky)
DTSTART:20231204T130000Z
DTEND:20231204T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/145
DESCRIPTION:Title: Consistent Dimer Models on Surfaces with Boundary\nby
Jonah Berggren (Kentucky) as part of Paris algebra seminar\n\n\nAbstract\n
A dimer model is a quiver with faces embedded in a surface. Dimer models o
n the disk and torus are particularly well-studied\, though these theories
have remained largely separate. Various “consistency conditions” may
be imposed on dimer models on the disk or torus with implications relating
to 3-Calabi-Yau properties and categorification.\n \nWe extend many of th
ese definitions and results to the setting of general surfaces with bounda
ry. We show that the completed dimer algebra of a “strongly consistent
” dimer model is bimodule internally 3-Calabi-Yau with respect to its bo
undary idempotent. As a consequence\, the Gorenstein-projective module cat
egory of the completed boundary algebra of a suitable dimer model categori
fies the cluster algebra given by its underlying ice quiver. We give a cla
ss of examples of annulus models satisfying the requisite conditions. \n\n
This talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Sherman-Bennett (MIT)
DTSTART:20231218T130000Z
DTEND:20231218T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/146
DESCRIPTION:Title: Cluster structures on braid and Richardson varieties\n
by Melissa Sherman-Bennett (MIT) as part of Paris algebra seminar\n\n\nAbs
tract\nIn 2014\, Leclerc gave a construction of a conjectural cluster stru
cture on open Richardson varieties in types ADE. His construction was cate
gorical in nature\, involving preprojective algebra modules. His conjectur
e inspired work on cluster structures on braid varieties in arbitrary type
\, which generalize open Richardsons. Two cluster structures on braid vari
eties were recently constructed. The first one\, based on ideas and techni
ques from symplectic topology\, is due to Casals-Gorsky-Gorsky-Le-Shen-Sim
ental. I will discuss the other\, which is joint work with Galashin\, Lam
and Speyer. Our main geometric tool is the Deodhar decomposition. In type
A\, our quivers are given by "3D plabic graphs"\, which generalize Postnik
ov's plabic graphs for the Grassmannian. Time permitting\, I will also dis
cuss related work with Serhiyenko\, where we show that for type A Richards
ons\, Leclerc's conjectural categorical construction does in fact give a c
luster structure\, with quivers again given by 3D plabic graphs.\n\nThis t
alk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JiaRui Fei (Shanghai Jiao Tong)
DTSTART:20231211T130000Z
DTEND:20231211T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/147
DESCRIPTION:Title: Crystal Structure of Upper Cluster Algebras\nby JiaRui
Fei (Shanghai Jiao Tong) as part of Paris algebra seminar\n\n\nAbstract\n
We describe the upper seminormal crystal structure for the $\\mu$-supporte
d $\\delta$-vectors for any quiver with potential with reachable frozen ve
rtices\, or equivalently for the tropical points of the corresponding clus
ter $\\mathcal{X}$-variety. We show that the crystal structure can be alge
braically lifted to the generic basis of the upper cluster algebra. This c
an be viewed as an additive categorification of the crystal structure aris
ing from cluster algebras. We introduce the biperfect bases and the strong
biperfect bases in the cluster algebra setting and give a description of
all strong biperfect bases.\n\nThis talk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Asplund (Stony Brook U.)
DTSTART:20240115T130000Z
DTEND:20240115T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/148
DESCRIPTION:Title: Relative Ginzburg algebras and Chekanov-Eliashberg dg-alge
bras\nby Johan Asplund (Stony Brook U.) as part of Paris algebra semin
ar\n\n\nAbstract\nThe Chekanov-Eliashberg dg-algebra yields a powerful iso
topy invariant of (possibly singular) Legendrian submanifolds in a class o
f contact manifolds\, and is also intimately related to Fukaya categories
of a class of non-compact symplectic manifolds. The goal for this talk is
to explain how the relative Ginzburg algebra associated to any ice quiver
with trivial potential is quasi-isomorphic to some Chekanov-Eliashberg dg-
algebra. The proof is constructive. I will give a gentle introduction to C
hekanov-Eliashberg dg-algebras and will discuss how the relation to relati
ve Ginzburg algebras is interesting to contact and symplectic geometers.\n
\nThis talk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Beijing Normal)
DTSTART:20240122T130000Z
DTEND:20240122T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/149
DESCRIPTION:Title: Applications of the freezing operators on cluster algebras
\nby Fan Qin (Beijing Normal) as part of Paris algebra seminar\n\n\nAb
stract\nWe utilize freezing operators to establish connections among disti
nct (quantum) upper cluster algebras. This approach enables us to compare
the quantized coordinate rings of different varieties. We prove that these
operators send localized (quantum) cluster monomials to localized (quantu
m) cluster monomials. Furthermore\, in many instances\, they also preserve
bases. Remarkably\, the bases constructed via freezing operators coincide
with those obtained via localization.\n\nThis talk will take place in hyb
rid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabin Cautis (U. of British Columbia)
DTSTART:20240311T130000Z
DTEND:20240311T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/150
DESCRIPTION:Title: Categorical cluster structure of Coulomb branches\nby
Sabin Cautis (U. of British Columbia) as part of Paris algebra seminar\n\n
\nAbstract\nCoulomb branches are certain moduli spaces arising in supersym
metric field theory. They include as special cases many spaces of independ
ent interest such as double affine Hecke algebras\, certain open Richardso
n varieties\, multiplicative Nakajima quiver varieties etc. In the four-di
mensional case\, one expects that their coordinate rings can be categorifi
ed by abelian monoidal categories carrying a cluster structure.\n\nAfter r
eviewing the mathematical construction of these Coulomb branches we will e
xplain how these categories are constructed and why the cluster structure
appears. This is joint work with Harold Williams. \n\n\n\nThis talk will t
ake place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Till Wehrhan (Bonn)
DTSTART:20240129T130000Z
DTEND:20240129T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/151
DESCRIPTION:Title: Chevalley-Monk formulas for bow varieties\nby Till Weh
rhan (Bonn) as part of Paris algebra seminar\n\n\nAbstract\nThe theory of
stable envelopes\, introduced by Maulik and Okounkov\, provides a fascinat
ing interplay between the geometry of holomorphic symplectic varieties and
integrable systems. We apply this theory to bow varieties which form a ri
ch family of holomorphic symplectic varieties including type A Nakajima qu
iver varieties. We then discuss a formula for the multiplication of torus
equivariant first Chern classes of tautological bundles of bow varieties w
ith respect to the stable envelope basis. This formula naturally generaliz
es the classical Chevalley-Monk formula and can be expressed in terms of m
oves on skein-type diagrams that label the stable envelope basis. \n\nThis
talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dirceu Bagio (Fed. U. of Santa Catarina)
DTSTART:20240108T130000Z
DTEND:20240108T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/152
DESCRIPTION:Title: Tameness of a restricted enveloping algebra\nby Dirceu
Bagio (Fed. U. of Santa Catarina) as part of Paris algebra seminar\n\n\nA
bstract\nWe will describe a 5-dimensional Lie algebra over an algebraicall
y\nclosed field of characteristic 2 and show that its restricted envelopin
g algebra is special biserial\, hence tame. We obtain an explicit descript
ion of all of its families of finite-dimensional indecomposable modules us
ing Crawley-Boevey's description via strings and bands of the indecomposab
le modules over a special biserial algebra. This is joint work with N. And
ruskiewitsch\, S. D. Flora and D. Flores.\n\nThis talk will take place in
hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Janssens (UCLouvain)
DTSTART:20240212T130000Z
DTEND:20240212T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/153
DESCRIPTION:Title: Group invariants observed through a representation-theoret
ical lens\nby Geoffrey Janssens (UCLouvain) as part of Paris algebra s
eminar\n\n\nAbstract\nThe leitfaden of this talk will be the general probl
em of determining which invariants of a finite group G are determined by w
hich piece of the representation category of G over a commutative ring R.
