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BEGIN:VEVENT
SUMMARY:Harrison Chen (Academia Sinica)
DTSTART:20230224T070000Z
DTEND:20230224T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/1
DESCRIPTION:Title: Circle actions\, coherent Springer theory and classical Springer t
heory\nby Harrison Chen (Academia Sinica) as part of Algebra and Geome
try Seminar @ HKUST\n\nLecture held in Room 5564.\n\nAbstract\nCoherent Sp
ringer theory is related to the representation theory of p-adic groups\, a
nd involves the study of certain coherent sheaves on moduli stacks of Lang
lands parameters\, whose unipotent part is the derived loop space of the e
quivariant nilpotent cone. On the other hand\, classical Springer theory
is related to the representation of finite groups of Lie type\, and involv
es the study of certain constructible sheaves on the equivariant nilpotent
cone itself. Passing between the two involves equivariant localization\,
imposition of circle equivariance\, and a Koszul duality. In the first p
art of this talk\, we will give a gentle introduction to circle actions wi
th many examples. In the second part\, we will describe how this provides
the mechanism for passing between coherent and constructible sheaves.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Xu (Penn State University)
DTSTART:20230303T070000Z
DTEND:20230303T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/2
DESCRIPTION:Title: Duflo-Kontsevich type theorem for dg manifolds\nby Ping Xu (Pe
nn State University) as part of Algebra and Geometry Seminar @ HKUST\n\nLe
cture held in Room 4472.\n\nAbstract\nIn this talk\, we describe a Duflo-K
ontsevich type theorem for dg manifolds.\nThe Duflo theorem of Lie theory
and the Kontsevich theorem regarding the Hoschschild cohomology of complex
manifolds can both be derived as special cases of this Duflo--Kontsevich
type theorem for dg manifolds. This is joint work with Hsuan-Yi Liao and
Mathieu Stienon.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Le (The Australian National University)
DTSTART:20230315T070000Z
DTEND:20230315T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/3
DESCRIPTION:Title: Cluster structures on braid varieties\nby Ian Le (The Australi
an National University) as part of Algebra and Geometry Seminar @ HKUST\n\
nLecture held in 4621.\n\nAbstract\nMany varieties in Lie theory--partial
flag varieties\, Schubert varieties\, moduli of local systems on surfaces-
-admit cluster structures\, which give a combinatorial way of encoding qua
ntum deformations of these varieties. Braid varieties give a unifying fram
ework for constructing these cluster structures. I will start by defining
braid varieties and give some motivations coming from knot homology and mi
rror symmetry. Then I will introduce the main tool\, Legendrian weaves\, w
hich allow us to construct clusters in a concrete and diagrammatic way. Th
e diagrams will be familiar to anyone who has seen Soergel calculus. This
is joint work with Roger Casals\, Eugene Gorsky\, Mikhail Gorsky\, Linhui
Shen and Jose Simental.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (École Polytechnique Fédérale de Lausanne)
DTSTART:20230419T070000Z
DTEND:20230419T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/4
DESCRIPTION:Title: Orbital L-functions and knot superpolynomials\nby Oscar Kivine
n (École Polytechnique Fédérale de Lausanne) as part of Algebra and Geo
metry Seminar @ HKUST\n\nLecture held in 4504.\n\nAbstract\nOrbital L-func
tions for GL(n) have appeared in a number of works related to automorphic
representation theory. Their importance has recently been highlighted by A
rthur. It turns out that for function fields\, the local factors of these
L-functions have long been studied in algebraic geometry\, as Hilbert zeta
functions of curve singularities. Drawing inspiration from the Oblomkov-R
asmussen-Shende conjecture\, I will formulate a closely related conjecture
equating the local factors with what are essentially the knot superpolyno
mials introduced by Cherednik-Danilenko\, Dunfield-Gukov-Rasmussen\, and o
thers. This applies in the tamely ramified case over any non-archimedean l
ocal field\, even when there is no knot in the picture. I will then explai
n recent progress towards this conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhao Yu (Kavli IPMU)
DTSTART:20230322T070000Z
DTEND:20230322T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/5
DESCRIPTION:Title: Hecke Correspondences on smooth surfaces and categorical commutato
rs\nby Zhao Yu (Kavli IPMU) as part of Algebra and Geometry Seminar @
HKUST\n\nLecture held in 2405.\n\nAbstract\nGiven a complex smooth surface
\, Negut constructed an action of the quantum toroidal algebra on the Grot
hendieck group of moduli space of stable sheaves\, which generalized the c
onstruction of Nakajima\, Grojnowski\, Baranovsky in cohomology. In this t
alk\, we will obtain a weak categorification of Negut's action\, by constr
ucting explicit natural transformations and compute the categorical commut
ators of the positive and negative part.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (Universität Wuppertal)
DTSTART:20230405T070000Z
DTEND:20230405T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/6
DESCRIPTION:Title: A K-theoretic Approach to Geometric Representation Theory\nby
Jens Eberhardt (Universität Wuppertal) as part of Algebra and Geometry Se
minar @ HKUST\n\nLecture held in 5564.\n\nAbstract\nPerverse sheaves and i
ntersection cohomology are central objects in geometric representation the
ory. This talk is about their long-lost K-theoretic cousins\, called K-mot
ives. We will discuss definitions and basic properties of K-motives and ex
plore potential applications to geometric representation theory. For examp
le\, K-motives shed a new light on Beilinson-Ginzburg-Soergel's Koszul dua
lity — a remarkable symmetry in the representation theory and geometry o
f two Langlands dual reductive groups. We will see that this leads to a ne
w “universal” Koszul duality that does not involve any gradings or mix
ed geometry which are as essential as mysterious in the classical approach
es.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gufang Zhao (University of Melbourne)
DTSTART:20230426T070000Z
DTEND:20230426T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/7
DESCRIPTION:Title: Quasimaps to quivers with potentials\nby Gufang Zhao (Universi
ty of Melbourne) as part of Algebra and Geometry Seminar @ HKUST\n\nLectur
e held in CYTG001.\n\nAbstract\nThis talk concerns non-compact GIT quotien
t of a vector space\, in the presence of an abelian group action and an eq
uivariant regular function (potential) on the quotient. We define virtual
counts of quasimaps from prestable curves to the critical locus of the pot
ential. The construction borrows ideas from the theory of gauged linear si
gma models as well as recent development in shifted symplectic geometry an
d Donaldson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual count
s arising from quivers with potentials are discussed. This is based on wor
k in preparation\, in collaboration with Yalong Cao.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Frenkel (Yale University)
DTSTART:20230412T070000Z
DTEND:20230412T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/8
DESCRIPTION:Title: Representation Theory in Mathematics and Physics\nby Igor Fren
kel (Yale University) as part of Algebra and Geometry Seminar @ HKUST\n\nL
ecture held in CYTG001.\n\nAbstract\nIn this talk\, we overview some centr
al ideas and historical developments of representation theory and its rela
tions to other areas of mathematics and physics. We'll start with a brief
review of the sources and first successes of representation theory of fini
te and finite-dimensional groups and its applications. Then we will recall
the remarkable generalizations of this theory to central extensions of lo
op groups and Virasoro group and consider further relations to mathematics
and physics. We will describe the programs of "geometrization" and "categ
orification" of the previous results in representation theory developed si
nce 90th and their successes. We conclude with potential new developments
in representation theory and discuss some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingyuan Jiang (University of Edinburgh)
DTSTART:20230426T083000Z
DTEND:20230426T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/9
DESCRIPTION:Title: Derived projectivizations and Grassmannians and their applications
\nby Qingyuan Jiang (University of Edinburgh) as part of Algebra and G
eometry Seminar @ HKUST\n\nLecture held in CYTG001.\n\nAbstract\nWe will e
xplore some applications of the Derived Algebraic Geometry (DAG)\, a power
ful framework developed by Toen-Vezzosi\, Lurie and many others. DAG allow
s us to extend Grothendieck’s theory of projectivizations and Grassmanni
ans of sheaves to the cases of complexes. This derived extension is very u
seful for constructing and studying moduli spaces\, especially when the sp
aces are singular and difficult to analyze in the classical framework. We
will discuss the constructions of derived projectivizations and Grassmanni
ans as well as their properties\, with a focus on their applications to Ab
el maps for singular curves and Hecke correspondences for smooth surfaces.
\nBased on papers arXiv:2202.11636 and arXiv:2212.10488 and works in prep
aration.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Minets (The University of Edinburgh)
DTSTART:20230510T030000Z
DTEND:20230510T043000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/10
DESCRIPTION:Title: A proof of $P=W$ conjecture\nby Sasha Minets (The University
of Edinburgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture h
eld in 5564.\n\nAbstract\nLet $C$ be a smooth projective curve. The non-ab
elian Hodge theory of Simpson is a diffeomorphism between the character va
riety $M_B$ of $C$ and the moduli of (semi)stable Higgs bundles $M_D$ on $
C$. Since this diffeomorphism is not algebraic\, it induces an isomorphism
of cohomology rings\, but does not preserve finer information\, such as t
he weight filtration. Based on computations in small rank\, de Cataldo-Hau
sel-Migliorini conjectured that the weight filtration on $H^*(M_B)$ gets s
ent to the perverse filtration on $H^*(M_D)$\, associated to the Hitchin m
ap. In this talk\, I will explain a recent proof of this conjecture\, whic
h crucially uses the action of Hecke correspondences on $H^*(M_D)$. Based
on joint work with T. Hausel\, A. Mellit\, O. Schiffmann.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro van Ekeren (Instituto de Matemática Pura e Aplicada (IMPA)
)
DTSTART:20230816T070000Z
DTEND:20230816T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/11
DESCRIPTION:Title: Chiral homology\, the Zhu algebra\, and Rogers-Ramanujan\nby
Jethro van Ekeren (Instituto de Matemática Pura e Aplicada (IMPA)) as par
t of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5506.\n\
nAbstract\nGraded dimensions of rational vertex algebras are modular funct
ions. The proof of this celebrated theorem by Y. Zhu centres on geometric
objects attached to elliptic curves known as conformal blocks\, and their
behaviour in the limit as the underlying curve becomes singular. In this l
imit\, roughly speaking\, conformal blocks pass to the degree zero Hochsch
ild homology of Zhu's associative algebra. On the other hand\, conformal b
locks have been interpreted by Beilinson and Drinfeld as the degree zero c
omponent of a theory of chiral homology. It is therefore natural to wonder
if the relationship extends to higher homological degrees. We are indeed
able to extend this story to homological degree 1 for classically free ver
tex algebras\, and in the process we discover relations with objects of nu
mber theory such as the Rogers-Ramanujan identity and its generalisations.
