BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Harrison Chen (Academia Sinica)
DTSTART:20230224T070000Z
DTEND:20230224T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/1
DESCRIPTION:Title: Circle actions\, coherent Springer theory and classical Springer theory\nby Harrison Chen (Academia Sinica) as part of Algebra and Geometry Sem
inar @ HKUST\n\nLecture held in Room 5564.\n\nAbstract\nCoherent Springer
theory is related to the representation theory of p-adic groups\, and invo
lves the study of certain coherent sheaves on moduli stacks of Langlands p
arameters\, whose unipotent part is the derived loop space of the equivari
ant nilpotent cone. On the other hand\, classical Springer theory is rela
ted to the representation of finite groups of Lie type\, and involves the
study of certain constructible sheaves on the equivariant nilpotent cone i
tself. Passing between the two involves equivariant localization\, imposi
tion of circle equivariance\, and a Koszul duality. In the first part of
this talk\, we will give a gentle introduction to circle actions with many
examples. In the second part\, we will describe how this provides the me
chanism for passing between coherent and constructible sheaves.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ping Xu (Penn State University)
DTSTART:20230303T070000Z
DTEND:20230303T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/2
DESCRIPTION:Title: Duflo-Kontsevich type theorem for dg manifolds\nby Ping Xu (Penn Stat
e University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture h
eld in Room 4472.\n\nAbstract\nIn this talk\, we describe a Duflo-Kontsevi
ch type theorem for dg manifolds.\nThe Duflo theorem of Lie theory and the
Kontsevich theorem regarding the Hoschschild cohomology of complex manifo
lds can both be derived as special cases of this Duflo--Kontsevich type th
eorem for dg manifolds. This is joint work with Hsuan-Yi Liao and Mathieu
Stienon.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Le (The Australian National University)
DTSTART:20230315T070000Z
DTEND:20230315T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/3
DESCRIPTION:Title: Cluster structures on braid varieties\nby Ian Le (The Australian Nati
onal University) as part of Algebra and Geometry Seminar @ HKUST\n\nLectur
e held in 4621.\n\nAbstract\nMany varieties in Lie theory--partial flag va
rieties\, Schubert varieties\, moduli of local systems on surfaces--admit
cluster structures\, which give a combinatorial way of encoding quantum de
formations of these varieties. Braid varieties give a unifying framework f
or constructing these cluster structures. I will start by defining braid v
arieties and give some motivations coming from knot homology and mirror sy
mmetry. Then I will introduce the main tool\, Legendrian weaves\, which al
low us to construct clusters in a concrete and diagrammatic way. The diagr
ams will be familiar to anyone who has seen Soergel calculus. This is join
t work with Roger Casals\, Eugene Gorsky\, Mikhail Gorsky\, Linhui Shen an
d Jose Simental.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (École Polytechnique Fédérale de Lausanne)
DTSTART:20230419T070000Z
DTEND:20230419T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/4
DESCRIPTION:Title: Orbital L-functions and knot superpolynomials\nby Oscar Kivinen (Éco
le Polytechnique Fédérale de Lausanne) as part of Algebra and Geometry S
eminar @ HKUST\n\nLecture held in 4504.\n\nAbstract\nOrbital L-functions f
or GL(n) have appeared in a number of works related to automorphic represe
ntation theory. Their importance has recently been highlighted by Arthur.
It turns out that for function fields\, the local factors of these L-funct
ions have long been studied in algebraic geometry\, as Hilbert zeta functi
ons of curve singularities. Drawing inspiration from the Oblomkov-Rasmusse
n-Shende conjecture\, I will formulate a closely related conjecture equati
ng the local factors with what are essentially the knot superpolynomials i
ntroduced by Cherednik-Danilenko\, Dunfield-Gukov-Rasmussen\, and others.