In the first part of the talk\, we will recall the information encoded by
the monoidal category of complex representations and its (braided) auto-eq
uivalences. By doing so we will stumble on a question concerning the conne
ction between two types of rigidity associated to G. The first is given by
the group of class-preserving outer automorphisms of G and the second is
a birational invariant of the quotient variety V/G\, where V is a faithful
representation of G. The aim of the second part of the talk will be to pr
esent some new perspective on them. Thereafter\, in the last part\, we wil
l explain how the situation changes when taking R to be a number field or
its ring of integers. In particular\, the role of the theory of arithmetic
groups will be emphasized. All along the talk\, we will mention some open
questions and some recent contributions.\n\nThis talk will take place in
hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaofa Chen (USTC Hefei)
DTSTART:20240205T130000Z
DTEND:20240205T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/154
DESCRIPTION:Title: Exact dg categories and higher Auslander correspondences\nby Xiaofa Chen (USTC Hefei) as part of Paris algebra seminar\n\n\nAbst
ract\nExact dg categories allow to enhance extriangulated categories and\n
to perform constructions like functor categories or tensor products\nfor w
hich the extriangulated structure alone does not suffice.\nIn particular\,
they yield a new approach to and a generalization\nof higher versions of
Auslander correspondences as established\nby Iyama and by Iyama-Solberg\,
for example. In this talk\, I will give \nan introduction to exact dg cate
gories and sketch their application\nto correspondences on the example of
0-Auslander categories. \nWe will see in particular that the framework of
exact dg\ncategories allows to enhance the correspondences to equivalences
\nof infinity-groupoids.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Qiu (Tsinghua)
DTSTART:20240226T130000Z
DTEND:20240226T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/156
DESCRIPTION:Title: On cluster braid groups\nby Yu Qiu (Tsinghua) as part
of Paris algebra seminar\n\n\nAbstract\nWe introduce cluster braid groups\
, with motivations coming from the study of stability conditions on triang
ulated categories. In the Coxeter-Dynkin case\, they are naturally isomorp
hic to the corresponding Artin braid groups (1407.5986 and 2310.02871). In
the surface case\, they are naturally isomorphic to braid twist groups (1
407.0806\, 1703.10053 and 1805.00030). If time permits\, I will mention an
application to quadratic differentials.\n\nThis talk will take place on Z
oom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Lancaster)
DTSTART:20240318T130000Z
DTEND:20240318T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/157
DESCRIPTION:Title: Donaldson--Thomas invariants for the Bridgeland--Smith cor
respondence\nby Nicholas Williams (Lancaster) as part of Paris algebra
seminar\n\n\nAbstract\nCelebrated work of Bridgeland and Smith shows a co
rrespondence between quadratic differentials on Riemann surfaces and stabi
lity conditions on certain 3-Calabi--Yau triangulated categories. Part of
this correspondence is that finite-length trajectories of the quadratic di
fferential correspond to stable objects of phase 1. Speaking roughly\, the
se stable objects are then counted by an associated Donaldson--Thomas inva
riant. Work of Iwaki and Kidwai predicts particular values for these Donal
dson--Thomas invariants according to the different types of finite-length
trajectories\, based on the output of topological recursion. We show that
the category recently studied by Christ\, Haiden\, and Qiu produces Donald
son--Thomas invariants matching these predictions. This is joint work with
Omar Kidwai.\n\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich (Hamburg)
DTSTART:20240513T120000Z
DTEND:20240513T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/158
DESCRIPTION:Title: A braided monoidal (infinity\,2)-category from link homolo
gy\nby Paul Wedrich (Hamburg) as part of Paris algebra seminar\n\n\nAb
stract\nAn early highlight of quantum topology was the observation that th
e Jones polynomial -- and many other knot and link invariants -- arise fro
m braided monoidal categories of quantum group representations. In hindsig
ht\, this can be understood as underlying reason for the existence of asso
ciated topological quantum field theories (TQFTs) in 3 and 4 dimensions.\n
\nNot much later\, Khovanov discovered a link homology theory that categor
ifies the Jones polynomial. It associates graded chain complexes to links\
, from which the Jones polynomials can be recovered. It was therefore spec
ulated that Khovanov homology and its variants may themselves be expressib
le in terms of certain braided monoidal 2-categories and that there should
exist associated TQFTs in 4 and 5 dimensions that may be sensitive to smo
oth structure.\n\nA major challenge in fully realizing this dream is the p
roblem of coherence: Link homology theories live in the world of homologic
al algebra\, where constructing a braided monoidal structure in principle
requires an infinite amount of higher and higher homological coherence dat
a. In this talk\, I will sketch a proposed solution to this problem\, join
t with Leon Liu\, Aaron Mazel-Gee\, David Reutter\, and Catharina Stroppel
\, and explain how we use the language of infinity-categories to build an
E2-monoidal (infinity\,2)-category which categorifies the Hecke braided mo
noidal category underlying the HOMFLYPT link polynomial.\n\n\nThis talk wi
ll take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Voloshyn (Pohang)
DTSTART:20240408T120000Z
DTEND:20240408T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/159
DESCRIPTION:Title: Generalized cluster structures on the special linear group
\nby Dmitriy Voloshyn (Pohang) as part of Paris algebra seminar\n\n\nA
bstract\nThe Gekhtman-Shapiro-Vainshtein conjecture (the GSV conjecture) s
tates that for any any given simple complex algebraic group G and any Pois
son bracket from the Belavin-Drinfeld class\, there exists a compatible ge
neralized cluster structure. In this talk\, I will review the process of c
onstructing compatible generalized cluster structures\, as well as the cur
rent state-of-the-art on the GSV conjecture. After that\, I will describe
a construction of generalized cluster structures on SL_n compatible with P
oisson brackets induced from the Poisson dual of SL_n endowed with the Poi
sson structure determined by a BD triple of\ntype A_{n-1}. I will also des
cribe the associated family of birational quasi-isomorphisms. The talk wil
l be based on the preprint arXiv:2312.04859 (joint work with M. Gekhtman).
\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hussein Mourtada (U. Paris Cité)
DTSTART:20240325T130000Z
DTEND:20240325T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/160
DESCRIPTION:Title: Singularities of algebraic varieties and integer partition
s\nby Hussein Mourtada (U. Paris Cité) as part of Paris algebra semin
ar\n\n\nAbstract\nI will talk about a link between arc spaces of singulari
ties\, which are algebro-geometric objects\, and identities of integer par
titions.\n\nThis link allows us to discover new partition identities in th
e spirit of the work of Ramanujan. The talk is accessible to a wide audien
ce. \n\nThis talk will take place in hybrid mode at the Institut Henri Poi
ncaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Cruz (Stuttgart)
DTSTART:20240422T120000Z
DTEND:20240422T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/161
DESCRIPTION:Title: Relative Auslander-Gorenstein pairs\nby Tiago Cruz (St
uttgart) as part of Paris algebra seminar\n\n\nAbstract\nA famous result i
n representation theory is Auslander’s correspondence which connects fin
ite-dimensional algebras of finite representation-type with Auslander alge
bras. Over the years\, many generalisations of Auslander algebras have bee
n proposed: for instance n-Auslander algebras (by Iyama)\, n-minimal Ausla
nder–Gorenstein algebras (by Iyama and Solberg)\, among others. All of t
he concepts above require the existence of a faithful projective-injective
module and use classical dominant dimension. Now replace the faithful pro
jective-injective module with a self-orthogonal module and classical domin
ant dimension with relative dominant dimension with respect to a module an
d you get a relative Auslander-Gorenstein pair.\n\nIn this talk\, we intro
duce relative Auslander-Gorenstein pairs. Further\, we will characterise r
elative Auslander pairs (those whose underlying algebras have finite globa
l dimension) by the existence and uniqueness of tilting-cotilting modules
having the highest values of relative dominant and codominant dimension wi
th respect to the self-orthogonal module. At the end\, we discuss explicit
examples of relative Auslander pairs. (This is joint work with Chrysostom
os Psaroudakis.)\n\nThis talk will take place in hybrid mode at the Instit
ut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Robalo (Sorbonne U.)
DTSTART:20240429T120000Z
DTEND:20240429T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/162
DESCRIPTION:Title: Choices of HKR isomorphisms and exponential maps\nby M
arco Robalo (Sorbonne U.) as part of Paris algebra seminar\n\n\nAbstract\n
In this talk\, I will explain a computation describing the space of choice
s of functorial HKR isomorphisms as choices of exponential maps from the a
dditive to the multiplicative formal group. This computation uses the cons
truction of a filtered circle obtained in collaboration with with Moulinos
and Toën\, which combines the HKR filtration and the circle action on Ho
chschild homology even when the characteristic of the base field is positi
ve. We will review the construction of the filtered circle and the relati
on with Witt vectors.\n\nThis talk will take place in hybrid mode at the I
nstitut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke
DTSTART:20240506T120000Z
DTEND:20240506T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/163
DESCRIPTION:Title: Floer potentials\, cluster algebras and quiver representat
ions\nby Markus Reineke as part of Paris algebra seminar\n\n\nAbstract
\nWe interpret Floer potentials (encoding certain Gromov-Witten invariants
) of "exotic" monotone Lagrangian tori in dle Pezzo surfaces as cluster ch
aracters of representations of certain quivers with potential.\n\nThis tal
k will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (Paris)
DTSTART:20240304T130000Z
DTEND:20240304T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/164
DESCRIPTION:Title: Complexes of stable infinity-categories and perverse schob
ers\nby Merlin Christ (Paris) as part of Paris algebra seminar\n\n\nAb
stract\nA complex of stable infinity-categories is a categorification of a
chain complex\, meaning a sequence of stable infinity-categories together
with a differential that squares to the zero functor. Examples of such ca
tegorical complexes arise for instance via a categorification of the total
ization construction\, which produces a categorical complex from a categor
ical multi-complex\, such as a commuting cube of stable infinity-categorie
s. We will then explain how categorified perverse sheaves\, also known as
perverse schobers\, on C^n (with a certain stratification) can be describe
d in terms of categorical cubes and categorical complexes of spherical fun
ctors\, and what categorical totalization means in this case geometrically
. This talk is based on joint work with T. Dyckerhoff and T. Walde. \n\nTh
is talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Pauksztello (Lancaster)
DTSTART:20240527T120000Z
DTEND:20240527T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/165
DESCRIPTION:Title: Convex geometry for (co)fans of abelian categories\nby
David Pauksztello (Lancaster) as part of Paris algebra seminar\n\n\nAbstr
act\nArising in cluster theory\, the g-vector fan is a convex geometric in
variant encoding the mutation behaviour of clusters. In representation the
ory\, the g-vector fan encodes the mutation theory of support tau-tilting
objects or\, equivalently\, two-term silting objects. In this talk\, we wi
ll describe a generalisation of the g-vector fan which in some sense “co
mpletes” the g-vector fan: the heart fan of an abelian category. This co
nvex geometric invariant encodes many important homological properties: e.