This is joint work with R. Heluani and G. Andrews.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230811T060000Z
DTEND:20230811T070000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/12
DESCRIPTION:Title: Motives in Geometric Representation Theory I\nby Jens Eberhar
dt (University of Wuppertal) as part of Algebra and Geometry Seminar @ HKU
ST\n\nLecture held in CYTG003.\n\nAbstract\nRecent constructions in motivi
c homotopy theory offer exciting new applications in geometric representat
ion theory. For example\, they allow to consider mixed perverse sheaves (a
graded version of perverse sheaves) with integral coefficients or K-motiv
es (a K-theoretic analogue of constructible sheaves).\n\nIn this lecture s
eries\, we will explain how to work with motives in practice. We focus on
motivic cohomology\, the motivic six functor formalism\, Tate motives\, an
d weight structures. We will then explain the notion of stratified mixed T
ate motives which\, when specialized to (affine/partial) flag varieties\,
yields a geometric perspective on Koszul duality. Lastly\, we will introdu
ce results and conjectures relating K-motives and the geometric Langlands
program.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230814T060000Z
DTEND:20230814T070000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/13
DESCRIPTION:Title: Motives in Geometric Representation Theory II\nby Jens Eberha
rdt (University of Wuppertal) as part of Algebra and Geometry Seminar @ HK
UST\n\nLecture held in Room 2503.\n\nAbstract\nRecent constructions in mot
ivic homotopy theory offer exciting new applications in geometric represen
tation theory. For example\, they allow to consider mixed perverse sheaves
(a graded version of perverse sheaves) with integral coefficients or K-mo
tives (a K-theoretic analogue of constructible sheaves).\n\nIn this lectur
e series\, we will explain how to work with motives in practice. We focus
on motivic cohomology\, the motivic six functor formalism\, Tate motives\,
and weight structures. We will then explain the notion of stratified mixe
d Tate motives which\, when specialized to (affine/partial) flag varieties
\, yields a geometric perspective on Koszul duality. Lastly\, we will intr
oduce results and conjectures relating K-motives and the geometric Langlan
ds program.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230815T060000Z
DTEND:20230815T070000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/14
DESCRIPTION:Title: Motives in Geometric Representation Theory III\nby Jens Eberh
ardt (University of Wuppertal) as part of Algebra and Geometry Seminar @ H
KUST\n\nLecture held in Room 5510.\n\nAbstract\nRecent constructions in mo
tivic homotopy theory offer exciting new applications in geometric represe
ntation theory. For example\, they allow to consider mixed perverse sheave
s (a graded version of perverse sheaves) with integral coefficients or K-m
otives (a K-theoretic analogue of constructible sheaves).\n\nIn this lectu
re series\, we will explain how to work with motives in practice. We focus
on motivic cohomology\, the motivic six functor formalism\, Tate motives\
, and weight structures. We will then explain the notion of stratified mix
ed Tate motives which\, when specialized to (affine/partial) flag varietie
s\, yields a geometric perspective on Koszul duality. Lastly\, we will int
roduce results and conjectures relating K-motives and the geometric Langla
nds program.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230817T060000Z
DTEND:20230817T070000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/15
DESCRIPTION:Title: Motives in Geometric Representation Theory IV\nby Jens Eberha
rdt (University of Wuppertal) as part of Algebra and Geometry Seminar @ HK
UST\n\nLecture held in Room 5510.\n\nAbstract\nRecent constructions in mot
ivic homotopy theory offer exciting new applications in geometric represen
tation theory. For example\, they allow to consider mixed perverse sheaves
(a graded version of perverse sheaves) with integral coefficients or K-mo
tives (a K-theoretic analogue of constructible sheaves).\n\nIn this lectur
e series\, we will explain how to work with motives in practice. We focus
on motivic cohomology\, the motivic six functor formalism\, Tate motives\,
and weight structures. We will then explain the notion of stratified mixe
d Tate motives which\, when specialized to (affine/partial) flag varieties
\, yields a geometric perspective on Koszul duality. Lastly\, we will intr
oduce results and conjectures relating K-motives and the geometric Langlan
ds program.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230818T060000Z
DTEND:20230818T070000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/16
DESCRIPTION:Title: Motives in Geometric Representation Theory V\nby Jens Eberhar
dt (University of Wuppertal) as part of Algebra and Geometry Seminar @ HKU
ST\n\nLecture held in Room 5510.\n\nAbstract\nRecent constructions in moti
vic homotopy theory offer exciting new applications in geometric represent
ation theory. For example\, they allow to consider mixed perverse sheaves
(a graded version of perverse sheaves) with integral coefficients or K-mot
ives (a K-theoretic analogue of constructible sheaves).\n\nIn this lecture
series\, we will explain how to work with motives in practice. We focus o
n motivic cohomology\, the motivic six functor formalism\, Tate motives\,
and weight structures. We will then explain the notion of stratified mixed
Tate motives which\, when specialized to (affine/partial) flag varieties\
, yields a geometric perspective on Koszul duality. Lastly\, we will intro
duce results and conjectures relating K-motives and the geometric Langland
s program.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dougal Davis (University of Melbourne)
DTSTART:20231009T070000Z
DTEND:20231009T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/17
DESCRIPTION:Title: Unitary representations of real groups and localisation theory fo
r Hodge modules\nby Dougal Davis (University of Melbourne) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbst
ract\nI will explain recent joint work with Kari Vilonen\, in which we pro
ve a conjecture of Schmid and Vilonen linking mixed Hodge modules on flag
varieties to unitary representations of real reductive Lie groups. The mai
n idea behind our work is to upgrade Beilinson-Bernstein localisation from
D-modules to mixed Hodge modules. When it applies\, this endows everythin
g in sight with a canonical filtration\, the Hodge filtration\, which we p
rove has some extremely nice properties\, such as cohomology vanishing and
global generation. In the context of real groups\, we also prove that the
Hodge filtration “sees” exactly which representations are unitary. We
hope that this will lead to new progress on the very old problem of deter
mining the unitary dual of a real group.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (The University of Edinburgh)
DTSTART:20231016T070000Z
DTEND:20231016T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/18
DESCRIPTION:Title: Cohomological integrality for 2-Calabi-Yau categories\nby Luc
ien Hennecart (The University of Edinburgh) as part of Algebra and Geometr
y Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nIn this talk\
, I will explain how one can decompose the cohomology of moduli stacks of
objects for a large class of 2-Calabi-Yau categories. Our main tools are c
ohomological Hall algebras (CoHAs) and their associated BPS algebras (in t
heir associative and Lie algebra versions). Important examples are given b
y representations of preprojective algebras of quivers and finite length s
heaves on surfaces. In the latter case\, we can recover the generating ser
ies of Betti numbers of the moduli stack in an efficient way.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Campion (Johns Hopkins University)
DTSTART:20230925T070000Z
DTEND:20230925T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/19
DESCRIPTION:Title: Smooth and proper algebras via stable $(\\infty\,2)$-categories\nby Timothy Campion (Johns Hopkins University) as part of Algebra and G
eometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nSince G
rothendieck\, the notion of an abelian 1-category has provided a natural s
etting to do algebra which encompasses both categories of modules and cate
gories of sheaves. Since Lurie\, the notion of a stable $(\\infty\,1)$-cat
egory has provided a similar setting to do derived algebra\, encompassing
derived categories of modules and sheaves\, and improving upon the notion
of a triangulated category due to Verdier.\n\nIn this talk\, we discuss a
few possible notions of stable $(\\infty\,2)$-category\, motivated by enri
ched category theory. Examples include the $(\\infty\,2)$-category of dg c
ategories\, the $(\\infty\,2)$-category of stable $(\\infty\,1)$-categorie
s\, and various $(\\infty\,2)$-categories of stacks of stable $(\\infty\,1
)$-categories. The intention is to provide a natural home for the study of
such $(\\infty\,2)$-categories\, which are of interest in areas such as t
he Geometric Langlands program\, secondary algebraic K-theory\, and derive
d algebraic geometry.\n\nWe discuss work in progress on showing that our n
otions of stable $(\\infty\,2)$-category are equivalent. As an application
\, we show for example that every smooth and proper algebra over a regular
commutative Noetherian ring k may be constructed from $k$ by iterating tw
o simple operations: glueing along a perfect bimodule\, and 2-idempotent s
plitting.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20231025T070000Z
DTEND:20231025T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/20
DESCRIPTION:Title: Microlocalization on derived moduli spaces\nby Adeel Khan (Ac
ademia Sinica) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in Room 5566.\n\nAbstract\nThe classical formalism of microlocal shea
f theory à la Kashiwara-Schapira is very useful in the study of manifolds
. I will describe a generalization to the context of derived algebraic ge
ometry\, which is useful in the study of derived moduli spaces. For examp
le\, I will discuss how it gives a new perspective on topics like the virt
ual fundamental class\, categorified Donaldson-Thomas theory\, and the cri
tical or 3d cohomological Hall algebras of Kontsevich-Soibelman. Based on
forthcoming joint work with Tasuki Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (colloquium) (Academia Sinica)
DTSTART:20231027T070000Z
DTEND:20231027T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/21
DESCRIPTION:Title: Derived Fourier analysis\nby Adeel Khan (colloquium) (Academi
a Sinica) as part of Algebra and Geometry Seminar @ HKUST\n\n\nAbstract\nI
will discuss incarnations of the Fourier transform in algebraic geometry
and topology. Like its prototype\, these "sheafy" or categorified forms o
f Fourier analysis have proven unreasonably effective in applications. Af
ter giving an overview of the sheaf-theoretic Fourier transform\, I will e
xplain a new "derived" version and some concrete problems in enumerative g
eometry and number theory this abstract piece of machinery has proven usef
ul for so far.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penghui Li (Tsinghua University)
DTSTART:20230927T070000Z
DTEND:20230927T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/22
DESCRIPTION:Title: Graded character sheaves\, HOMFLY-PT homology\, and Hilbert schem
es of points on $\\mathbb{C}^2$\nby Penghui Li (Tsinghua University) a
s part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 447
5.\n\nAbstract\nUsing a geometric argument building on our new theory of g
raded sheaves\, we compute the categorical trace and Drinfel'd center of t
he (graded) finite Hecke category $\\mathsf{H}_W$ in terms of the catego
ry of (graded) unipotent character sheaves\, upgrading results of Ben-Zvi-
Nadler and Bezrukavninov-Finkelberg-Ostrik. In type $A$\, we relate the c
ategorical trace to the category of 2-periodic coherent sheaves on the Hi
lbert schemes of points on $\\mathbb{C}^2$ (equivariant with respect to
the natural $\\mathbb{C}^* \\times \\mathbb{C}^*$ action)\, yielding a
proof of a conjecture of Gorsky-Negut-Rasmussen which relates HOMFLY-PT li
nk homology and the spaces of global sections of certain coherent sheaves
on Hilbert schemes. As an important computational input\, we also establi
sh a conjecture of Gorsky-Hogancamp-Wedrich on the formality of the Hochsc
hild homology of $\\mathsf{H}_W$. This is a joint work with Quoc P. Ho.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aron Heleodoro (Hong Kong University)
DTSTART:20231030T070000Z
DTEND:20231030T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/23
DESCRIPTION:Title: Semi-orthogonal decomposition of conjugation equivariant sheaves
on the loop group\nby Aron Heleodoro (Hong Kong University) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbs
tract\nLet $k$ be an algebraically closed field and $L=k((t))$\, for $G$ a
connected reductive algebraic group consider $\\breve G:= G(L)$. We estab
lish a semi-orthogonal decomposition indexed by Newton strata of $D(\\frac