This applies in the tamely ramified case over any non-archimedean local fi
eld\, even when there is no knot in the picture. I will then explain recen
t progress towards this conjecture.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhao Yu (Kavli IPMU)
DTSTART:20230322T070000Z
DTEND:20230322T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/5
DESCRIPTION:Title: Hecke Correspondences on smooth surfaces and categorical commutators\
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\, Negu
t constructed an action of the quantum toroidal algebra on the Grothendiec
k group of moduli space of stable sheaves\, which generalized the construc
tion of Nakajima\, Grojnowski\, Baranovsky in cohomology. In this talk\, w
e will obtain a weak categorification of Negut's action\, by constructing
explicit natural transformations and compute the categorical commutators o
f the positive and negative part.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (Universität Wuppertal)
DTSTART:20230405T070000Z
DTEND:20230405T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/6
DESCRIPTION:Title: A K-theoretic Approach to Geometric Representation Theory\nby Jens Eb
erhardt (Universität Wuppertal) as part of Algebra and Geometry Seminar @
HKUST\n\nLecture held in 5564.\n\nAbstract\nPerverse sheaves and intersec
tion cohomology are central objects in geometric representation theory. Th
is talk is about their long-lost K-theoretic cousins\, called K-motives. W
e will discuss definitions and basic properties of K-motives and explore p
otential applications to geometric representation theory. For example\, K-
motives shed a new light on Beilinson-Ginzburg-Soergel's Koszul duality
— a remarkable symmetry in the representation theory and geometry of two
Langlands dual reductive groups. We will see that this leads to a new “
universal” Koszul duality that does not involve any gradings or mixed ge
ometry which are as essential as mysterious in the classical approaches.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gufang Zhao (University of Melbourne)
DTSTART:20230426T070000Z
DTEND:20230426T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/7
DESCRIPTION:Title: Quasimaps to quivers with potentials\nby Gufang Zhao (University of M
elbourne) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held
in CYTG001.\n\nAbstract\nThis talk concerns non-compact GIT quotient of a
vector space\, in the presence of an abelian group action and an equivaria
nt regular function (potential) on the quotient. We define virtual counts
of quasimaps from prestable curves to the critical locus of the potential.
The construction borrows ideas from the theory of gauged linear sigma mod
els as well as recent development in shifted symplectic geometry and Donal
dson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual counts arisi
ng from quivers with potentials are discussed. This is based on work in pr
eparation\, in collaboration with Yalong Cao.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Frenkel (Yale University)
DTSTART:20230412T070000Z
DTEND:20230412T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/8
DESCRIPTION:Title: Representation Theory in Mathematics and Physics\nby Igor Frenkel (Ya
le University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in CYTG001.\n\nAbstract\nIn this talk\, we overview some central idea
s and historical developments of representation theory and its relations t
o other areas of mathematics and physics. We'll start with a brief review
of the sources and first successes of representation theory of finite and
finite-dimensional groups and its applications. Then we will recall the re
markable generalizations of this theory to central extensions of loop grou
ps and Virasoro group and consider further relations to mathematics and ph
ysics. We will describe the programs of "geometrization" and "categorifica
tion" of the previous results in representation theory developed since 90t
h and their successes. We conclude with potential new developments in repr
esentation theory and discuss some open problems.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingyuan Jiang (University of Edinburgh)
DTSTART:20230426T083000Z
DTEND:20230426T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/9
DESCRIPTION:Title: Derived projectivizations and Grassmannians and their applications\nb
y Qingyuan Jiang (University of Edinburgh) as part of Algebra and Geometry
Seminar @ HKUST\n\nLecture held in CYTG001.\n\nAbstract\nWe will explore
some applications of the Derived Algebraic Geometry (DAG)\, a powerful fra
mework developed by Toen-Vezzosi\, Lurie and many others. DAG allows us to
extend Grothendieck’s theory of projectivizations and Grassmannians of
sheaves to the cases of complexes. This derived extension is very useful f
or constructing and studying moduli spaces\, especially when the spaces ar
e singular and difficult to analyze in the classical framework. We will di
scuss the constructions of derived projectivizations and Grassmannians as
well as their properties\, with a focus on their applications to Abel maps
for singular curves and Hecke correspondences for smooth surfaces. \nBase
d on papers arXiv:2202.11636 and arXiv:2212.10488 and works in preparation
.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Minets (The University of Edinburgh)
DTSTART:20230510T030000Z
DTEND:20230510T043000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/10
DESCRIPTION:Title: A proof of $P=W$ conjecture\nby Sasha Minets (The University of Edin
burgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in
5564.\n\nAbstract\nLet $C$ be a smooth projective curve. The non-abelian H
odge theory of Simpson is a diffeomorphism between the character variety $
M_B$ of $C$ and the moduli of (semi)stable Higgs bundles $M_D$ on $C$. Sin
ce this diffeomorphism is not algebraic\, it induces an isomorphism of coh