g. one can detect from the convex geometry whether an abelian category is
length\, whether it has finitely many torsion pairs\, and whether a given
Happel-Reiten-Smaloe tilt is length. This talk will be a report on joint w
ork with Nathan Broomhead\, David Ploog and Jon Woolf.\n\nThis talk will t
ake place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/165/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Pressland (Glasgow)
DTSTART:20240617T120000Z
DTEND:20240617T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/166
DESCRIPTION:Title: Categorical cluster ensembles\nby Matthew Pressland (G
lasgow) as part of Paris algebra seminar\n\n\nAbstract\nIn their geometric
approach to cluster theory\, Fock–Goncharov and Gross–Hacking–Keel
construct cluster varieties beginning with a seed datum. This consists of
a lattice which contains various distinguished sublattices\, has a preferr
ed basis\, and carries a partially defined bilinear form. A process of mut
ation allows one to construct more such seed data\, and birational gluing
maps between the tori dual to the lattices\, leading to two cluster variet
ies known as A and X. By enhancing the initial data to a cluster ensemble\
, in which the bilinear form is extended to the whole lattice\, one also o
btains a map from A to X.\nIn this talk\, based on joint work with Jan Gra
bowski\, I will explain how one can obtain a seed datum\, and in many case
s a full cluster ensemble\, from each cluster-tilting subcategory of an ap
propriate 2-Calabi–Yau category. Furthermore\, I will explain how the se
ed data of different cluster-tilting subcategories are related\, generalis
ing the relationship between a seed datum and its mutations.\n\nThis talk
will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/166/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Théo Pinet (Paris Cité)
DTSTART:20240624T120000Z
DTEND:20240624T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/167
DESCRIPTION:Title: Inflations for representations of shifted quantum affine a
lgebras\nby Théo Pinet (Paris Cité) as part of Paris algebra seminar
\n\n\nAbstract\nThe only finite-dimensional simple Lie algebra admitting a
2-dimensional irreducible representation is sl(2). The restriction functo
rs arising from Dynkin diagram inclusions in (classical) Lie theory are th
us in general not essentially surjective on finite-dimensional simple modu
les. The goal of this talk is to specify whether or not this "surjectivity
defect" remains in the case of Finkelberg-Tsymbaliuk's shifted quantum af
fine algebras (SQAAs).\n\nSQAAs are infinite-dimensional associative algeb
ras parametrized by a simple finite-dimensional Lie algebra and a coweight
in the corresponding coweight lattice. They appear naturally in the study
of Coulomb branches\, of quantum integrable systems and of cluster algebr
as. In this presentation\, we will give a brief introduction to the vast r
epresentation theory of SQAAs and will state some results about the existe
nce of remarkable modules\, that we call "inflations"\, which are construc
ted as special preimages for different canonical restriction functors (ass
ociated here also to Dynkin diagram inclusions). We will finally\, if time
permits\, discuss potential applications of our results to the study of c
luster structures on Grothendieck rings. \n\nThis talk will take place in
hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/167/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Rognerud (Paris Cité)
DTSTART:20240603T120000Z
DTEND:20240603T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/168
DESCRIPTION:Title: The fractionally Calabi-Yau combinatorics of the Tamari la
ttice\nby Baptiste Rognerud (Paris Cité) as part of Paris algebra sem
inar\n\n\nAbstract\nA poset is said to be fractionally Calabi-Yau if the b
ounded derived category of its incidence algebra over a field is fractiona
lly Calabi-Yau. In other words\, a power of the Serre functor is isomorphi
c to a shift. When going from a poset to its derived category\, one looses
almost all the combinatorics of the poset. However in some favorable cas
es\, part of the combinatorics is encoded in the Serre functor.\n\nIn this
talk\, I will present the combinatorics of the Serre functor of the Tamar
i lattice. This leads to a more algebraic proof of its fractional Calabi-Y
au property. It is also the first step toward a generalization to a larger
family of posets. \n\nThis talk will take place in hybrid mode at the Ins
titut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/168/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyang Liu (USTC\, Hefei)
DTSTART:20240610T120000Z
DTEND:20240610T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/169
DESCRIPTION:Title: Singularity categories via McKay quivers with potential\nby Junyang Liu (USTC\, Hefei) as part of Paris algebra seminar\n\n\nAbs
tract\nIn 2018\, Kalck and Yang showed that the singularity categories ass
ociated with 3-dimensional Gorenstein quotient singularities are triangle
equivalent (up to direct summands) to small cluster categories associated
with McKay quivers with potential. I introduce graded McKay quivers with p
otential and generalize Kalck-Yang's theorem to arbitrary dimensions. The
singularity categories I consider occur as stable categories of categories
of maximal Cohen-Macaulay modules. I refine my description of the singula
rity categories by showing that these categories of maximal Cohen-Macaulay
modules are equivalent to Higgs categories in the sense of Wu. Moreover\,
I describe the singularity categories in the non-Gorenstein case. \n\nThi
s talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/169/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Vienna)
DTSTART:20240701T120000Z
DTEND:20240701T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/170
DESCRIPTION:Title: Deep points in cluster varieties\nby Mikhail Gorsky (V
ienna) as part of Paris algebra seminar\n\n\nAbstract\nMany important alge
braic varieties\, such as open positroid strata in Grassmannians\, Richard
son varieties\, or augmentation varieties of certain Legendrian links\, ar
e known to carry cluster structures. In particular\, each such variety is
covered\, up to codimension 2\, by a collection of overlapping open tori.
In this talk\, I will discuss the ``deep locus'' of a cluster variety\, th
at is\, the complement to the union of all cluster toric charts. I will ex
plain a conjectural relation between the deep locus and the natural torus
action compatible with the cluster structure. For many positroid strata in
Gr(2\,n) and Gr(3\,n)\, and for cluster varieties of types ADE\, this rel
ation is made precise: we show that the deep locus consists precisely of t
he points with non-trivial stabilizer for this action. If time permits\, I
will explain how these results can be applied in the context of homologic
al mirror symmetry and say a few words on the geometry of deep loci. The t
alk is based on joint work with Marco Castronovo\, José Simental\, and Da
vid Speyer (arXiv:2402.16970).\n\n\nThis talk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/170/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isambard Goodbody (Glasgow)
DTSTART:20240930T120000Z
DTEND:20240930T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/171
DESCRIPTION:Title: Reflexivity and Hochschild Cohomology\nby Isambard Goo
dbody (Glasgow) as part of Paris algebra seminar\n\n\nAbstract\nReflexivit
y is about a duality between two kinds of derived categories appearing in
algebra and geometry. The motivating examples are the bounded derived cate
gory of a finite dimensional algebra vs its perfect complexes and the boun
ded derived category of a projective scheme vs its perfect complexes. In t
he smooth case\, these categories coincide but even in the non-smooth case
these two categories share some common information. In this talk I'll pro
vide a conceptual justification for this phenomenon. The main result is a
monoidal characterisation of reflexive DG-categories as introduced by Kuzn
etsov and Shinder. As applications of this new perspective one can prove i
nvariance results for Hochschild cohomology\, derived Picard groups and a
bijection between semi-orthogonal decompositions. \n\nThis talk will take
place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/171/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumanskiy (MIT)
DTSTART:20241014T120000Z
DTEND:20241014T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/172
DESCRIPTION:Title: Quantum loop group and coherent Satake category\nby Il
ya Dumanskiy (MIT) as part of Paris algebra seminar\n\n\nAbstract\nThe cat
egory of equivariant perverse sheaves on the affine Grassmannian has a coh
erent counterpart\, called the coherent Satake category. Cautis and Willia
ms proved for GL and conjectured for other types that this category has a
cluster structure. I will talk about work in progress towards the proof of
this conjecture for simply-laced types. Our approach is based on relating
the coherent Satake category with the category of finite-dimensional modu
les over the affine quantum group. The bridge between these two categories
is provided by the notion of Feigin-Loktev fusion product for modules ove
r the current algebra. In particular\, it helps to construct cluster short
exact sequences of perverse coherent sheaves using the existence of exact
sequences of modules over the quantum affine group.\n\nThis talk will tak
e place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/172/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Edmund Heng (IHES)
DTSTART:20241007T120000Z
DTEND:20241007T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/173
DESCRIPTION:Title: Fusion categories as quantum symmetries: on Bridgeland sta
bility conditions\nby Edmund Heng (IHES) as part of Paris algebra semi
nar\n\n\nAbstract\nClassically\, finite symmetries are captured by the act
ion of a finite group. Moving to the quantum world\, one has to allow for
possibly non-invertible symmetries\, which are instead captured by the act
ion of a more general algebraic structure\, known as a fusion category. Su
ch symmetries are actually ubiquitous in mathematics\; for example\, given
a category with an action of a finite group G (e.g. A-mod\, Coh(X))\, its
G-equivariant category (A#G-mod\, Coh(X//G) resp.) has instead the action
of the category of G-representations rep(G)\, which has the structure of
a fusion category. There are also other more “exotic” fusion categorie
s\, which nonetheless capture “hidden” symmetries on familiar (non-“
exotic”) categories. \nThe aim of this talk is to discuss the applicatio
n of fusion categorical symmetries to the study of Bridgeland stability co
nditions. I will discuss how the fusion-equivariant stability conditions
— a generalisation of G-invariant stability conditions (i.e. G-fixed poi
nts) — form a closed submanifold of the Bridgeland stability manifold. M
oreover\, we will see the following duality result inspired by a categoric
al Morita duality: let D be a triangulated category with a G-action\, so t
hat its G-equivariant category D^G has a rep(G)-action. The manifold of G-
invariant stability conditions (associated to D) is homeomorphic to the ma
nifold of rep(G)-equivariant stability conditions (associated to D^G). - T
his is part of joint work with Hannah Dell and Anthony Licata.\n\nThis tal
k will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/173/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Myungho Kim (Kyung Hee University)
DTSTART:20241104T130000Z
DTEND:20241104T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/174
DESCRIPTION:Title: Exchange matrices of $\\bold i$-boxes\nby Myungho Kim
(Kyung Hee University) as part of Paris algebra seminar\n\n\nAbstract\nAdm
issible chains of $\\bold i$-boxes are important combinatorial tools in th
e monoidal categorification of cluster algebras via representations of qua
ntum affine algebras\, since they provide some seeds of the cluster algebr
a. For a given sequence $\\bold i$ with indices ranging over the interval
[a\,b]\, we define a subinterval [x\,y] of [a\,b] as an $\\bold i$-box if
the color of $\\bold i$ at x matches the color at y. Two $\\bold i$-boxes
are said to commute if the extension of one of the $\\bold i$-boxes by one
step to the left and one step to the right properly contains the other $\
\bold i$-box. A maximal commuting family of $\\bold i$-boxes yields a seed
in the category of finite-dimensional modules over the quantum affine alg
ebra\, and any such family can be constructed from an admissible chain. I
n this talk\, I will introduce the notion of $\\bold i$-boxes and present
recent results on the exchange matrices of a maximal commuting family of $
\\bold i$-boxes. This is a joint work with Masaki Kashiwara.\n\nThis talk
will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/174/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Severin Barmeier (Cologne)
DTSTART:20250113T130000Z
DTEND:20250113T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/175
DESCRIPTION:Title: Deformations of gentle algebras and gluing of Fukaya categ
ories of surfaces\nby Severin Barmeier (Cologne) as part of Paris alge
bra seminar\n\n\nAbstract\nGentle algebras can be obtained by gluing quive
rs of type A with square-zero relations along vertices. This observation h
as a beautiful geometric incarnation: partially wrapped Fukaya categories
of smooth surfaces can be obtained by gluing derived categories of type A
quivers. In this talk\, I will explain how this can be generalized to surf
aces with orbifold singularities and how this relates to A∞ deformations
of graded gentle algebras. This interplay between the geometry of surface
s and algebraic deformation theory has two fascinating consequences. On th
e one hand\, it leads to the proof of (a singular surface version of) a co
njecture of Kontsevich on the local-to-global properties of Fukaya categor
ies of noncompact manifolds. On the other hand\, it sheds light on the rel
ationship between deformations of Fukaya categories and partial compactifi
cations (as advocated in Seidel's ICM 2002 address) in the presence of sto
p data. This talk is based on https://arxiv.org/abs/2407.16358 joint with
Sibylle Schroll and Zhengfang Wang.\n\nThis talk will take place in hybrid
mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/175/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Neville (Michigan)
DTSTART:20241021T120000Z
DTEND:20241021T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/176
DESCRIPTION:Title: Cyclically ordered quivers\nby Scott Neville (Michigan
) as part of Paris algebra seminar\n\n\nAbstract\nQuivers and their mutati
ons play a fundamental role in the theory of cluster algebras. We focus on
the problem of deciding whether two given quivers are mutation equivalent
to each other. Our approach is based on introducing an additional structu
re of a cyclic ordering on the set of vertices of a quiver. This leads to
new powerful invariants of quiver mutation. These invariants can be used t
o show that various quivers are not mutation acyclic\, i.e.\, they are not
mutation equivalent to an acyclic quiver. This talk is partially based on
joint work with Sergey Fomin [arXiv:2406.03604]. \n\nThis talk will take
place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/176/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Ovenhouse (Yale)
DTSTART:20241209T130000Z
DTEND:20241209T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/177
DESCRIPTION:Title: Higher q-Rational Numbers\nby Nick Ovenhouse (Yale) as
part of Paris algebra seminar\n\n\nAbstract\nThe classical q-integers wer
e generalized to rational numbers by Morier-Genoud and Ovsienko by q-defor
ming the continued fraction expressions. These "q-rationals" have several
nice properties\, and are related to many interesting things (such as clus
ter algebras\, hyperbolic geometry\, and Jones polynomials). I will discus
s how one natural generalization of the q-rationals is given by ratios of
generating functions for "P-partitions" on certain types of posets\, and t
hat some of the properties of q-rationals hold more generally in this case
. We are able to use this to give some quantizations of cubic (and other a
lgebraic) numbers\, generalizing a result of Morier-Genoud and Leclere on
quadratic irrationals.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/177/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Beijing Normal U.)