{\\breve G}{\\breve G})$\, the DG category of $\\breve G$-equivariant cons
tructible etale sheaves on $\\breve G$. In this talk I will explain (1) ho
w to consider (ind-)constructible etale sheaves on such infinite-dimension
al spaces\, (2) what notion of semi-orthogonal decomposition we consider\,
(3) the definiton of Newton strata and the geometric input about them we
need for the theory\, and (4) how this category relates to the affine Heck
e category. This is joint work with Xuhua He.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostiantyn Tolmachov (The University of Edinburgh)
DTSTART:20231011T070000Z
DTEND:20231011T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/24
DESCRIPTION:Title: Equivariant derived category of a reductive group as a categorica
l center\nby Kostiantyn Tolmachov (The University of Edinburgh) as par
t of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5566.\n\
nAbstract\nThere is a classical relationship between representations of th
e Iwahori-Hecke algebra associated with a Weyl group of a split reductive
group G\, defined over a finite field\, and the (principal series) represe
ntations of the corresponding finite group of Lie type. I will discuss a c
ategorification of this relationship in the context of various triangulate
d categories of constructible sheaves on the group G. In particular\, I wi
ll present a new approach to connecting the categories of character sheave
s to a version of a categorical\ncenter of the constructible Hecke categor
y. Based on a joint work with R. Bezrukavnikov\, A. Ionov\, and Y. Varshav
sky.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamil Rychlewicz (Institute of Science and Technology Austria)
DTSTART:20231106T080000Z
DTEND:20231106T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/25
DESCRIPTION:Title: Cohomology theories and rings of functions\nby Kamil Rychlewi
cz (Institute of Science and Technology Austria) as part of Algebra and Ge
ometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nExtendin
g the classical Poincare-Hopf theorem\, the work of Akyildiz\, Carrell\, L
iebermann\, Sommese shows how to recover the cohomology ring of a smooth p
rojective variety from isolated zeros of a vector field. Thirty years late
r\, Brion and Carrell showed how to find the spectrum of the torus-equivar
iant cohomology as a geometrically defined scheme\, provided that the Bore
l of SL_2 acts with a single fixed point of the regular unipotent. In a jo
int work with Tamas Hausel we demonstrate how to see the spectrum of G-equ
ivariant cohomology\, if G is a linear group acting with similar assumptio
ns. This condition covers many interesting cases\, including flag varietie
s and Bott–Samelson resolutions. I will present this work and also show
how to see the equivariant cohomology rings of spherical varieties as ring
s of functions on non-affine schemes. Besides\, there are a lot of new dir
ections and open questions I would like to advertise. This in particular c
oncerns general\, potentially singular varieties\, as well as other equiva
riant cohomology theories.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaoxiang Wen (Korea Institute For Advanced Study)
DTSTART:20231115T070000Z
DTEND:20231115T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/26
DESCRIPTION:Title: Mirror symmetries for parabolic Hitchin systems\, from classical
to global\, II\nby Yaoxiang Wen (Korea Institute For Advanced Study) a
s part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 3598.\n\
nAbstract\nIn the second talk\, I will focus on the moduli space of parabo
lic Higgs bundles of type B and C. With the mirror pair of parabolic struc
tures (or nilpotent orbits)\, I will briefly explain how to prove SYZ and
topological mirror symmetries. The main ingredient here is the local parab
olic Higgs bundles\, which serve as a bridge between classical and global.
This talk is based on the in-progress joint work with X. Su\, B. Wang\, a
nd X. Wen.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaoxiang Wen (Korea Institute For Advanced Study)
DTSTART:20231113T070000Z
DTEND:20231113T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/27
DESCRIPTION:Title: Mirror symmetries for parabolic Hitchin systems\, from classical
to global\, I\nby Yaoxiang Wen (Korea Institute For Advanced Study) as
part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 5510.\n\n
Abstract\nIn the first talk\, I will briefly review the Hitchin system's h
istory and mirror symmetries. Then\, mention our motivation for the parabo
lic Hitchin system. I will explain how the parabolic structures connect to
nilpotent orbits. In the rest of the talk\, I will explain the mirror sym
metry for nilpotent orbit closures\, i.e.\, the classical mirror symmetry.
This talk is mainly based on the joint work with B. Fu and Y. Ruan (arXiv
:2207.10533).\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (Peking University)
DTSTART:20231127T070000Z
DTEND:20231127T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/28
DESCRIPTION:Title: Quantum Bruhat graphs and tilted Richardson varieties\nby Yib
o Gao (Peking University) as part of Algebra and Geometry Seminar @ HKUST\
n\nLecture held in 3598.\n\nAbstract\nThe quantum Bruhat graph is introduc
ed by Brenti-Fomin-Postnikov to study structure constants of the quantum c
ohomology ring of the flag variety\, with very rich combinatorial structur
es. In this talk\, we provide an explicit formula for the minimal degree a
ppearing in the quantum product of any two Schubert classes. Building upon
that\, we obtain an Ehresmann-like criterion for the tilted Bruhat order
studied by Brenti-Fomin-Postnikov. These results motivate the definition o
f tilted Richardson varieties\, which provide geometrical interpretations
of tilted Bruhat orders. Tilted Richardson varieties are indexed by pairs
of permutations and generalize Richardson varieties in the flag variety. M
oreover\, they equal the two-pointed curve neighborhoods of opposite Schub
ert varieties studied by Buch-Chaput-Mihalcea-Perrin. We establish several
geometrical properties of tilted Richardson varieties including a Deodhar
-like decomposition. This is a joint work with Jiyang Gao and Shiliang Gao
.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20240111T073000Z
DTEND:20240111T090000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/29
DESCRIPTION:Title: Okounkov's conjecture via BPS Lie algebras\nby Ben Davison (U
niversity of Edinburgh) as part of Algebra and Geometry Seminar @ HKUST\n\
nLecture held in 4503.\n\nAbstract\nGiven an arbitrary finite quiver Q\, M
aulik and Okounkov defined a new Yangian-style quantum group. It is built
via their construction of R matrices on the cohomology of Nakajima quiver
varieties\, which in turn is constructed via their construction of stable
envelopes. Just as in the case of ordinary Yangians\, there is a Lie algeb
ra g_Q inside their new algebra\, and the Yangian is a deformation of the
current algebra of this Lie algebra.\n\nOutside of extended ADE type\, num
erous basic features of g_Q have remained mysterious since the outset of t
he subject\, for example\, the dimensions of the graded pieces. A conjectu
re of Okounkov predicts that these dimensions are given by the coefficient
s of Kac's polynomials\, which count isomorphism classes of absolutely ind
ecomposable Q-representations over finite fields. I will present a recent
result with Tommaso Botta: we prove that the Maulik-Okounkov Lie algebra g
_Q is isomorphic to a certain BPS Lie algebra constructed in my previous w
ork with Sven Meinhardt. This implies Okounkov's conjecture\, as well as
essentially determining g_Q\, thanks to recent joint work of myself with H
ennecart and Schlegel Mejia.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Unive
rsity)
DTSTART:20240115T070000Z
DTEND:20240115T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/30
DESCRIPTION:Title: Wall-crossing formula I. Stable quasimaps and their wall-crossing
formula\nby Yang Zhou (Shanghai Center for Mathematical Sciences\, Fu
dan University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in 1410.\n\nAbstract\nIn this lecture\, we will introduce the notion
of quasimaps and their stability conditions. We will establish the essent
ial geometric properties of the moduli of epsilon-stable quasimaps. After
defining the small I-function using quasimap graph space\, we will introdu
ce the quasi-map wall-crossing formula and explain its geometric meaning.\
n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Unive
rsity)
DTSTART:20240117T080000Z
DTEND:20240117T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/31
DESCRIPTION:Title: Wall-crossing formula II. The master space technique and its appl
ication to weighted pointed curves\nby Yang Zhou (Shanghai Center for
Mathematical Sciences\, Fudan University) as part of Algebra and Geometry
Seminar @ HKUST\n\nLecture held in 1410.\n\nAbstract\nThe master space tec
hnique is an important tool for proving the wall-crossing formula. In this
lecture\, we will demonstrate this technique via a simple example\, namel
y\, the moduli of weighted pointed curves.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Unive
rsity)
DTSTART:20240122T070000Z
DTEND:20240122T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/32
DESCRIPTION:Title: Wall-crossing formula III. Entangled tails and the wall-crossing
formula\nby Yang Zhou (Shanghai Center for Mathematical Sciences\, Fud
an University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in 1410.\n\nAbstract\nIn this lecture\, we will introduce the notion
of weighted prestable curves with entangled tails. Combining that with the
master space technique\, we will prove the quasimaps wall-crossing formul
a for a general GIT quotient.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Unive
rsity)
DTSTART:20240124T070000Z
DTEND:20240124T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/33
DESCRIPTION:Title: Wall-crossing formula IV. Applications and generalizations\nb
y Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan University)
as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 1410.\
n\nAbstract\nIn this lecture\, we will discuss some applications and gener
alizations of the quasimaps wall-crossing formula. The applications includ
e the genus 1 Lefschetz hyperplane principle and the genus 0 orbifold Grom
ov-Witten invariants for non-convex complete intersections. One generaliza
tion (of the idea of stable quasimaps) is a notion of Omega-stable Mixed-S
pin-P fields for GIT quotients.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Unive
rsity)
DTSTART:20240125T070000Z
DTEND:20240125T083000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/34
DESCRIPTION:Title: Wall-crossing formula V. Applications and generalizations\nby
Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan University)
as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 2504.\n
\nAbstract\nIn this lecture\, we will discuss some applications and genera
lizations of the quasimaps wall-crossing formula. The applications include
the genus 1 Lefschetz hyperplane principle and the genus 0 orbifold Gromo
v-Witten invariants for non-convex complete intersections. One generalizat
ion (of the idea of stable quasimaps) is a notion of Omega-stable Mixed-Sp
in-P fields for GIT quotients.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (The University of Edinburgh)
DTSTART:20240306T080000Z
DTEND:20240306T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/35
DESCRIPTION:Title: Quantum A-polynomial from TQFT\nby David Jordan (The Universi
ty of Edinburgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLectur
e held in 2405.\n\nAbstract\nThe classical A-polynomial of a knot encodes
the "peripheral map" from the fundamental group of the two-torus to the fu
ndamental group of the knot complement. Much work has gone into studying
various q-deformations of the A-polynomial\, known as the quantum A-polyno
mial\, and its relationship to the Jones polynomial. In this talk\, I wil
l report on joint work with Jennifer Brown\, which constructs the quantum
A-polynomial using skein modules with defects\, refining an earlier constr
uction of Dimofte involving cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaowei Wang (Rutgers University)
DTSTART:20240131T083000Z
DTEND:20240131T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/36
DESCRIPTION:Title: Moment map and convex function\nby Xiaowei Wang (Rutgers Univ
ersity) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in
4472.\n\nAbstract\nThe concept moment map plays a central role in the stu
dy of Hamiltonian actions of compact Lie groups $K$ on symplectic manifold
s $(Z\, \\omega)$. In this talk\, we propose a theory of moment maps coupl
ed with an $Ad_K$-invariant convex function $f$ on $\\mathfrak{t}^*$\, the
dual of Lie algebra of $K$\, and study the structure of the stabilizer of
the critical point of $f\\circ\\mu$ with moment map $\\mu: Z \\to \\mathf
rak{t}^*$. This work is motivated by the work of Donaldson on Ding functio
nal\, which is an example of infinite dimensional version of our setting.