omology rings\, but does not preserve finer information\, such as the weig
ht filtration. Based on computations in small rank\, de Cataldo-Hausel-Mig
liorini conjectured that the weight filtration on $H^*(M_B)$ gets sent to
the perverse filtration on $H^*(M_D)$\, associated to the Hitchin map. In
this talk\, I will explain a recent proof of this conjecture\, which cruci
ally uses the action of Hecke correspondences on $H^*(M_D)$. Based on join
t work with T. Hausel\, A. Mellit\, O. Schiffmann.\n
LOCATION:https://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:20260422T123036Z
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 part of Al
gebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5506.\n\nAbstra
ct\nGraded dimensions of rational vertex algebras are modular functions. T
he proof of this celebrated theorem by Y. Zhu centres on geometric objects
attached to elliptic curves known as conformal blocks\, and their behavio
ur in the limit as the underlying curve becomes singular. In this limit\,
roughly speaking\, conformal blocks pass to the degree zero Hochschild hom
ology of Zhu's associative algebra. On the other hand\, conformal blocks h
ave been interpreted by Beilinson and Drinfeld as the degree zero componen
t 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 vertex alg
ebras\, and in the process we discover relations with objects of number th
eory such as the Rogers-Ramanujan identity and its generalisations. This i
s joint work with R. Heluani and G. Andrews.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230811T060000Z
DTEND:20230811T070000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/12
DESCRIPTION:Title: Motives in Geometric Representation Theory I\nby Jens Eberhardt (Uni
versity of Wuppertal) as part of Algebra and Geometry Seminar @ HKUST\n\nL
ecture held in CYTG003.\n\nAbstract\nRecent constructions in motivic homot
opy theory offer exciting new applications in geometric representation the
ory. For example\, they allow to consider mixed perverse sheaves (a graded
version of perverse sheaves) with integral coefficients or K-motives (a K
-theoretic analogue of constructible sheaves).\n\nIn this lecture series\,
we will explain how to work with motives in practice. We focus on motivic
cohomology\, the motivic six functor formalism\, Tate motives\, and weigh
t structures. We will then explain the notion of stratified mixed Tate mot
ives which\, when specialized to (affine/partial) flag varieties\, yields
a geometric perspective on Koszul duality. Lastly\, we will introduce resu
lts and conjectures relating K-motives and the geometric Langlands program
.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230814T060000Z
DTEND:20230814T070000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/13
DESCRIPTION:Title: Motives in Geometric Representation Theory II\nby Jens Eberhardt (Un
iversity of Wuppertal) as part of Algebra and Geometry Seminar @ HKUST\n\n
Lecture held in Room 2503.\n\nAbstract\nRecent constructions in motivic ho
motopy theory offer exciting new applications in geometric representation
theory. For example\, they allow to consider mixed perverse sheaves (a gra
ded version of perverse sheaves) with integral coefficients or K-motives (
a K-theoretic analogue of constructible sheaves).\n\nIn this lecture serie
s\, we will explain how to work with motives in practice. We focus on moti
vic cohomology\, the motivic six functor formalism\, Tate motives\, and we
ight structures. We will then explain the notion of stratified mixed Tate
motives which\, when specialized to (affine/partial) flag varieties\, yiel
ds a geometric perspective on Koszul duality. Lastly\, we will introduce r
esults and conjectures relating K-motives and the geometric Langlands prog
ram.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230815T060000Z
DTEND:20230815T070000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/14
DESCRIPTION:Title: Motives in Geometric Representation Theory III\nby Jens Eberhardt (U
niversity of Wuppertal) as part of Algebra and Geometry Seminar @ HKUST\n\
nLecture held in Room 5510.\n\nAbstract\nRecent constructions in motivic h
omotopy theory offer exciting new applications in geometric representation
theory. For example\, they allow to consider mixed perverse sheaves (a gr
aded version of perverse sheaves) with integral coefficients or K-motives
(a K-theoretic analogue of constructible sheaves).\n\nIn this lecture seri
es\, we will explain how to work with motives in practice. We focus on mot
ivic cohomology\, the motivic six functor formalism\, Tate motives\, and w
eight structures. We will then explain the notion of stratified mixed Tate
motives which\, when specialized to (affine/partial) flag varieties\, yie
lds a geometric perspective on Koszul duality. Lastly\, we will introduce
results and conjectures relating K-motives and the geometric Langlands pro
gram.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230817T060000Z
DTEND:20230817T070000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/15
DESCRIPTION:Title: Motives in Geometric Representation Theory IV\nby Jens Eberhardt (Un
iversity of Wuppertal) as part of Algebra and Geometry Seminar @ HKUST\n\n
Lecture held in Room 5510.\n\nAbstract\nRecent constructions in motivic ho
motopy theory offer exciting new applications in geometric representation
theory. For example\, they allow to consider mixed perverse sheaves (a gra
ded version of perverse sheaves) with integral coefficients or K-motives (
a K-theoretic analogue of constructible sheaves).\n\nIn this lecture serie
s\, we will explain how to work with motives in practice. We focus on moti
vic cohomology\, the motivic six functor formalism\, Tate motives\, and we
ight structures. We will then explain the notion of stratified mixed Tate
motives which\, when specialized to (affine/partial) flag varieties\, yiel