DTSTART:20241202T130000Z
DTEND:20241202T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/178
DESCRIPTION:Title: Based cluster algebras of infinite rank and their applicat
ions to double Bott-Samelson cells\nby Fan Qin (Beijing Normal U.) as
part of Paris algebra seminar\n\n\nAbstract\nWe introduce based cluster al
gebras of infinite rank. By extending cluster algebras arising from double
Bott-Samelson cells to the infinite rank setting\, we recover certain inf
inite rank cluster algebras connected to monoidal categories of representa
tions of (shifted) quantum affine algebras. Several conjectures follow as
a result.\n\nThis talk will take place in hybrid mode at the Institut Henr
i Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/178/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dylan Allegretti (Tsinghua)
DTSTART:20241125T130000Z
DTEND:20241125T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/179
DESCRIPTION:Title: Skein algebras and quantized Coulomb branches\nby Dyla
n Allegretti (Tsinghua) as part of Paris algebra seminar\n\n\nAbstract\nCh
aracter varieties of surfaces are fundamental objects in modern mathematic
s\, appearing in low-dimensional topology\, representation theory\, and ma
thematical physics\, among other areas. Given a reductive algebraic group
G\, the G-character variety of a surface is a moduli space parametrizing G
-local systems on the surface.\n\nCharacter varieties of surfaces are expe
cted to arise in physics as Coulomb branches of certain quantum field theo
ries. A Coulomb branch is a kind of moduli space that was recently given a
precise mathematical definition in the work of Braverman\, Finkelberg\, a
nd Nakajima.\n\nIn this talk\, I will focus on the SL(2\,C)-character vari
ety of a surface. It has a quantization given by a noncommutative algebra
called the Kauffman bracket skein algebra. I will describe a precise relat
ionship between skein algebras and quantized Coulomb branches\, confirming
the physics prediction in some cases. This is joint work with Peng Shan.\
n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/179/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Hanson (North Caroline State U.)
DTSTART:20241118T130000Z
DTEND:20241118T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/180
DESCRIPTION:Title: Mutation of tau-exceptional sequences\nby Eric Hanson
(North Caroline State U.) as part of Paris algebra seminar\n\n\nAbstract\n
By the work of Crawley-Boevey and Ringel\, the set of complete exceptional
sequences over a finite-dimensional hereditary algebra admits a transitiv
e braid group action. This can also be viewed as a "mutation theory" for e
xceptional sequences. In this talk\, we discuss recent joint work with Asl
ak Buan and Bethany Marsh which extends this into a mutation theory for (c
omplete) tau-exceptional sequences over an arbitrary finite-dimensional al
gebra. In addition to giving the formulas for this mutation\, we discuss t
he existence of non-mutable sequences\, the problem of transitivity\, and
the (lack of) braid relations. \n\nThis talk will be on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/180/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern)
DTSTART:20250512T120000Z
DTEND:20250512T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/181
DESCRIPTION:Title: Bethe subalgebras in type A\, tame representations\, and a
cactus group action\nby Iva Halacheva (Northeastern) as part of Paris
algebra seminar\n\n\nAbstract\nThe Bethe subalgebras of the Yangian Y(gl(
n)) are a family of maximal commutative subalgebras that generalize the Ge
lfand-Tsetlin algebras. Moreover\, they are indexed by points of the Delig
ne-Mumford compactification of the moduli space M(0\,n+2). We consider poi
nts C in the real locus of this parameter space. For a fixed tame represen
tation of Y(gl(n))\, the Bethe subalgebra B(C) corresponding to any real p
oint C acts with simple spectrum\, resulting in an unramified covering of
the parameter space whose fiber over C is the set of eigenlines for the ac
tion of B(C). I will discuss how to identify each fiber with a collection
of Gelfand-Tsetlin keystone patterns\, carrying a gl(n)-crystal structure\
, as well as the monodromy action for the covering realized by the mirabol
ic cactus group. Large parts of this construction are expected to generali
ze to arbitrary semisimple Lie algebras. This is joint work with Anfisa Gu
renkova and Leonid Rybnikov.\n\nThis talk will take place in hybrid mode a
t the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/181/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christof Geiss (UNAM)
DTSTART:20250120T130000Z
DTEND:20250120T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/182
DESCRIPTION:Title: Representations of shifted quantum affine algebras and clu
ster algebras\nby Christof Geiss (UNAM) as part of Paris algebra semin
ar\n\n\nAbstract\nThis is a report on an ongoing joint project with David
Hernandez (Université Paris Cité) and Bernard Leclerc (Université de
Caen). We define for each Cartan matrix of finite type a skew symmetric c
luster algebra A of infinite rank in terms of an almost periodic quiver.
By choosing an initial seed\, where the cluster variables are certain form
al power series\, which fulfill the q-difference equations of a QQ-system
\, we can identify an adequate completion of A with the Grothendieck ring
of the category\nO_Z of the corresponding (untwisted) shifted quantum affi
ne algebras. We conjecture that under this identification the cluster mon
omials become the q-characters of the real simple representations in this
category. \n\nThis talk will take place in hybrid mode at the Institut Hen
ri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/182/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Min Huang (Sun Yat Sen U.)
DTSTART:20241216T130000Z
DTEND:20241216T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/183
DESCRIPTION:Title: Non-commutative surfaces\, symmetry and positivity\nby
Min Huang (Sun Yat Sen U.) as part of Paris algebra seminar\n\n\nAbstract
\nThe aim of my talk (based on joint work in progress with Arkady Berenste
in and Vladimir Retakh) is to introduce and study certain noncommutative c
luster algebras A from marked orbifolds. They are non-commutative versions
of the generalized cluster algebras defined by Chekhov and Shapiro. These
algebras admit noncommutative clusters\, i.e.\, embeddings of a given gro
up G which is either free or one-relator (we call it a triangle group) int
o the multiplicative monoid A×. The clusters are parametrized by triangul
ations of the orbifold and exhibit a noncommutative Laurent Phenomenon\, w
hich asserts that generators of the algebra can be written as sums of the
images of elements of G for any noncommutative cluster. In particular\, if
the surface is unpunctured\, then our algebra A can be specialized to the
ordinary quantum cluster algebra\, and the noncommutative Laurent Phenome
non becomes the (positive) quantum one. \n\nThis talk will take place in h
ybrid mode in Conference Hall B of the New York University Abu Dhabi.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/183/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregg Musiker (U. of Minnesota)
DTSTART:20250210T130000Z
DTEND:20250210T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/184
DESCRIPTION:Title: Super Fibonacci and Super Markov Numbers\nby Gregg Mus
iker (U. of Minnesota) as part of Paris algebra seminar\n\n\nAbstract\nIn
this talk\, I will describe joint work with N. Ovenhouse and S. Zhang prov
iding combinatorial formulas for super lambda lengths in the context of de
corated super Teichmueller space of a marked disc or an annulus. The lat
ter leads to a notion of Super Fibonacci Numbers\, as will be discussed.
The talk will then describe recent research applying these methods instead
on the once-punctured torus and how this leads to Super Markov Numbers wh
ere associated combinatorial formulas are no longer positive generating fu
nctions but instead involve signed enumeration.\n\nThis talk will take pla
ce on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/184/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstanze Rietsch (King's College London)
DTSTART:20250203T130000Z
DTEND:20250203T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/185
DESCRIPTION:Title: A Tropical Edrei theorem\nby Konstanze Rietsch (King's
College London) as part of Paris algebra seminar\n\n\nAbstract\nA classic
al theorem proved by Edrei in the 1950's (building on work with Aissen\, S
choenberg and Whitney) gives a parametrisation for infinite upper-triangul
ar totally positive Toeplitz matrices using pairs of sequences of positive
real parameters with finite sum. These infinite Toeplitz matrices (and th
eir parameters) are central for understanding characters of the infinite s
ymmetric group\, as was discovered by Thoma\, who reproved Edrei's theorem
in the 1960's. There is also a totally different (totally positive) theor
em about Toeplitz matrices that relates to quantum cohomology of flag vari
eties and mirror symmetry [R\,06]. This talk will be about new tropical ve
rsions of these parametrisation results and the relationship between them.