In particular\, we obtain a natural interpretation of Tian-Zhu's generaliz
ed Futaki-invariant and Calabi-decomposition.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaobo Liu (Peking University)
DTSTART:20240227T020000Z
DTEND:20240227T033000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/37
DESCRIPTION:Title: Tautological Relations and Their Applications\nby Xiaobo Liu
(Peking University) as part of Algebra and Geometry Seminar @ HKUST\n\nLec
ture held in 3598.\n\nAbstract\nRelations among tautological classes on mo
duli spaces of stable curves have important applications in cohomological
field theory. For example\, relations among psi-classes and boundary class
es give universal equations for generating functions of Gromov-Witten inva
riants of all compact symplectic manifolds. In this talk\, I will talk abo
ut such relations and their applications to Gromov-Witten theory and integ
rable systems.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaobo Liu (Peking University)
DTSTART:20240227T083000Z
DTEND:20240227T100000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/38
DESCRIPTION:Title: Intersection numbers and symmetric polynomials\nby Xiaobo Liu
(Peking University) as part of Algebra and Geometry Seminar @ HKUST\n\nLe
cture held in 4503.\n\nAbstract\nGenerating functions of intersection numb
ers on moduli spaces of curves provide geometric solutions to integrable s
ystems. Notable examples are the Kontsevich-Witten tau function and Brezin
-Gross-Witten tau function. In this talk I will first describe how to use
Schur's Q-polynomials to obtain simple formulas for these functions. I wil
l then discuss possible extensions for more general geometric models using
Hall-Littlewood polynomials. This talk is based on joint works with Cheng
lang Yang.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexis Bouthier (Sorbonne Université – Campus Pierre et Marie C
urie)
DTSTART:20240228T083000Z
DTEND:20240228T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/39
DESCRIPTION:Title: Torsors on loop groups\nby Alexis Bouthier (Sorbonne Universi
té – Campus Pierre et Marie Curie) as part of Algebra and Geometry Semi
nar @ HKUST\n\nLecture held in 2303.\n\nAbstract\nFor various applications
in geometric representation theory\, such as affine Springer theory or th
e more recent Ben-Zvi--Sakellaridis--Venkatesh program\, it has become nec
essary to develop a set of foundational results on loop space and torsors
on loop groups. We will survey different techniques on them and explain ho
w they can be applied to explicit situations.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yucheng Liu (Chongqing University)
DTSTART:20240229T080000Z
DTEND:20240229T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/40
DESCRIPTION:Title: Continuum envelopes on Fargues-Fontaine curve and elliptic curves
\nby Yucheng Liu (Chongqing University) as part of Algebra and Geometr
y Seminar @ HKUST\n\nLecture held in 4472.\n\nAbstract\nAbstract: In this
talk\, I will discuss some of the applications of Bridgeland stability con
ditions\, which was originated from string theory\, on Fargues-Fontaine cu
rve. This leads us to the notion of continuum \nenvelope on the curve and
SL(2\,Z) variants of Colmez-Fontaine‘s division algebra. Fargues-Fontain
e curve presents strong similarity to elliptic curves and noncommutative t
ori in this perspective.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (Università degli Studi di Milano)
DTSTART:20240305T083000Z
DTEND:20240305T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/41
DESCRIPTION:Title: Stability conditions: from curve to hyperkaehler manifolds (I)\nby Paolo Stellari (Università degli Studi di Milano) as part of Algeb
ra and Geometry Seminar @ HKUST\n\nLecture held in 4503.\n\nAbstract\nIn t
hese lectures we will review the basic material about stability conditions
and focus on examples. We will start reviewing the simplest example given
by algebraic curves and illustrate how this allows us to move to higher d
imensions passing through the case of noncommutative surfaces. The goal is
to illustrate how to construct stability conditions on special hyperkaehl
er manifolds which are Hilbert schemes of points on special K3 surfaces an
d to apply this to the geometry of hyperkaehler manifolds. The new results
are a joint work in progress with Chunyi Li\, Emanuele Macri'\, Alex Perr
y and Xiaolei Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (Università degli Studi di Milano)
DTSTART:20240307T083000Z
DTEND:20240307T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/42
DESCRIPTION:Title: Stability conditions: from curve to hyperkaehler manifolds (II)\nby Paolo Stellari (Università degli Studi di Milano) as part of Alge
bra and Geometry Seminar @ HKUST\n\nLecture held in 5510.\n\nAbstract\nIn
these lectures we will review the basic material about stability condition
s and focus on examples. We will start reviewing the simplest example give
n by algebraic curves and illustrate how this allows us to move to higher
dimensions passing through the case of noncommutative surfaces. The goal i
s to illustrate how to construct stability conditions on special hyperkaeh
ler manifolds which are Hilbert schemes of points on special K3 surfaces a
nd to apply this to the geometry of hyperkaehler manifolds. The new result
s are a joint work in progress with Chunyi Li\, Emanuele Macri'\, Alex Per
ry and Xiaolei Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (Academia Sinica)
DTSTART:20240430T083000Z
DTEND:20240430T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/43
DESCRIPTION:Title: Universal Virasoro constraints for quivers with relations\nby
Arkadij Bojko (Academia Sinica) as part of Algebra and Geometry Seminar @
HKUST\n\nLecture held in 3598.\n\nAbstract\nThe recent reformulation of s
heaf-theoretic Virasoro constraints opens many doors for future research.
In particular\, one may consider its analog for quivers. After phrasing a
universal approach to Virasoro constraints for moduli of quiver-representa
tions\, I will sketch their proof for any finite quiver with relations\, w
ith frozen vertices\, but without cycles. I will use partial flag varietie
s which are a special case of moduli of framed representations as a guidin
g example throughout. Using derived equivalences to quivers with relation
s\, I give self-contained proofs of Virasoro constraints for all Gieseker
semistable sheaves on $S = \\mathbb{P}^2\,\\mathbb{P}^1 \\times \\mathbb{
P}^1$\, and $\\mathrm{Bl}_\\mathrm{pt}\\mathbb{P}^2$. Combined with an exi
sting universality argument for Virasoro constraints on Hilbert schemes of
points of surface\, this leads to a proof for any $S$ which is independen
t of the previous results in GW theory.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (Academia Sinica)
DTSTART:20240502T083000Z
DTEND:20240502T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/44
DESCRIPTION:Title: Wall-crossing for Calabi-Yau fourfolds and applications\nby A
rkadij Bojko (Academia Sinica) as part of Algebra and Geometry Seminar @ H
KUST\n\nLecture held in 3598.\n\nAbstract\nMy work focuses on proving wall
-crossing for sheaves and pairs on Calabi-Yau fourfolds. It is desirable t
hat the end result can have many concrete applications to existing conject
ures. For this purpose\, I introduce a new structure into the picture - fo
rmal families of vertex algebras. Apart from being a natural extension of
the vertex algebras introduced by Joyce\, they allow to wall-cross with in
sertions instead of the plain virtual fundamental classes. Many fundament
al hurdles needed to be overcome to prove wall-crossing in this setting. T
hey included constructing Calabi-Yau four obstruction theories on (enhance
d) master spaces and showing that the invariants counting semistable torsi
on-free sheaves are well-defined. At the end\, I will use the complete pac
kage to address existing conjectures with applications to 3-fold DT/PT cor
respondences.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cailan Li (Columbia University)
DTSTART:20240410T060000Z
DTEND:20240410T073000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/45
DESCRIPTION:Title: Ext enhanced Soergel bimodules\, link homology\, and Gomi's trace
\nby Cailan Li (Columbia University) as part of Algebra and Geometry S
eminar @ HKUST\n\nLecture held in 2126D.\n\nAbstract\nSoergel Bimodules be
gan as an alternative approach to proving the illustrious Kazhdan-Lusztig
conjectures and have since become a cornerstone of representation theory a
nd link homology. In this talk\, we will give a diagrammatic presentation
for Ext groups between Soergel Bimodules in rank 2 à la Elias-Khovanov an
d Elias-Williamson. We then use our results to (1) show how it helps with
computing triply graded link homology for braids on 3 strands (2) show how
Ext groups of Soergel Bimodules in rank 2 categorifies Gomi's Trace\, a g
eneralization of Markov's trace to the Hecke algebra of any finite Coxeter
group.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240501T083000Z
DTEND:20240501T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/46
DESCRIPTION:Title: Higher Segal spaces and algebraic structures\nby Walker Stern
(Bilkent University) as part of Algebra and Geometry Seminar @ HKUST\n\nL
ecture held in 3598.\n\nAbstract\nIn this talk\, I will introduce the 2-Se
gal conditions of Dyckerhoff and Kapranov\, describing both the algebraic
and geometric intuitions which lead to the 2-Segal conditions. I will then
give an overview of how the algebraic intuition can be extended to classi
fy various algebraic structures in (higher) categories of spans. I will ad
ditionally explain how the geometric intuition can be used to provide stat
e-sum-style invariants of surfaces. Time permitting\, I will then discuss
work in progress on higher cyclic operads\, inspired by intuitions which a
rise from the algebraic characterization of 2-Segal objects.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuai Guo (Peking University)
DTSTART:20240417T083000Z
DTEND:20240417T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/47
DESCRIPTION:Title: Conjectural structures for Calabi-Yau threefolds\nby Shuai Gu
o (Peking University) as part of Algebra and Geometry Seminar @ HKUST\n\nL
ecture held in 4472.\n\nAbstract\nIn this talk\, I will review the conject
ural structures for the Calabi-Yau threefold proposed by physists. And exp
lain how they solve the generating function by using these conjectures for
one-parameter models\, especially for the quintic threefold.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuai Guo (Peking University)
DTSTART:20240418T083000Z
DTEND:20240418T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/48
DESCRIPTION:Title: Mathematical approaches to the BCOV’s conjectures\nby Shuai
Guo (Peking University) as part of Algebra and Geometry Seminar @ HKUST\n
\nLecture held in 3598.\n\nAbstract\nIn this talk\, I will try to explain
the mathematical approaches to the BCOV’s conjectures. I will review the
definition of NMSP theory\, and how to use it to calculate the Gromov-Wit
ten potential for the quintic threefold and the Calabi-Yau hypersurface in
P2 x P2.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Chen (Rutgers University)
DTSTART:20240514T083000Z
DTEND:20240514T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/49
DESCRIPTION:Title: Symmetric polynomials and interpolation polynomials\nby Hong
Chen (Rutgers University) as part of Algebra and Geometry Seminar @ HKUST\
n\nLecture held in 4504.\n\nAbstract\nSymmetric polynomials---for example\
, Schur\, Jack\, and Macdonald polynomials---are classical objects in the
study of algebra\, representation theory\, and combinatorics. Interpolatio
n polynomials are certain inhomogeneous versions of Jack and Macdonald pol
ynomials. In this talk\, after reviewing some basics on symmetric polynomi
als\, I will introduce interpolation polynomials and discuss our recent wo
rk on their properties. As an application\, I will give a characterization
of the containment partial order in terms of Schur positivity or Jack pos
itivity. This result parallels the works of Cuttler--Greene--Skandera\, Sr
a\, and Khare--Tao\, which characterize two other partial orders in terms
of Schur positivity. This work is joint with Siddhartha Sahi.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20240507T083000Z
DTEND:20240507T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/50
DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, a
nd algebraic cycles I\nby Junliang Shen (Yale University) as part of A
lgebra and Geometry Seminar @ HKUST\n\nLecture held in Room 2408 (Lifts 17
/18)\, Academic Building\, HKUST.\n\nAbstract\nThis is a series of 3 talks
\, where we will focus on geometry and topology of abelian fibrations ---
these are maps whose general fibers are complex tori but special fibers ma
y be highly singular and complicated. The decomposition theorem of Beilins
on\, Bernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for s
tudying these maps\; Corti-Hanamura further conjectured that the sheaf-the
oretic BBDG decomposition is governed by algebraic cycles. In my talks\, I
will explain how to find these algebraic cycles for certain geometries. I
will start with the case of an abelian scheme (i.e.\, an abelian fibratio
n without singular fiber)\, where the desired cycles have been found by Be
auville and Deninger-Murre more than 30 years ago. Then I will discuss the
case with singular fibers. Our ultimate goal for this lecture series is t
o explain how to find the cycles for Hitchin’s integrable system. If tim
e permits\, I will discuss how/why these cycles can help us to understand
various cohomological and sheaf-theoretic questions/conjectures for the Hi
tchin system. Based on joint work (in progress) with Davesh Maulik and Qiz
heng Yin.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20240508T083000Z
DTEND:20240508T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/51
DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, a
nd algebraic cycles II\nby Junliang Shen (Yale University) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 2408 (Lifts 1
7/18)\, Academic Building\, HKUST.\n\nAbstract\nThis is a series of 3 talk
s\, where we will focus on geometry and topology of abelian fibrations ---
these are maps whose general fibers are complex tori but special fibers m
ay be highly singular and complicated. The decomposition theorem of Beilin
son\, Bernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for
studying these maps\; Corti-Hanamura further conjectured that the sheaf-th
eoretic BBDG decomposition is governed by algebraic cycles. In my talks\,
I will explain how to find these algebraic cycles for certain geometries.
I will start with the case of an abelian scheme (i.e.\, an abelian fibrati
on without singular fiber)\, where the desired cycles have been found by B
eauville and Deninger-Murre more than 30 years ago. Then I will discuss th
e case with singular fibers. Our ultimate goal for this lecture series is
to explain how to find the cycles for Hitchin’s integrable system. If ti
me permits\, I will discuss how/why these cycles can help us to understand
various cohomological and sheaf-theoretic questions/conjectures for the H
itchin system. Based on joint work (in progress) with Davesh Maulik and Qi
zheng Yin.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20240509T083000Z
DTEND:20240509T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/52
DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, a
nd algebraic cycles III\nby Junliang Shen (Yale University) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 2408 (Lifts
17/18)\, Academic Building\, HKUST.\n\nAbstract\nThis is a series of 3 tal
ks\, where we will focus on geometry and topology of abelian fibrations --
- these are maps whose general fibers are complex tori but special fibers
may be highly singular and complicated. The decomposition theorem of Beili
nson\, Bernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for
studying these maps\; Corti-Hanamura further conjectured that the sheaf-t
heoretic BBDG decomposition is governed by algebraic cycles. In my talks\,
I will explain how to find these algebraic cycles for certain geometries.
I will start with the case of an abelian scheme (i.e.\, an abelian fibrat
ion without singular fiber)\, where the desired cycles have been found by
Beauville and Deninger-Murre more than 30 years ago. Then I will discuss t
he case with singular fibers. Our ultimate goal for this lecture series is
to explain how to find the cycles for Hitchin’s integrable system. If t
ime permits\, I will discuss how/why these cycles can help us to understan
d various cohomological and sheaf-theoretic questions/conjectures for the
Hitchin system. Based on joint work (in progress) with Davesh Maulik and Q
izheng Yin.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Huang (Texas A&M University)
DTSTART:20240730T083000Z
DTEND:20240730T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/53
DESCRIPTION:Title: Syzygies of determinantal thickenings and gl(m|n) representations
\nby Amy Huang (Texas A&M University) as part of Algebra and Geometry
Seminar @ HKUST\n\nLecture held in Room 2463 (Lift 25/26).\n\nAbstract\nTh
e coordinate ring $S = \\mathbb{C}[x_{i\,j}]$ of space of $m \\times n$ ma
trices carries an action of the group $\\mathrm{GL}_m \\times \\mathrm{GL}
_n$ via row and column operations on the matrix entries. If we consider an
y $\\mathrm{GL}_m \\times \\mathrm{GL}_n$-invariant ideal $I$ in $S$\, the
syzygy modules $\\mathrm{Tor}_i(I\,\\mathbb{C})$ will carry a natural act
ion of $\\mathrm{GL}_m \\times \\mathrm{GL}_n$. Via BGG correspondence\, t
hey also carry an action of $\\bigwedge^{\\bullet} (\\mathbb{C}^m \\otimes
\\mathbb{C}^n)$. It is a result by Raicu and Weyman that we can combine t
hese actions together and make them modules over the general linear Lie su
peralgebra $\\mathfrak{gl}(m|n)$. We will explain how this works and how i
t enables us to compute all Betti numbers of any $\\mathrm{GL}_m \\times \
\mathrm{GL}_n$-invariant ideal $I$.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanze Chen (University of Alberta)
DTSTART:20240906T083000Z
DTEND:20240906T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/54
DESCRIPTION:Title: Whittaker coefficients of metaplectic Eisenstein series and multi
ple Dirichlet series\nby Yanze Chen (University of Alberta) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in 4472.\n\nAbstract
\nWe investigate the Whittaker coefficients of an Eisenstein series on a g
lobal metaplectic cover of a semisimple algebraic group induced from the B
orel subgroup and establish the relation with Weyl group multiple Dirichle
t series\, verifying a conjecture of Brubaker-Bump-Friedberg. This is a jo
int work with Manish Patnaik.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gufang Zhao (University of Melbourne)
DTSTART:20240911T080000Z
DTEND:20240911T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/55
DESCRIPTION:Title: Cousins of relative Donaldson-Thomas theory in dimension 4\nb
y Gufang Zhao (University of Melbourne) as part of Algebra and Geometry Se
minar @ HKUST\n\nLecture held in 4472.\n\nAbstract\nThe goal of this talk
is to give a few examples of moduli spaces originated from relative Donald
son-Thomas theory in dimension 4. Attempts in finding numerical invariants
via these moduli spaces lead to a question of functoriality of the cohomo
logy or K-theory of these moduli spaces. Invariants arising from the funct
oriality in examples will be given. The original parts of the talk are bas
ed on a project joint with Cao\, and partially with Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaping Yang (University of Melbourne)
DTSTART:20240913T080000Z
DTEND:20240913T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/56
DESCRIPTION:Title: Higher spin representations of the Yangian of sl_2 and R-matrices
\nby Yaping Yang (University of Melbourne) as part of Algebra and Geom
etry Seminar @ HKUST\n\nLecture held in 4472.\nAbstract: TBA\n\nFor the Ya
ngian of sl_2\, higher spin representations are tensor products of the eva
luation pullback of the $\\ell_i+1$-dimensional irreducible representation
s of sl_2\, where $\\ell_i$ are the highest weights. In my talk\, I will g
ive a geometric realization of the higher spin representations in terms of
the critical cohomology of representations of the quiver with potential o
f Bykov and Zinn-Justin. I will also talk about the construction of R-mat
rices via the lattice model and the weight functions.\n\nThis is based on
my joint work with Paul Zinn-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (Aalto University)
DTSTART:20241030T080000Z
DTEND:20241030T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/58
DESCRIPTION:Title: A Lie-theoretic generalization of some Hilbert schemes\nby Os
car Kivinen (Aalto University) as part of Algebra and Geometry Seminar @ H
KUST\n\nLecture held in Room 4475 (Lifts 25/26).\n\nAbstract\nI will intro
duce several varieties attached to a complex reductive group\, generalizin
g for example $\\mathsf{Hilb}^n(\\mathbb{C}^2)$ and Haiman’s isospectral
Hilbert scheme\, which pertain to the $\\mathsf{GL}_n$-case. I will then
explain what is currently known about these varieties (including some low-
rank examples) and what else one would like to know about them.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yau Wing Li (The University of Melbourne)
DTSTART:20240919T083000Z
DTEND:20240919T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/59
DESCRIPTION:Title: Endoscopy for affine Hecke category\nby Yau Wing Li (The Univ
ersity of Melbourne) as part of Algebra and Geometry Seminar @ HKUST\n\nLe
cture held in 5506.\n\nAbstract\nAffine Hecke categories are categorificat
ions of Iwahori-Hecke algebras\, which are essential in the classification
of irreducible representations of loop group LG with Iwahori-fixed vector
s. The affine Hecke category has a monodromic counterpart\, which contains
sheaves with prescribed monodromy under the left and right actions of the
maximal torus. We show that the neutral block of this monoidal category i
s equivalent to the neutral block of the affine Hecke category (with trivi
al torus monodromy) for the endoscopic group H. It is consistent with the
Langlands functoriality conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241113T084500Z
DTEND:20241113T094500Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/61
DESCRIPTION:Title: On the theory of double $\\infty$-categories I\nby Jaco Ruit
(Utrecht University) as part of Algebra and Geometry Seminar @ HKUST\n\nLe
cture held in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three t
alks aims to give a detailed introduction to double $\\infty$-categories.