This work builds on results of Judd and Ludenbach and relates also to Lus
ztig's parametrisation of his canonical basis.\n\nThis talk will take plac
e in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/185/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niels Kowalzig (Rome 2)
DTSTART:20250303T130000Z
DTEND:20250303T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/186
DESCRIPTION:Title: Higher structures on homology groups\nby Niels Kowalzi
g (Rome 2) as part of Paris algebra seminar\n\n\nAbstract\nWe dualise the
classical fact that an operad with multiplication leads to cohomology\ngro
ups which form a Gerstenhaber algebra to the context of cooperads: as a re
sult\, a cooperad\nwith comultiplication induces a homology theory that is
endowed with the structure of a Gerstenhaber coalgebra\, that is\, it com
es with a (graded cocommutative) coproduct which is compatible with a cobr
acket in a dual Leibniz sense. As an application\, one obtains Gerstenhabe
r coalgebra structures on Tor groups over bialgebras or Hopf algebras\, as
well as on Hochschild homology for Frobenius algebras. Joint work with Fr
ancesca Pratali.\n\n\nThis talk will take place in hybrid mode at the Inst
itut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/186/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongjian Wu (Tsinghua U.)
DTSTART:20250217T130000Z
DTEND:20250217T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/187
DESCRIPTION:Title: Relative Bridgeland Stability Conditions\nby Dongjian
Wu (Tsinghua U.) as part of Paris algebra seminar\n\n\nAbstract\nThe notio
n of a stability condition on a triangulated category was introduced by Br
idgeland\, based on the study of slope stability of vector bundles over cu
rves and the Π-stability of D-branes in string theory. The theory of stab
ility conditions has since played an important role in many branches of ma
thematics\, such as mirror symmetry\, Donaldson-Thomas invariants and clus
ter theory.\n\nIn this talk\, I will provide an overview of the theory of
Bridgeland stability conditions. Following this\, I will introduce the not
ion of relative stability conditions on triangulated categories and illust
rate the deformation property of the spaces of relative stability conditio
ns. The motivation for this concept arises from the link between Bridgelan
d stability and deformed Hermitian-Yang-Mills metrics. The talk is based o
n joint work with Bowen Liu. \n\nThis talk will take place in hybrid mode
at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/187/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Lehmann (Antwerp)
DTSTART:20250224T130000Z
DTEND:20250224T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/188
DESCRIPTION:Title: Curved algebras and deformations of triangulated categorie
s\nby Alessandro Lehmann (Antwerp) as part of Paris algebra seminar\n\
n\nAbstract\nIs well known that the deformation theory of dg-algebras —
and by extension\, triangulated categories — has some pathological aspec
ts\, due to the existence of curved deformations\; this is the so-called c
urvature problem. I will discuss a construction that associates a triangul
ated category\, called the n-derived category\, to a curved deformation of
a dg-algebra. I’ll explain how this category can be interpreted as a de
formation of the derived category of the base algebra and how this leads t
o considering a novel notion of deformation for (enhanced) triangulated ca
tegories. This talk is based on joint work with Wendy Lowen.\n\nThis talk
will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/188/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Launois (Caen)
DTSTART:20250127T130000Z
DTEND:20250127T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/189
DESCRIPTION:Title: Derivations of quantum algebras\nby Stéphane Launois
(Caen) as part of Paris algebra seminar\n\n\nAbstract\nIn this talk\, I wi
ll discuss derivations of a class of noncommutative polynomial algebras\,
the so-called quantum nilpotent algebras\, and their primitive quotients.
This is joint work in progress with Samuel Lopes (Porto) and Isaac Oppong
(Greenwich). \n\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/189/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Gorsky (Hamburg)
DTSTART:20250317T130000Z
DTEND:20250317T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/190
DESCRIPTION:Title: Hall algebras and counting in Calabi-Yau categories\nb
y Mikhail Gorsky (Hamburg) as part of Paris algebra seminar\n\n\nAbstract\
nI will discuss a replacement of the notion of homotopy cardinality in the
setting of even-dimensional Calabi-Yau categories and their relative gene
ralizations. This includes cases where the usual definition does not apply
\, such as Z/2-graded dg categories. As an application of the definition i
n the relative case\, we define a version of Hall algebras for odd-dimensi
onal Calabi-Yau categories. I will explain its relation to some previously
known non-intrinsic constructions of Hall algebras. Whenever a 1CY catego
ry C is equivalent to the Z/2-graded derived category of a hereditary abel
ian category A\, our intrinsically defined Hall algebra of C realises the
Drinfeld double of the twisted Hall algebra of A. If time permits\, I will
also briefly discuss another application in the context of invariants of
smooth and graded Legendrian links\, where we prove a conjecture of Ng-Rut
herford-Shende-Sivek relating ruling polynomials with augmentation categor
ies.The talk is based on joint work with Fabian Haiden\, arxiv:2409.10154.
\n\n\n\nThis talk will take place in hybrid mode at the Institut Henri Poi
ncaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/190/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Brussels)
DTSTART:20250310T130000Z
DTEND:20250310T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/191
DESCRIPTION:Title: Nichols algebras over groups\nby Leandro Vendramin (Br
ussels) as part of Paris algebra seminar\n\n\nAbstract\nNichols algebras a
ppear in various areas of mathematics\, ranging from Hopf algebras and qua
ntum groups to Schubert calculus and conformal field theory. In this talk\
, I will review the main challenges in classifying Nichols algebras over g
roups and discuss some recent classification theorems. In particular\, I w
ill highlight a recent classification result (https://arxiv.org/abs/2411.0
2304)\, achieved in collaboration with Andruskiewitsch and Heckenberger\,
concerning finite-dimensional Nichols algebras over solvable groups.\n\nTh
is talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/191/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Xu (Penn State)
DTSTART:20250428T120000Z
DTEND:20250428T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/192
DESCRIPTION:Title: Noncommutative Calculus for DG Manifolds\nby Ping Xu (
Penn State) as part of Paris algebra seminar\n\n\nAbstract\nIt is a classi
cal theorem that for any DG algebra $A$\, the pair of its Hochschild (co)h
omologies $(H^\\bullet (A\, A)\, H_\\bullet (A\, A))$\nadmits rich algeb
raic structures\, resembling the usual Cartan calculus\, called noncommuta
tive calculus. DG manifolds are a useful geometric notion for describing s
paces with singularities. In this talk\, I will discuss the noncommutative
calculus for the DGA associated with a DG manifold and present a Duflo–
Kontsevich type theorem for DG manifolds. This is joint work with Hsuan-Yi
Liao and Mathieu Stienon.\n\nThis talk will take place in hybrid mode at
the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/192/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hironori Oya
DTSTART:20250407T120000Z
DTEND:20250407T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/193
DESCRIPTION:Title: Algebraic study of quantum configuration spaces of decorat
ed flags\nby Hironori Oya as part of Paris algebra seminar\n\n\nAbstra
ct\nLet G be a simply-connected simple algebraic group over the complex nu
mbers\, and U its maximal unipotent subgroup. An element of G/U is called
a decorated flag. In this talk\, we study algebraic structure of a quantum
analogue of the ring of regular functions on the configuration space of n
decorated flags. I explain its relation with the quantum coordinate rings
of G and its Borel subgroup B. It can be considered as a quantum analogue
of Wilson lines on the moduli space of decorated twisted G-local systems
on the polygons. We also discuss its quantum cluster algebra structure. -
This talk is based on joint work with Tsukasa Ishibashi.\n\nThis talk will
take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/193/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gleb Koshevoy (CEMI\, Moscow)
DTSTART:20250331T120000Z
DTEND:20250331T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/194
DESCRIPTION:Title: Products of Kirillov-Reshetikhin modules and maximal gree
n sequences\nby Gleb Koshevoy (CEMI\, Moscow) as part of Paris algebra
seminar\n\n\nAbstract\nWe show that a $q$-character of a Kirillov-Resheti
khin module (KR modules) for untwisted quantum affine algebras of simply l
aced types $A_n^{(1)}$\, $D_n^{(1)}$\, $E_6^{(1)}$\, $E_7^{(1)}$\, $E_8^{(
1)}$ might be obtained from a specific cluster variable of a seed obtaine
d by applying a maximal green sequence to the initial (infinite) quiver of
the Hernandez-Leclerc cluster algebra. For a collection of KR-modules wi
th nested supports\, we show an explicit construction of a cluster seed\,
which has cluster variables corresponding to the $q$-characters of KR-modu
les of such a collection.\nWe prove that the product of KR-modules of such
a collection is a simple module. We also have an explicit construction of
cluster seeds with cluster variables corresponding to $q$-characters of K
R-modules of some non-nested collections. We make a conjecture that tensor
products of KR-modules for such non-nested collections are simple. \nIf t
ime permits\, I explain that the cluster Donaldson-Thomas transformations
for double Bruhat cells for $ADE$ types can be computed using $q$-charact
ers of KR-modules\, and new algorithm to compute $q$-characters KR-modules
. The talk is based on joint work with Y.Kanakubo and T.Nakashima.\n\nThis
talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/194/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Rota (Paris Saclay)
DTSTART:20250505T120000Z
DTEND:20250505T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/195
DESCRIPTION:Title: Towards Curve contractibility via non-commutative deformat
ions\nby Franco Rota (Paris Saclay) as part of Paris algebra seminar\n
\n\nAbstract\nDeciding whether a subvariety of an algebraic variety is con
tractible is a deep problem of algebraic geometry. Even when the subvariet
y is a single smooth rational curve C\, the question is extremely subtle.\
n\nIn this talk\, I will assume moreover that the ambient variety is a Cal
abi-Yau threefold.\nWhen C is contractible\, its Donovan-Wemyss contractio
n algebra (which pro-represents the deformation theory of C) governs much
of the geometry. Our expectation is that deformation theory not only contr
ols contractibility but detects it\, even when C is not known to contract.