Double $\\infty$-categories can be viewed as generalizations of $(\\infty\
,2)$-categories that admit two directions for morphisms. The series starts
by motivating these categorical constructions\, and we will see how these
appear in mathematics. We will discuss their definitions\, including diff
erent completeness assumptions. Moreover\, we will see how double $\\infty
$-categories can be used to model $(\\infty\,2)$-categories. We highlight
some important examples of double $\\infty$-categories throughout.\n\nWe
will then continue to study the notions of companionships and conjunctions
in double $\\infty$-categories. These are important and useful concepts t
hat can be used to describe the universal property of so-called squares co
nstructions\, as we will see. Moreover\, we will study functors between do
uble $\\infty$-categories and show that they assemble into double $\\infty
$-categories of functors with vertical and horizontal natural transformati
ons. We present a new result that characterizes the companions and conjoin
ts in these functor double $\\infty$-categories. On the way\, we will see
how this double categorical machinery can be specialized to prove results
in $(\\infty\,2)$-category theory.\n\nDuring the first talk\, we will reca
ll some relevant background material on $\\infty$-categories that will be
needed to follow the series. No knowledge of $(\\infty\,2)$-categories is
assumed.\n\nLecture series: On the theory of double $\\infty$-categories\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241120T084500Z
DTEND:20241120T094500Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/63
DESCRIPTION:Title: On the theory of double $\\infty$-categories III\nby Jaco Rui
t (Utrecht University) as part of Algebra and Geometry Seminar @ HKUST\n\n
Lecture held in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three
talks aims to give a detailed introduction to double $\\infty$-categories
. Double $\\infty$-categories can be viewed as generalizations of $(\\inft
y\,2)$-categories that admit two directions for morphisms. The series star
ts by motivating these categorical constructions\, and we will see how the
se appear in mathematics. We will discuss their definitions\, including di
fferent completeness assumptions. Moreover\, we will see how double $\\inf
ty$-categories can be used to model $(\\infty\,2)$-categories. We highlig
ht some important examples of double $\\infty$-categories throughout.\n\nW
e will then continue to study the notions of companionships and conjunctio
ns in double $\\infty$-categories. These are important and useful concepts
that can be used to describe the universal property of so-called squares
constructions\, as we will see. Moreover\, we will study functors between
double $\\infty$-categories and show that they assemble into double $\\inf
ty$-categories of functors with vertical and horizontal natural transforma
tions. We present a new result that characterizes the companions and conjo
ints in these functor double $\\infty$-categories. On the way\, we will se
e how this double categorical machinery can be specialized to prove result
s in $(\\infty\,2)$-category theory.\n \nDuring the first talk\, we will r
ecall some relevant background material on $\\infty$-categories that will
be needed to follow the series. No knowledge of $(\\infty\,2)$-categories
is assumed.\n\nLecture series: On the theory of double $\\infty$-categorie
s\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241115T090000Z
DTEND:20241115T103000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/64
DESCRIPTION:Title: On the theory of double $\\infty$-categories II\nby Jaco Ruit
(Utrecht University) as part of Algebra and Geometry Seminar @ HKUST\n\nL
ecture held in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three
talks aims to give a detailed introduction to double $\\infty$-categories.
Double $\\infty$-categories can be viewed as generalizations of $(\\infty
\,2)$-categories that admit two directions for morphisms. The series start
s by motivating these categorical constructions\, and we will see how thes
e appear in mathematics. We will discuss their definitions\, including dif
ferent completeness assumptions. Moreover\, we will see how double $\\inft
y$-categories can be used to model $(\\infty\,2)$-categories. We highligh
t some important examples of double $\\infty$-categories throughout.\n\nWe
will then continue to study the notions of companionships and conjunction
s in double $\\infty$-categories. These are important and useful concepts
that can be used to describe the universal property of so-called squares c
onstructions\, as we will see. Moreover\, we will study functors between d
ouble $\\infty$-categories and show that they assemble into double $\\inft
y$-categories of functors with vertical and horizontal natural transformat
ions. We present a new result that characterizes the companions and conjoi
nts in these functor double $\\infty$-categories. On the way\, we will see
how this double categorical machinery can be specialized to prove results
in $(\\infty\,2)$-category theory.\n\nDuring the first talk\, we will rec
all some relevant background material on $\\infty$-categories that will be
needed to follow the series. No knowledge of $(\\infty\,2)$-categories is
assumed.\n\nLecture series: On the theory of double $\\infty$-categories\
n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael McBreen (The Chinese University of Hong Kong)
DTSTART:20241023T080000Z
DTEND:20241023T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/65
DESCRIPTION:Title: The Hamiltonian reduction of hypertoric mirror symmetry\nby M
ichael McBreen (The Chinese University of Hong Kong) as part of Algebra an
d Geometry Seminar @ HKUST\n\nLecture held in 4475.\n\nAbstract\nI will de
scribe recent work with Vivek Shende and Peng Zhou\, which relates the Fuk
aya category of a multiplicative hypertoric variety to the Fukaya category
of its associated toric arrangement. This provides evidence for a general
conjecture which describes the `hamiltonian reduction' of a Fukaya catego
ry at singular values of the moment parameter. Despite the subject\, the t
alk should be accessible to someone unfamiliar with the Fukaya category.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiraku Nakajima (Kavli Institute for the Physics and Mathematics o
f the Universe)
DTSTART:20241106T080000Z
DTEND:20241106T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/66
DESCRIPTION:Title: Nilpotent orbits for classical groups\nby Hiraku Nakajima (Ka
vli Institute for the Physics and Mathematics of the Universe) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4475 (Lifts 2
5/26).\n\nAbstract\nKraft-Procesi realized nilpotent orbits for classical
groups as orthosymplectic quiver varieties\, which are defined as quiver v
arieties\, but replacing products of GL by products of O and Sp. Motivated
by study of Coulomb branches\, we introduce variants of these\, which rem
ove `bad' behavior of nilpotent orbit closures\, such as non-irreducibilit
y\, non-normality\, etc. This talk is based on on-going project with Finke
lberg and Hanany.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Pădurariu (CNRS\, IMJ-PRG\, Sorbonne Université)
DTSTART:20241220T030000Z
DTEND:20241220T043000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/68
DESCRIPTION:Title: Conjectural equivalences of derived categories of Higgs bundles\nby Tudor Pădurariu (CNRS\, IMJ-PRG\, Sorbonne Université) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 6580 (lift 2
7/28).\n\nAbstract\nI will report on joint work with Yukinobu Toda (partia
lly in progress) about the derived category of coherent sheaves of semista
ble Higgs bundles on a curve. \n\nThese categories have semiorthogonal dec
ompositions in certain categories analogous to the ``window categories”
of Halpern-Leistner\, Ballard-Favero-Katzarkov\, Špenko-Van den Bergh. In
the first half of the talk\, I will discuss the general theory of ``windo
w categories”.\n\nNext\, I will focus on two conjectural dualities. The
first is between semistable Higgs bundles of degree zero and a "limit" cat
egory. This equivalence aims to make precise the proposal of Donagi-Pantev
of considering the classical limit of the de Rham Langlands equivalence.