To investigate the deformation theory of C\, we use technology developed
by Brown and Wemyss to describe a local model for C. \n\nI will introduce
the key ideas and tools appearing in this problem\, the leading conjecture
s\, and I will describe the (partial) results I obtained so far in collabo
ration with G. Brown and M. Wemyss.\n\nThis talk will take place in hybrid
mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/195/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk because of the
DTSTART:20250324T130000Z
DTEND:20250324T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/196
DESCRIPTION:Title: Viazovska-Fest\nby No talk because of the as part of P
aris algebra seminar\n\n\nAbstract\nThere will be no talk because of the V
iazovska-Fest\, cf.\n\nhttps://viazovska-fest.sciencesconf.org/?lang=en\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/196/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Qunell (UCLA)
DTSTART:20250602T120000Z
DTEND:20250602T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/197
DESCRIPTION:Title: 2-categorical affine symmetries and q-boson algebras\n
by Sam Qunell (UCLA) as part of Paris algebra seminar\n\n\nAbstract\nRepre
sentations of KLR (quiver Hecke) algebras categorify the positive part of
the quantum group associated to any symmetrizable Cartan matrix. This cate
gorical perspective makes certain symmetries more natural to study. For ex
ample\, the induction and restriction functors between categories of KLR a
lgebra modules play an important role in the theory. A closer investigatio
n of these functors reveals surprising new symmetries. In this talk\, I wi
ll explain how the induction and restriction functors for KLR algebras can
be used to obtain a 2-representation of the corresponding affine positive
part in type A. I will also describe a new categorification of a closely
related algebra\, the q-boson algebra\, in all symmetrizable Kac-Moody typ
es.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Wemyss (Glasgow)
DTSTART:20251013T120000Z
DTEND:20251013T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/198
DESCRIPTION:Title: The classification of 3-fold flops\nby Michael Wemyss
(Glasgow) as part of Paris algebra seminar\n\n\nAbstract\nI will give an o
verview of the analytic classification of smooth\, simple\, 3-fold flops.
There are three main aspects: (1) reducing the problem to the classificati
on of certain noncommutative finite dimensional algebras\, (2) a complete
understanding of those algebras\, then lastly (3) building the associated
geometry for each algebra in that class. The talk will focus on (1) and (
2)\, as they are the most algebraic. In the process of proving the above
results\, we also obtain various bonus (and very surprising) geometric cor
ollaries\, including to curve-counting invariants\, and also to 3-fold cre
pant divisor-to-curve contractions. Part (1) is joint with Joe Karmazyn a
nd Emma Lepri\, the rest is joint with Gavin Brown.\n\nThis talk will take
place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (Amiens)
DTSTART:20250526T120000Z
DTEND:20250526T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/199
DESCRIPTION:Title: Cohomological Mackey formula for representations of reduct
ive groups\nby Lucien Hennecart (Amiens) as part of Paris algebra semi
nar\n\n\nAbstract\nI will describe the construction of induction and restr
iction morphisms on the critical cohomology associated with a function on
a representation of a reductive group. The induction morphism plays a key
role in obtaining a cohomological integrality decomposition\, which is a d
ecomposition into finite-dimensional pieces with enumerative significance.
After discussing this decomposition and its geometric meaning\, I will pr
esent a cohomological version of the Mackey formula that relates the induc
tion and restriction operations.\n\nThis talk will take place in hybrid fo
rmat at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/199/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Vogel (Paris Cité)
DTSTART:20250519T120000Z
DTEND:20250519T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/200
DESCRIPTION:Title: Regular exact categories and algebraic K-theory\nby Pi
erre Vogel (Paris Cité) as part of Paris algebra seminar\n\n\nAbstract\nW
e introduce a new notion of regularity for rings and exact \ncategories an
d we show important results in algebraic homology and\nalgebraic K-theory.
In particular we prove that any acyclic complex \nof projective modules o
ver a regular ring is contractible. We have\nalso two conjectures about Wh
itehead groups.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Reineke (Bochum)
DTSTART:20260119T130000Z
DTEND:20260119T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/201
DESCRIPTION:Title: Varieties of complexes and canonical bases of quantum grou
ps\nby Markus Reineke (Bochum) as part of Paris algebra seminar\n\n\nA
bstract\nWe compute the local intersection cohomology of the irreducible c
omponents of varieties of complexes by using Lusztig’s geometric approac
h to quantum groups and explicit constructions of elements of Lusztig’s
canonical bases.\n\nThis talk will take place in hybrid mode at the Instit
ut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Coulembier (Sydney)
DTSTART:20250929T120000Z
DTEND:20250929T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/203
DESCRIPTION:Title: Oligomorphic groups and new tensor categories\nby Kevi
n Coulembier (Sydney) as part of Paris algebra seminar\n\n\nAbstract\nIn t
he 90’s Deligne ‘classified’ symmetric tensor categories of moderate
growth in characteristic zero and initiated the study of categories of fa
ster growth. Since then a lot of progress has been made in positive charac
teristic and for categories of fast growth. In this talk we will review th
is and then introduce and combine two successful contributing theories: ol
igomorphic groups and abelian envelopes. Joint with Andrew Snowden.\n\nThi
s talk will take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Calvin Pfeifer (Cologne)
DTSTART:20251020T120000Z
DTEND:20251020T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/204
DESCRIPTION:Title: Serre cyclotomic algebras\nby Calvin Pfeifer (Cologne)
as part of Paris algebra seminar\n\n\nAbstract\nIn 2013\, de la Peña ini
tiated the systematic study of algebras of cyclotomic type\, that is finit
e-dimensional algebras of finite global dimension such that some power of
their Coxeter matrix is unipotent. For example\, fractionally Calabi–Yau
algebras have periodic Coxeter matrices. In this talk\, we propose a clas
s of algebras\, which we call Serre cyclotomic\, as a generalization of fr
actionally Calabi–Yau algebras\, and as a categorification of algebras o
f cyclotomic type. We study dynamical properties of their Nakayama functor
s and the complexity of their trivial extension algebras. Based on recent
work of Chang–Schroll\, we characterize Serre cyclotomic gentle algebras
. Finally\, we provide further examples coming from generalized species. P
arts of this ongoing work are joint with Sibylle Schroll.\n\n\nThis talk w
ill take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Merlin Christ (IMJ-PRG)
DTSTART:20250922T120000Z
DTEND:20250922T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/205
DESCRIPTION:Title: Cluster tilting in topological Fukaya categories for highe
r Teichmüller theory\nby Merlin Christ (IMJ-PRG) as part of Paris alg
ebra seminar\n\n\nAbstract\nThe (decorated) higher Teichmüller space of a
marked surface is a space of local systems valued in a split simple Lie g
roup of a Dynkin type I. There is a corresponding cluster algebra\, which
gives rise to coordinates on the higher Teichmüller space. We will discus
s additive categorifications of these cluster algebras. We first associate
a (relative) 3-Calabi--Yau dg category with the surface and Dynkin type I
. This dg category arises by gluing\, along a perverse (co)sheaf of catego
ries. The fundamental building block is associated with the 3-gon surface
(=the basic triangle). The 3-CY category of the basic triangle was introdu
ced and studied in recent work of B. Keller and M. Liu. We then discuss an
equivalence between the following three Frobenius exact dg/infinity-categ
ories\, categorifying the cluster algebra:\n\n1) The Higgs category associ
ated with the 3-CY category.\n\n2) The cosingularity category of the 3-CY
category.\n\n3) The topological Fukaya category of the surface valued in t
he 2-periodic 1-CY cluster category of type I.\n\nThis talk will take plac
e in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Francone (Rome Tor Vergata)
DTSTART:20251006T120000Z
DTEND:20251006T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/206
DESCRIPTION:Title: Schemes of bands and their cluster structures\nby Luca
Francone (Rome Tor Vergata) as part of Paris algebra seminar\n\n\nAbstrac
t\nIn a recent joint work with Bernard Leclerc\, we introduce a family of
infinite-dimensional affine schemes called schemes of (G\,c)-bands. Here\,
G denotes a simple\, simply laced\, and simply connected algebraic group\
, and c is a Coxeter element of its Weyl group. These schemes offer a comm
on geometric framework for understanding certain cluster algebras which pl
ay a central role in the representation theory of (untwisted) quantum affi
ne algebras\, their Borel subalgebras\, and shifted quantum affine algebra
s. The goal of this talk is to introduce these schemes and explore their c
onnections with cluster algebras and representation theory.\n\nThis talk w
ill take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Serge Bouc (Amiens)
DTSTART:20251103T130000Z
DTEND:20251103T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/207
DESCRIPTION:Title: On Alperin's conjecture and functorial equivalence of bloc
ks\nby Serge Bouc (Amiens) as part of Paris algebra seminar\n\n\nAbstr
act\nAlperin's weight conjecture (1987) is one of the most important\nso-c
alled "local-global" conjectures in the block theory of finite groups.\nIt
relates "global" information on a block algebra of a finite group G\n- ty
pically\, the number of its simple modules - to information attached\nto "
local" subgroups of G - typically\, the number of their projective simple\
nmodules. In this talk\, I will show how this conjecture can be interprete
d\n- and proved to hold "stably" - in the category of diagonal p-permutati
on\nfunctors.\nThis is joint work with Deniz Yılmaz (Bilkent)\, and Deniz
Yılmaz and Robert\nBoltje (UCSC). \n\nThis talk will take place in hybri
d mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yingchun Zhang (Shanghai Jiao Tong)
DTSTART:20251110T130000Z
DTEND:20251110T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/208
DESCRIPTION:Title: On the Seiberg duality conjecture at the geometric level a
nd its applications\nby Yingchun Zhang (Shanghai Jiao Tong) as part of
Paris algebra seminar\n\n\nAbstract\nIn the first part\, I will introduce
our work in progress on the Seiberg duality conjecture at the geometric l
evel. Consider a quiver with potential. It has been proved by many people
that its quasimap I function is preserved under quiver mutation in some se
nse. In this work\, we further consider the behaviour of the representatio
n scheme under quiver mutation.\nIn the second part\, I will talk about an
expected application of this result to the relation between cluster algeb
ras and quantum cohomology rings. From a given quiver\, one can construct
a cluster algebra. One the other hand\, one can consider the quantum cohom
ology ring of the quiver variety when it is smooth. We expect that there i
s an algebra homomorphism from the cluster algebra to the quantum cohomolo
gy ring. \nThis is a joint work with Zijun Zhou and Yaoxiong Wen.\n\nThis
talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/208/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanpeng Li (Sichuan U.)
DTSTART:20251027T130000Z
DTEND:20251027T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/209
DESCRIPTION:Title: Cluster structures\, integrable systems and symplectic gro
upoids\nby Yanpeng Li (Sichuan U.) as part of Paris algebra seminar\n\
n\nAbstract\nWe introduce two operations applicable to a compatible cluste
r structure on a Poisson variety. (1) We present a construction of an inte
grable system on the tangent space equipped with the Poisson bivector whic
h is the linearization of a Poisson-cluster variety\; (2) If a Poisson-clu
ster variety integrates into a symplectic groupoid\, it is a natural quest
ion to ask whether a compatible cluster structure exists on the total spac
e. We give a positive answer to such a question when the base varieties ar
e the standard Poisson Lie groups and Schubert varieties. This is joint wo
rk with Yu Li and Jiang-Hua Lu.\n\nThis talk will take place on Zoom only.
\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/209/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lang Mou (UC Davis)
DTSTART:20251117T130000Z
DTEND:20251117T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/210
DESCRIPTION:Title: Positivity of generalized cluster algebras\nby Lang Mo
u (UC Davis) as part of Paris algebra seminar\n\n\nAbstract\nI will discus
s the recent proof of positivity of generalized cluster algebras\, in coll
aboration with Amanda Burcroff and Kyungyong Lee (arXiv:2503.03719). We pr
ove that the generalized cluster scattering diagram\, extending the constr
uction of Gross-Hacking-Keel-Kontsevich\, has positive wall-function coeff
icients\, implying Laurent positivity of cluster variables and strong posi
tivity of theta functions. The argument reduces to the rank-2 case\, where
positivity is shown to follow from a combinatorial solution to certain ge
neralized Lee–Li–Zelevinsky greedy recurrences via counting special cl
asses of Rupel’s compatible gradings.\n\nThis talk will take place on Zo
om only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Kleinau (Bonn)
DTSTART:20251124T130000Z
DTEND:20251124T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/211
DESCRIPTION:Title: Cambrian lattices are fractionally Calabi-Yau via 2-cluste
r combinatorics\nby Markus Kleinau (Bonn) as part of Paris algebra sem
inar\n\n\nAbstract\nCambrian lattices originate in the theory of Coxeter g
roups. They appear as 1-skeletons of generalised associahedra or as lattic
es of torsion classes of representation finite hereditary algebras. Rogner
ud has shown that Cambrian lattices of linear type A\, better known as Tam
ari lattices\, are fractionally Calabi-Yau. That is a power of the Serre f
unctor on the derived category of their incidence algebra agrees with a po
wer of the shift.\nThe m-cluster categories are an m+1 Calabi-Yau version
of cluster categories. They contain a family of m-cluster tilting objects
connected by a notion of mutation. In this talk I will introduce a family
of intervals in crystallographic Cambrian lattices that exhibit the same c
ombinatorics as 2-cluster tilting objects in 2-cluster categories. As a co
nsequence I will show that Cambrian lattices are fractionally Calabi-Yau.\
n\nThis talk will take place in hybrid mode at the Institut Henri Poincar
é.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Voloshyn (Pohang)
DTSTART:20251201T130000Z
DTEND:20251201T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/212
DESCRIPTION:Title: New normal forms in Lie theory and cluster algebras\nb
y Dmitriy Voloshyn (Pohang) as part of Paris algebra seminar\n\n\nAbstract
\nI will describe a new family of rational normal forms in Lie theory. The
family arises as a tool for constructing cluster structures on dual Poiss
on-Lie groups\, and it gives rise to some interesting combinatorics of wha
t I call rational Weyl group elements. The talk will be based on the prepr
int arXiv:2506.01530.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryu Tomonaga (Tokyo)
DTSTART:20251215T130000Z
DTEND:20251215T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/213
DESCRIPTION:Title: Weak del Pezzo surfaces yield 2-hereditary algebras and 3-
Calabi-Yau algebras\nby Ryu Tomonaga (Tokyo) as part of Paris algebra
seminar\n\n\nAbstract\nThe importance of studying d-tilting bundles\, whic
h are tilting bundles whose endomorphism algebras have global dimension d
(or less)\, on d-dimensional smooth projective varieties has been recogniz
ed recently. Previous work conjectured that a smooth projective surface ha
s a 2-tilting bundle if and only if is is a weak del Pezzo surface. In our
research\, we prove this conjecture affirmatively. Moreover\, this endomo
rphism algebra becomes a 2-representation infinite algebra whose 3-Calabi-
Yau completion gives a non-commutative crepant resolution (NCCR) of the co
rresponding Du Val del Pezzo cone\, generalizing a result of Van den Bergh
. This talk is based on arXiv:2510.26199.\n\nThis talk will take place on
Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/213/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fan Qin (Beijing Normal)
DTSTART:20260126T130000Z
DTEND:20260126T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/214
DESCRIPTION:Title: Quantum cluster algebras over commutative rings and quanti
zed coordinate rings of simple algebraic groups\nby Fan Qin (Beijing N
ormal) as part of Paris algebra seminar\n\n\nAbstract\nWe introduce quantu
m cluster algebras over arbitrary commutative rings. We also present a gen
eral method to construct (partially compactified) quantum cluster structur
es on quantized coordinate rings from those defined on localizations\, in
a setting where the standard codimension-two arguments used in the classic
al case are no longer available.\n\nAs an application\, we obtain natural
quantum cluster structures on the quantized coordinate rings of all simple
algebraic groups over arbitrary commutative rings. This is based on a ser
ies of joint papers with Milen Yakimov and Hironori Oya.\n\nThis talk will
take place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/214/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoine de Saint Germain (U. of Hong Kong)
DTSTART:20251208T130000Z
DTEND:20251208T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/215
DESCRIPTION:Title: On the correspondence between root systems and cluster alg
ebras\nby Antoine de Saint Germain (U. of Hong Kong) as part of Paris
algebra seminar\n\n\nAbstract\nOne of the first remarkable results in the
structure theory of cluster algebras of finite type is their classificatio
n by root systems. Since its discovery by Fomin and Zelevinsky\, many more
surprising connections between cluster algebras and root systems have app
eared. In this talk\, I will give an overview of old connections\, mention
new connections\, and propose a geometric explanation for these connectio
ns. This is partly based on joint work with Jiang-Hua Lu\, available at ar
xiv: 2503.11391.\n\nThis talk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/215/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Hohlweg (Montréal)
DTSTART:20260309T130000Z
DTEND:20260309T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/216
DESCRIPTION:Title: Reflections on Coxeter Systems\nby Christophe Hohlweg
(Montréal) as part of Paris algebra seminar\n\n\nAbstract\nThere are thre
e families of Coxeter systems: finite\, affine\, and indefinite. By far\,
the class of indefinite Coxeter systems (which includes\, for instance\, h
yperbolic discrete reflection groups) is the least understood. One reason
is the lack of tools to control the set of reflections\, or equivalently\,
the root system and the Coxeter arrangement. In this talk\, I will discus
s recent developments of such tools and some open problems involving the n
otions of Garside shadows (introduced in the context of Artin–Tits monoi
ds) and Shi arrangements. As an example of an application\, we will explai
n their relationship with the Osajda–Przytycki biautomatic structure for
Coxeter systems.\n\nThis talk will take place in hybrid mode at the Insti
tut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/216/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuki Mizuno (Utrecht)
DTSTART:20260223T130000Z
DTEND:20260223T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/217
DESCRIPTION:Title: Bondal–Orlov’s reconstruction theorem in noncommutativ
e projective geometry\nby Yuki Mizuno (Utrecht) as part of Paris algeb
ra seminar\n\n\nAbstract\nThe (derived) category of coherent sheaves on a
scheme encodes rich information about the underlying geometry. P. Gabriel
showed that for noetherian schemes X and Y\, if Coh X and Coh Y are equiva
lent as abelian categories\, then X and Y are isomorphic. Furthermore\, A.
Bondal and D. Orlov proved that for smooth projective schemes X and Y wit
h (anti-)ample canonical bundles\, if D^b(Coh X) and D^b(Coh Y) are equiva
lent as triangulated categories\, then X and Y are isomorphic. On the othe
r hand\, J.-P. Serre showed that the category of coherent sheaves on a pro
jective scheme can be described as the quotient category of finitely gener
ated graded modules over the homogeneous coordinate ring by the subcategor
y of torsion modules. Motivated by the results of Gabriel and Serre\, the
quotient category of finitely generated graded modules over a (not necessa
rily commutative) graded ring by the subcategory of torsion modules is cal
led a noncommutative projective scheme. In this talk\, I will present an a
nalogue of Bondal–Orlov’s reconstruction theorem in the setting of non
commutative projective geometry.\n\nThis talk will take place in hybrid mo
de at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/217/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (USTC Hefei)
DTSTART:20260209T130000Z
DTEND:20260209T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/218
DESCRIPTION:Title: The tropical invariant and the $F$-invariant in cluster al
gebras\nby Peigen Cao (USTC Hefei) as part of Paris algebra seminar\n\
n\nAbstract\nThe Lambda-invariant and the d-invariant are two integer-valu
ed invariants introduced by Kang-Kashiwara-Kim-Oh and by Kashiwara-Kim-Oh-
Park in their study of monoidal categorification of cluster algebras using
finite-dimensional modules over quiver Hecke algebras and quantum affine
algebras. The Lambda-invariant can be viewed as a monoidal categorificatio
n of the compatible Poisson structure on those cluster algebras. The d-inv
ariant is defined as half the symmetrized sum of Lambda-invariants\, and i
t can be used to characterize the strong commutativity between real simple
s.\n\n\nIn this talk\, we introduce the tropical invariant and the F-invar
iant in cluster algebras. The tropical invariant is defined for any cluste
r algebra with a compatible Poisson structure and it generalizes the Lambd
a-invariant. The F-invariant is defined as the symmetrized sum of the trop
ical invariants and it simultaneously generalizes all of the following inv
ariants: the d-invariant\, Derksen-Weyman-Zelevinsky’s E-invariant\, Fu-
Gyoda’s f-compatibility degree\, Fomin-Zelevinsky’s compatibility degr
ee\, and Qiu-Zhou’s f-intersection number on marked surfaces.\n\nThis ta
lk will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/218/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyang Liu (U. of Tokyo)
DTSTART:20260202T130000Z
DTEND:20260202T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/219
DESCRIPTION:Title: Calabi-Yau structures on derived and singularity categorie
s of symmetric orders\nby Junyang Liu (U. of Tokyo) as part of Paris a
lgebra seminar\n\n\nAbstract\nThis is a report on recent work in collabora
tion with Norihiro Hanihara (arXiv:2512.03836). We develop a differential
graded enhancement of Amiot's construction of Calabi-Yau structures on Ver
dier quotients. Using this framework\, we establish the existence of a rig
ht Calabi-Yau structure on the dg singularity category associated with a s
ymmetric order. Combining this with a structure theorem in collaboration w
ith Bernhard Keller\, we establish a triangle equivalence between the sing
ularity category with a cluster-tilting object and the cluster category as
sociated with a Calabi-Yau dg algebra. We also construct a left Calabi-Yau
structure on the bounded dg derived category of a symmetric order\, which
is a non-commutative analogue of a result by Brav-Dyckerhoff.\n\nThis tal
k will take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/219/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Cerulli (Rome)
DTSTART:20260216T130000Z
DTEND:20260216T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/220
DESCRIPTION:Title: Quivers with Polynomial Identities\nby Giovanni Cerull
i (Rome) as part of Paris algebra seminar\n\n\nAbstract\nSeventy-five year
s have passed since Amitsur and Levitzki proved that the algebra of n x n
matrices satisfies the standard polynomial identity of degree 2n. Since th
en\, mathematicians have investigated algebras whose elements satisfy a po
lynomial identity\, meaning that every substitution of elements of the alg
ebra into a given noncommutative polynomial yields zero. Such algebras are
known as PI algebras.\n\n\n The theory of PI algebras has develope
d enormously over the years\, leading to deep and far-reaching results. In
this talk\, we address the following natural questions: which quivers hav
e a path algebra that is PI? What can be said about the corresponding T-id
eal of polynomial identities? And how does the situation change when relat
ions are imposed on the path algebra?\n\n\n This is joint work with
Elena Pascucci and Javier De Loera Chávez.\n\nThis talk will take in hyb
rid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/220/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen Chang (Shaanxi Normal U.)