The second is a primitive version of the first\, and it relates categories
of sheaves on moduli of semistable Higgs bundles (for various degrees). T
his equivalence may be regarded as a version of the D-equivalence conjectu
re / SYZ mirror symmetry. We can prove (partial) versions of these conject
ures for topological K-theory of these categories.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Neguț (Swiss Federal Technology Institute of Lausanne (EPF
L))
DTSTART:20250214T083000Z
DTEND:20250214T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/69
DESCRIPTION:Title: q-characters for quantum loop groups\nby Andrei Neguț (Swiss
Federal Technology Institute of Lausanne (EPFL)) as part of Algebra and G
eometry Seminar @ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbst
ract\nq-characters are a mainstay of the representation theory of quantum
affine algebras. We generalize this theory to all quantum loop algebras\,
that underlie arbitrary Kac-Moody Lie algebras instead of just semisimple
Lie algebras\, as well as introduce new techniques for the computation of
q-characters.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Lauda (The University of Southern California)
DTSTART:20250226T080000Z
DTEND:20250226T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/70
DESCRIPTION:Title: Nonsemisimple Topological Quantum Computation\nby Aaron Lauda
(The University of Southern California) as part of Algebra and Geometry S
eminar @ HKUST\n\nLecture held in Room 4472 (Lifts 25/26).\n\nAbstract\nSi
nce the foundational work of Freedman\, Kitaev\, Larsen\, and Wang\, it ha
s been understood that 3-dimensional topological quantum field theories (T
QFTs)\, described via modular tensor categories\, provide a universal mode
l for fault-tolerant topological quantum computation. These TQFTs\, derive
d from quantum groups at roots of unity\, achieve modularity by semisimpli
fying their representation categories—discarding objects with quantum tr
ace zero. The resulting semisimple categories describe anyons whose braidi
ng enables robust quantum computation.\n\nThis talk explores recent advanc
es in low-dimensional topology\, focusing on the use of nonsemisimple cate
gories that retain quantum trace zero objects to construct new TQFTs. Thes
e nonsemisimple TQFTs surpass their semisimple counterparts\, distinguishi
ng topological features inaccessible to the latter. For physical applicati
ons\, unitarity is essential\, ensuring Hom spaces form Hilbert spaces. We
present joint work with Nathan Geer\, Bertrand Patureau-Mirand\, and Josh
ua Sussan\, where nonsemisimple TQFTs are equipped with a Hermitian struct
ure. This framework introduces Hilbert spaces with possibly indefinite met
rics\, presenting new challenges.\n\nWe further discuss collaborative work
with Sung Kim\, Filippo Iulianelli\, and Sussan\, demonstrating that nons
emisimple TQFTs enable universal quantum computation at roots of unity whe
re semisimple theories fail. Specifically\, we show how Ising anyons withi
n this framework achieve universality through braiding alone. The resultin
g braiding operations are deeply connected to the Lawrence-Krammer-Bigelow
representations\, with the Hermitian structure providing a nondegenerate
inner product grounded in quantum algebra.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (University of Pisa)
DTSTART:20250319T080000Z
DTEND:20250319T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/71
DESCRIPTION:Title: Cohomological Hall algebras of 1-dimensional sheaves and Yangians
\nby Francesco Sala (University of Pisa) as part of Algebra and Geomet
ry Seminar @ HKUST\n\nLecture held in Room 3598 (Lift 27-28).\n\nAbstract\
nThe first part of this talk provides a brief and gentle introduction to t
he theory of 2-dimensional cohomological Hall algebras. The second part fo
cuses on the introduction of the nilpotent cohomological Hall algebra COHA
(S\, Z) of coherent sheaves on a smooth quasi-projective complex surface S
set-theoretically supported on a closed subscheme Z. When S is the minima
l resolution of an ADE singularity and Z is the exceptional divisor\, I wi
ll describe how to characterize COHA(S\, Z) via the Yangian of the corresp
onding affine ADE quiver. This is a joint project with Emanuel Diaconescu\
, Mauro Porta\, Oliver Schiffmann\, and Eric Vasserot.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonte Gödicke (Universität Hamburg)
DTSTART:20250326T080000Z
DTEND:20250326T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/72
DESCRIPTION:Title: Multi-fusion categories from 2-Segal spaces\nby Jonte Gödick
e (Universität Hamburg) as part of Algebra and Geometry Seminar @ HKUST\n
\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nIn the study of 3-d
imensional Topological Quantum Field Theories (short TQFTs)\, certain mono
idal categories called multi-fusion categories are of fundamental importan
ce. Well-known examples of these arise from finite groups through a linear
ization construction. However\, it is less well-known that the same constr
uction can produce more interesting examples of monoidal structures from a
ny 2-Segal space. These include so-called Hall monoidal structures\, which
are anticipated to have interesting connections to quantum topology and T
QFTs.\n\nIn this talk\, I will classify those 2-Segal spaces that induce m
ulti-fusion categories. For this\, I will introduce a 2-categorical charac
terization of multi-fusion categories to translate questions about these m
onoidal structures to questions about homotopy coherent algebra in span ca
tegories. Afterwards\, I will discuss extensions of this to the context of
derived categories and derived TQFTs.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhao (Beijing Institute of Technology)
DTSTART:20250218T020000Z
DTEND:20250218T033000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/73
DESCRIPTION:Title: Grassmannian of two term complexes and instantons on the blow ups
\nby Yu Zhao (Beijing Institute of Technology) as part of Algebra and
Geometry Seminar @ HKUST\n\nLecture held in Room 2303 (Lift 17-18).\n\nAbs
tract\nThe semi-orthogonal decomposition of the cohomological theory of Gr
assmannian of two-term complexes is studied by a series paper of Jiang. In
this talk\, we will reinterpret it as a representation of the Clifford al
gebra.\n\n As an application\, we will explain a relation between the basi
c representation of the affine Lie algebra and the moduli space of the ins
tanton spaces on the blow up of a point in a surface. It verifies the pred
ictions of Li-Qin and Feigin-Gukov. Based on joint work with Qingyuan Jian
g and Wei-ping Li.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Rozenblyum (University of Toronto)
DTSTART:20250423T080000Z
DTEND:20250423T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/74
DESCRIPTION:Title: Higher traces and characters of finite groups of Lie type\nby
Nick Rozenblyum (University of Toronto) as part of Algebra and Geometry S
eminar @ HKUST\n\nLecture held in Room 2128B (Lift 19).\n\nAbstract\nI wil
l give a brief overview of the theory of traces in higher categories and e
xplain how this gives a new approach to the study of representation of fin
ite groups of Lie type. Given an algebraic group $G$ over a finite field $
\\mathbb{F}_q$\, I will explain how representations of $G(\\mathbb{F}_q)$
arise as traces of categorical representations of $G$. Moreover\, I will e
xplain the higher categorical origin of Deligne-Lusztig representations an
d give a new conceptual computation of their characters which explains the
ir regularity as a function of $q$. This is joint work with Gaitsgory and
Varshavsky.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20250514T080000Z
DTEND:20250514T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/75
DESCRIPTION:Title: Microlocal categorical sheaves on shifted symplectic spaces\n
by Adeel Khan (Academia Sinica) as part of Algebra and Geometry Seminar @
HKUST\n\nLecture held in Room 4502 (near Lift 25/26).\n\nAbstract\nI will
describe a ladder of conjectural $(n+1)$-categorical invariants associated
to $n$-shifted symplectic derived stacks. For $n=0$ these generalize cat
egories of microsheaves on smooth symplectic schemes (closely related to F
ukaya categories). For $n=-1$ and $-2$ they should recover (categorificat
ions of) Donaldson-Thomas invariants of Calabi-Yau three- and four-folds\,
respectively\, thus giving a microlocal perspective on Donaldson-Thomas i
nvariants.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khoa Bang Pham (University of Rennes)
DTSTART:20250528T080000Z
DTEND:20250528T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/76
DESCRIPTION:Title: Motivic Nearby Functors and Recent Developments\nby Khoa Bang
Pham (University of Rennes) as part of Algebra and Geometry Seminar @ HKU
ST\n\n\nAbstract\nIn the quest for discovering exotic spheres\, Milnor stu
died the topology of complex hypersurface singularities\, which eventually
led to the notion of Milnor fibers. Around the same time\, Grothendieck a
nd Deligne globalized this concept to define the nearby and vanishing cycl
es functors\, which later played a crucial role in the proof of the Weil c
onjectures. These foundational ideas\, introduced over half a century ago\
, have since evolved in various directions. In motivic homotopy theory\, a
notable descendant is the motivic nearby functor\, originally constructed
by J. Ayoub. This functor can be regarded as the ``seventh operation'' in
the yoga of six-functor formalism developed by Grothendieck’s school\,
and it exhibits many remarkable properties. In this talk\, I will introduc
e the theory of motivic nearby functors and discuss some recent developmen
ts.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Huang (The University of Southern California)
DTSTART:20250618T020000Z
DTEND:20250618T030000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/77
DESCRIPTION:Title: High-rank motivic degree-zero Donaldson--Thomas theory on singula
r curves\, and q-series\nby Yifeng Huang (The University of Southern C
alifornia) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held
in 4502 (Lifts 25/26).\n\nAbstract\nMy main point is that high-rank motiv
ic degree-zero DT invariants on singular curves appear to give infinite pr
oducts of Rogers--Ramanujan type. This is based on explicit computation of
certain Quot schemes\, which is where the new ideas and results lie\, but
this seems to be a new phenomenon that I cannot explain from physics or o
ther conceptual connection. For context\, the rank-1 case has been observe
d to relate to knot theory and Catalan combinatorics in the last decade (k
eyword: Oblomkov--Rasmussen--Shende conjecture). \n\nA down-to-earth state
ment that captures all the essence is the following (stated for the singul
ar curve $y^2=x^3$): For a random $n\\times n$ matrix $A$ over a finite fi
eld $\\mathbb{F}_q$\, what is the expected number of matrices $B$ such tha
t $AB=BA$ and $A^3=B^2$? It turns out that as $n\\to \\infty$\, the limiti
ng answer is $\\prod (1-q^{-i})$ over all positive $i$ congruent to $1\,4$
mod $5$\, the famous Rogers--Ramanujan infinite product. \n\nThe reported
results contain joint work with Ruofan Jiang (on the $y^2=x^n$ case) and
joint work in progress with RJ and Alexei Oblomkov (on the $y^m=x^n$ case
with $m\,n$ coprime).\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaif Hilman (University of Bonn)
DTSTART:20250903T080000Z
DTEND:20250903T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/78
DESCRIPTION:Title: Atiyah-Bott's fixed point theorem via categorification\nby Ka
if Hilman (University of Bonn) as part of Algebra and Geometry Seminar @ H
KUST\n\nLecture held in Room 4472 (Lift 25/26).\n\nAbstract\nA famous resu
lt of Atiyah and Bott in geometric topology says that a smooth action by a
cyclic p-group on a smooth closed orientable manifold cannot have just a
single fixed point when p is an odd prime. This result was proved using th
e Atiyah-Singer index theorem. In this talk\, I will explain a different\,
purely homotopical\, proof which in particular exhibits that the theorem
is really a consequence of ``global'' homotopical reasons rather than ``lo
cal'' geometric ones. To this end\, I will introduce a theory of Poincare
duality for arbitrary topoi together with a suite of ``basechange'' princi
ples. I will then sketch how this abstract theory reduces the theorem to a
n elementary Tate cohomology calculation by working with an equivariant to
pos. This is based on joint work with D. Kirstein and C. Kremer from arXiv
:2405.17641.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhao (Beijing Institute of Technology)
DTSTART:20251001T080000Z
DTEND:20251001T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/80
DESCRIPTION:Title: The affine super Yangian of $\\mathfrak{gl}(1|1)$\nby Yu Zhao
(Beijing Institute of Technology) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 4504 (Lifts 25/26).\n\nAbstract\nNakajima
and Vafa-Witten noticed that the blow up formulae for the partition funct
ions of Euler numbers on the instanton moduli space is the character of af
fine vertex algebra at level 1\, and asked the CFT explanation. Together w
ith Jiang and Li\, we answered this question. However\, our proof leaves m
ore questions: how do we explain the Donaldson polynomials and the Seiberg
-Witten prepotential as correlation functions in Liouville theory? In this
talk\, I will discuss the affine Yangian of $\\mathfrak{gl}(1|1)$\, and d
iscuss how to solve the above problems through a larger algebra action.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Minets (Max Planck Institute for Mathematics)
DTSTART:20251119T080000Z
DTEND:20251119T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/81
DESCRIPTION:Title: Ersatz parity sheaves and stratifications of algebras\nby Sas
ha Minets (Max Planck Institute for Mathematics) as part of Algebra and Ge
ometry Seminar @ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstr
act\nMany important algebras\, notably quiver Hecke algebras\, can be real
ized as Ext-algebras of constructible sheaves on a given space. Since repr
esentation theorists like highest weight categories\, they want to know wh
en such algebras are quasi-hereditary (or polynomially quasi-hereditary\,
or properly stratified\, etc). In characteristic 0\, Kato proved a rather
general result of this sort\, under the assumption that the space has fini
tely many orbits under the action of an algebraic group. This was extended
to characteristic p by McNamara\, substituting perverse sheaves technique
s for parity sheaves of Juteau-Mautner-Williamson. Unfortunately\, this ap
proach do not apply to quiver Hecke algebras beyond Dynkin type. I will ex
plain how to extend the theory of parity sheaves to cover the first non-tr
ivial case of Kronecker quiver\, and speculate about how to approach other
affine types. Based on arXiv:2504.17430\, joint with R. Maksimau.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xun Lin (Hong Kong University of Science and Technology)
DTSTART:20251008T080000Z
DTEND:20251008T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/82
DESCRIPTION:Title: An introduction to (infinitesimal) categorical torelli\nby Xu
n Lin (Hong Kong University of Science and Technology) as part of Algebra
and Geometry Seminar @ HKUST\n\nLecture held in Room 2405 (Lifts 17/18).\n
\nAbstract\nIn the first part\, I will talk about the categorical torelli.
We prove the Kuznetsov components of a series of hypersurface in projecti
ve space reconstruct the hypersurfaces. Our method allow us to work for hy
persurfaces in weighted projective space\, and prove the reconstruction th
eorem for veronese double cone\, which is a long-time open case. Joint wit
h J. Rennemo and Shizhuo Zhang. In the second part\, I will talk about the
infinitesimal categorical torelli for Fano 3-folds. I will prove the cla
ssical infinitesimal torelli for Fano 3-folds using the infinitesimal cate
gorical torelli\, especially for special Gushel-Mukai 3-folds. Joint with
Shizhuo Zhang and Zheng Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaolei Zhao (University of California\, Santa Barbara)
DTSTART:20251203T080000Z
DTEND:20251203T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/83
DESCRIPTION:Title: Non-commutative abelian surfaces and Kummer type hyperkähler man
ifolds\nby Xiaolei Zhao (University of California\, Santa Barbara) as
part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4504
(Lift 25/26).\n\nAbstract\nExamples of non-commutative K3 surfaces arise f
rom semiorthogonal decompositions of the bounded derived category of certa
in Fano varieties. The most interesting cases are those of cubic fourfolds
and Gushel-Mukai varieties of even dimension. Using the deep theory of fa
milies of stability conditions\, locally complete families of hyperkähler
manifolds deformation equivalent to Hilbert schemes of points on a K3 sur
face have been constructed from moduli spaces of stable objects in these n
on-commutative K3 surfaces. On the other hand\, an explicit description of
a locally complete family of hyperkähler manifolds deformation equivalen
t to a generalized Kummer variety is not yet available.\n\nIn this talk we
will construct families of non-commutative abelian surfaces as equivarian
t categories of the derived category of K3 surfaces which specialize to Ku
mmer K3 surfaces. Then we will explain how to induce stability conditions
on them and produce examples of locally complete families of hyperkähler
manifolds of generalized Kummer deformation type. Applications to abelian
fourfolds of Weil type will be discussed.\n\nThis is joint work in prepara
tion with Arend Bayer\, Alex Perry and Laura Pertusi.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinfeng Song (The Hong Kong University of Science and Technology)
DTSTART:20251126T080000Z
DTEND:20251126T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/84
DESCRIPTION:Title: Quantization of symmetric pairs\nby Jinfeng Song (The Hong Ko
ng University of Science and Technology) as part of Algebra and Geometry S
eminar @ HKUST\n\nLecture held in Room 1104 (Lift 19).\n\nAbstract\nCheval
ley group schemes are group schemes defined over the integers that paramet
rize connected reductive groups over algebraically closed fields as geomet
ric fibers. Symmetric subgroups are fixed point subgroups of reductive gro
ups under an involutions. In this talk\, we construct closed subgroup sche
mes of Chevalley group schemes that parametrize symmetric subgroups of red
uctive groups as geometric fibers. Our construction relies crucially on th
e theory of quantum symmetric pairs and thus naturally admits a quantizati
on. As applications\, we obtain deeper insights into the structures of sym
metric spaces and their embeddings\, yielding applications to their dual c
anonical basis\, good filtrations\, integral models\, etc. This is based o
n joint works with Huanchen Bao (NUS).\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Heidersdorf (Newcastle University)
DTSTART:20260401T080000Z
DTEND:20260401T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/85
DESCRIPTION:Title: Koszulity for semi-infinite highest weight categories\nby Tho
rsten Heidersdorf (Newcastle University) as part of Algebra and Geometry S
eminar @ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nKos
zul algebras are positively graded algebras with very amenable homological
properties. Typical examples are the polynomial ring over a field or the
exterior and symmetric algebra of a vector space. A category is called Kos
zul if it has a grading with which it is equivalent to the category of gra
ded modules over a Koszul algebra. A famous example (due to Soergel) is th
e principal block of category $\\mathcal{O}$ for a semisimple Lie algebra.
Koszulity is a very nice property but often very difficult to check. I wi
ll give a criterion which allows to check Koszulity in case the category i
s a graded semi-infinite highest weight category (which is a structure tha
t appears often in representation theory). This is joint work with Jonas N
ehme \nand Catharina Stroppel.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Germán Stefanich (Max Planck Institute for Mathematics)
DTSTART:20260422T080000Z
DTEND:20260422T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/86
DESCRIPTION:by Germán Stefanich (Max Planck Institute for Mathematics) as
part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 1104
(Lift 19).\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonte Gödicke (Max-Plank-Institute for Mathematics)
DTSTART:20260311T080000Z
DTEND:20260311T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/87
DESCRIPTION:Title: On a braided monoidal Hall 2-category\nby Jonte Gödicke (Max
-Plank-Institute for Mathematics) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nAppearing
in different incarnations\, Hall algebras play an important role in classi
cal representation theory. Broadly speaking\, the Hall algebra constructio
n associates to an abelian category $A$ an algebra of functions on the mod
uli of objects $M(A)$ of $A$.\n\nThe goal of this talk is to describe a tw
ofold categorification of the Hall algebra construction. This new construc
tion associates to an abelian category $A$ a lax-braided monoidal 2-catego
ry of 2-sheaves on $M(A)$. Even in the simplest case of the abelian catego
ry of vector spaces\, this construction yields a rich and highly structure
d object. Focusing on this example\, I will explain the construction in de
tail and describe why it is desirable from the perspective of categorified
representation theory.\n\nThis is joint work with Quoc Ho\, Yang Hu\, and
Walker Stern.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Technical University of Munich)
DTSTART:20260318T080000Z
DTEND:20260318T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/88
DESCRIPTION:Title: More about spans than you ever wanted to know\nby Walker Ster
n (Technical University of Munich) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nHigher ca
tegories of spans\, also called correspondences\, play a key role in many
algebraic and algebro-geometric constructions --- from six functor formali
sms to the constructions of Hall algebras. In this talk\, I will describe
the fundamental categorical structures which underpin ongoing research (jo
int with Jonte Gödicke\, Quoc Ho\, and Yang Hu) aimed at constructing bra
ided monoidal categories using higher categories of spans. In particular\,
I will explain a new approach to $(\\infty\,n)$-categories of spans and d
educe from it a new universal property which allows us to construct the $E
_2$ (braided) algebras described in last week's talk by Jonte Gödicke.\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Liu (Kavli IPMU)
DTSTART:20260429T080000Z
DTEND:20260429T093000Z
DTSTAMP:20260404T100014Z
UID:HKUST-AG/90
DESCRIPTION:by Henry Liu (Kavli IPMU) as part of Algebra and Geometry Semi
nar @ HKUST\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/HKUST-AG/90/
END:VEVENT
END:VCALENDAR