DTSTART:20260323T130000Z
DTEND:20260323T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/221
DESCRIPTION:Title: Entropy of the Serre functor for partially wrapped Fukaya
categories of surfaces with stops\nby Wen Chang (Shaanxi Normal U.) as
part of Paris algebra seminar\n\n\nAbstract\nI will talk about the catego
rical entropy of the Serre functor for partially wrapped Fukaya categories
of graded surfaces with stops\, as well as for perfect derived categories
of homologically smooth graded gentle algebras (to which the aforemention
ed Fukaya categories are equivalent). We prove that the entropy of the Ser
re functor is a piecewise linear function determined by the winding number
s of the surface’s boundary components and the number of stops on each c
omponent. Specifically\, the function takes different linear forms for non
-negative and non-positive arguments\, with slopes related to the minimum
and maximum values derived from the ratio of each boundary component’s w
inding number to its stop count. We further derive the corresponding upper
and lower Serre dimensions. Additionally\, for ungraded homologically smo
oth gentle algebras\, we establish a Gromov–Yomdin-like equality\, linki
ng the categorical entropy of the Serre functor to the natural logarithm o
f the spectral radius of the Coxeter transformation. The talk is based on
the preprint arXiv:2508.14860\, which is joint with A. Elagin and S. Schro
ll.\n\nThis talk will take place in hybrid mode at the Institut Henri Poin
caré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/221/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Canesin (Paris Cité)
DTSTART:20260316T130000Z
DTEND:20260316T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/222
DESCRIPTION:Title: An additive interpretation of the monoidal $\\Lambda$-inva
riant\nby Ricardo Canesin (Paris Cité) as part of Paris algebra semin
ar\n\n\nAbstract\nThe Lambda-invariant for quantum affine algebras was int
roduced by Kashiwara-Kim-Oh-Park as an important tool in their study of th
e monoidal categorification of cluster algebras. At the level of the clust
er algebra\, it is related to a compatible Poisson structure\, and it was
recently shown to coincide with Peigen Cao’s tropical invariant.\n\nIn t
his talk\, we interpret these invariants using the additive categorificati
on of cluster algebras via Higgs categories in the sense of Yilin Wu. When
ever the relative Ginzburg algebra is proper\, we show that the Higgs cate
gory admits a canonical quantum structure in the sense of Grabowski-Pressl
and\, and we give a homological interpretation of the corresponding tropic
al invariant.\n\nFor certain finite-rank cluster algebras categorified by
Kashiwara-Kim-Oh-Park\, we show that the associated relative Ginzburg alge
bra is indeed proper\, and that our additive Lambda-invariant agrees with
their monoidal one.\n\nThis is joint work in progress with Geoffrey Jansse
ns and Peigen Cao.\n\nThis talk will take place in hybrid mode at the Inst
itut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/222/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viktoria Klasz (Bonn)
DTSTART:20260511T120000Z
DTEND:20260511T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/223
DESCRIPTION:by Viktoria Klasz (Bonn) as part of Paris algebra seminar\n\n\
nAbstract\nThis talk will take place in hybrid mode at the Institut Henri
Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/223/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dani Kaufmann (MPI MIS Leipzig)
DTSTART:20260427T120000Z
DTEND:20260427T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/224
DESCRIPTION:Title: Non-commutative Cluster Varieties and Moduli of Local Syst
ems\nby Dani Kaufmann (MPI MIS Leipzig) as part of Paris algebra semin
ar\n\n\nAbstract\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n\nGiven a split algebraic group G and an oriented surfa
ce S with punctures\, Fock and Goncharov defined a pair of moduli spaces w
hich parameterise G local systems on S with some extra data at the punctur
es. These spaces amazingly are Cluster Varieties which endows them with ma
ny extra properties\, including a well defined set of positive points. The
y show that these positive points give an algebraic realisation of the Hig
her Teichmüller space associated to G. \n\nIn this talk I will give an ov
erview of a generalisation of this story to non-split groups G with reduce
d root systems. Part of this story explains how to think of such groups as
a simpler split algebraic group G’ which is defined over a noncommutatv
e ring\, or more correctly a Jordan algebra. We show that the associated m
oduli spaces have a cluster structure which is a noncommutative deformatio
n of the associated cluster structure for the split group G’. We show th
at when the Jordan algebras involved are Euclidean i.e. have a positive co
ne \, the group G has a "Theta-positive structure" and there is a well def
ined set of positive points which parameterise a Higher Teichmüller space
associated to G. This gives an algebraic description of the emerging theo
ry of groups with Theta-positive structure. \n\nBased on joint work with Z
ack Greenberg\, Anna Wienhard\, and Merik Niemeyer.\n\nThis talk will take
place in hybrid mode at the Institut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/224/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Garcia (UQAM)
DTSTART:20260302T130000Z
DTEND:20260302T140000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/225
DESCRIPTION:Title: Infinite super friezes\nby Monica Garcia (UQAM) as par
t of Paris algebra seminar\n\n\nAbstract\nSuper friezes were introduced by
S. Morier-Genoud\, V. Ovsienko\, S. Tabachnikov as a supersymmetric analo
g of classical Coxeter friezes. They show analogous properties of classica
l friezes: they are determined by the first non-trivial even and odd quidd
ity rows\, they satisfy linear recurrence relations\, and exhibit glide sy
mmetry when of finite width. Moreover\, as shown by G. Musiker\, N. Ovenho
use and S. Zhang\, all finite width super friezes arise from a decorated t
riangulation of a polygon\, where even entries correspond to $\\lambda$-le
ngths of arcs\, and odd entries to $\\mu$-invariants of triangles in the p
olygon. In this talk\, I will report on joint work with A. Burcroff\, İ.
Çanakçı\, F. Fedele and V. Klász on how to construct infinite super fr
iezes from decorated skeletal triangulations of annuli. \n\nThis talk will
take place on Zoom only.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/225/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anya Nordskova (IPMU Tokyo)
DTSTART:20260504T120000Z
DTEND:20260504T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/226
DESCRIPTION:by Anya Nordskova (IPMU Tokyo) as part of Paris algebra semina
r\n\n\nAbstract\nThis talk will take place in hybrid mode at the Institut
Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/226/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yilin Wu (Luxembourg)
DTSTART:20260615T120000Z
DTEND:20260615T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/227
DESCRIPTION:by Yilin Wu (Luxembourg) as part of Paris algebra seminar\n\n\
nAbstract\nThis talk will take place in hybrid mode at the Institut Henri
Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/227/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Kano (Tohoku and Paris Cité)
DTSTART:20260601T120000Z
DTEND:20260601T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/228
DESCRIPTION:by Shunsuke Kano (Tohoku and Paris Cité) as part of Paris al
gebra seminar\n\n\nAbstract\nThis talk will take place in hybrid mode at t
he Instiut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/228/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lior Silberberg (Paris Cité)
DTSTART:20260413T120000Z
DTEND:20260413T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/229
DESCRIPTION:Title: Folding of cluster algebras and quantum toroidal algebras<
/a>\nby Lior Silberberg (Paris Cité) as part of Paris algebra seminar\n\n
\nAbstract\nIn this talk\, I will present a relationship between the repre
sentation theory of the infinite rank quantum affine algebra Uq(sl_∞) an
d that of the quantum toroidal algebra Uq(sl_2n\,tor). In particular\, I w
ill discuss folding techniques for cluster algebras arising from infinite
quivers\, and show that the monoidal categorifications associated to these
quantum algebras (due to Hernandez-Leclerc and Nakajima) are related by f
olding. I will explain how this allows us to verify a conjecture by Hernan
dez in new cases.\n\nThis talk will take place in hybrid mode at the Insti
tut Henri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/229/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuma Mizuno (Cork)
DTSTART:20260518T120000Z
DTEND:20260518T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/230
DESCRIPTION:by Yuma Mizuno (Cork) as part of Paris algebra seminar\n\n\nAb
stract\nThis talk will take place in hybrid mode at the Institut Henri Poi
ncaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/230/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryu Tomonaga (U. of Tokyo)
DTSTART:20260608T120000Z
DTEND:20260608T130000Z
DTSTAMP:20260423T094717Z
UID:paris-algebra-seminar/231
DESCRIPTION:by Ryu Tomonaga (U. of Tokyo) as part of Paris algebra seminar
\n\n\nAbstract\nThis talk will take place in hybrid mode at the Institut H
enri Poincaré.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/231/
END:VEVENT
END:VCALENDAR