ds a geometric perspective on Koszul duality. Lastly\, we will introduce r
esults and conjectures relating K-motives and the geometric Langlands prog
ram.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jens Eberhardt (University of Wuppertal)
DTSTART:20230818T060000Z
DTEND:20230818T070000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/16
DESCRIPTION:Title: Motives in Geometric Representation Theory V\nby Jens Eberhardt (Uni
versity of Wuppertal) as part of Algebra and Geometry Seminar @ HKUST\n\nL
ecture held in Room 5510.\n\nAbstract\nRecent constructions in motivic hom
otopy theory offer exciting new applications in geometric representation t
heory. For example\, they allow to consider mixed perverse sheaves (a grad
ed version of perverse sheaves) with integral coefficients or K-motives (a
K-theoretic analogue of constructible sheaves).\n\nIn this lecture series
\, we will explain how to work with motives in practice. We focus on motiv
ic cohomology\, the motivic six functor formalism\, Tate motives\, and wei
ght structures. We will then explain the notion of stratified mixed Tate m
otives which\, when specialized to (affine/partial) flag varieties\, yield
s a geometric perspective on Koszul duality. Lastly\, we will introduce re
sults and conjectures relating K-motives and the geometric Langlands progr
am.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dougal Davis (University of Melbourne)
DTSTART:20231009T070000Z
DTEND:20231009T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/17
DESCRIPTION:Title: Unitary representations of real groups and localisation theory for Hodge
modules\nby Dougal Davis (University of Melbourne) as part of Algebra
and Geometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nI
will explain recent joint work with Kari Vilonen\, in which we prove a co
njecture of Schmid and Vilonen linking mixed Hodge modules on flag varieti
es to unitary representations of real reductive Lie groups. The main idea
behind our work is to upgrade Beilinson-Bernstein localisation from D-modu
les to mixed Hodge modules. When it applies\, this endows everything in si
ght with a canonical filtration\, the Hodge filtration\, which we prove ha
s 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 t
hat this will lead to new progress on the very old problem of determining
the unitary dual of a real group.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucien Hennecart (The University of Edinburgh)
DTSTART:20231016T070000Z
DTEND:20231016T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/18
DESCRIPTION:Title: Cohomological integrality for 2-Calabi-Yau categories\nby Lucien Hen
necart (The University of Edinburgh) as part of Algebra and Geometry Semin
ar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nIn this talk\, I wil
l 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 cohomolo
gical Hall algebras (CoHAs) and their associated BPS algebras (in their as
sociative and Lie algebra versions). Important examples are given by repre
sentations of preprojective algebras of quivers and finite length sheaves
on surfaces. In the latter case\, we can recover the generating series of
Betti numbers of the moduli stack in an efficient way.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Campion (Johns Hopkins University)
DTSTART:20230925T070000Z
DTEND:20230925T083000Z
DTSTAMP:20260422T123036Z
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 Geometry
Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nSince Grothend
ieck\, the notion of an abelian 1-category has provided a natural setting
to do algebra which encompasses both categories of modules and categories
of sheaves. Since Lurie\, the notion of a stable $(\\infty\,1)$-category h
as provided a similar setting to do derived algebra\, encompassing derived
categories of modules and sheaves\, and improving upon the notion of a tr
iangulated category due to Verdier.\n\nIn this talk\, we discuss a few pos
sible notions of stable $(\\infty\,2)$-category\, motivated by enriched ca
tegory theory. Examples include the $(\\infty\,2)$-category of dg categori
es\, the $(\\infty\,2)$-category of stable $(\\infty\,1)$-categories\, and
various $(\\infty\,2)$-categories of stacks of stable $(\\infty\,1)$-cate
gories. The intention is to provide a natural home for the study of such $
(\\infty\,2)$-categories\, which are of interest in areas such as the Geom
etric Langlands program\, secondary algebraic K-theory\, and derived algeb
raic geometry.\n\nWe discuss work in progress on showing that our notions
of stable $(\\infty\,2)$-category are equivalent. As an application\, we s
how for example that every smooth and proper algebra over a regular commut
ative Noetherian ring k may be constructed from $k$ by iterating two simpl
e operations: glueing along a perfect bimodule\, and 2-idempotent splittin
g.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20231025T070000Z
DTEND:20231025T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/20
DESCRIPTION:Title: Microlocalization on derived moduli spaces\nby Adeel Khan (Academia
Sinica) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in
Room 5566.\n\nAbstract\nThe classical formalism of microlocal sheaf theor
y à la Kashiwara-Schapira is very useful in the study of manifolds. I wi
ll describe a generalization to the context of derived algebraic geometry\
, which is useful in the study of derived moduli spaces. For example\, I
will discuss how it gives a new perspective on topics like the virtual fun
damental class\, categorified Donaldson-Thomas theory\, and the critical o
r 3d cohomological Hall algebras of Kontsevich-Soibelman. Based on forthc
oming joint work with Tasuki Kinjo.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (colloquium) (Academia Sinica)
DTSTART:20231027T070000Z
DTEND:20231027T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/21
DESCRIPTION:Title: Derived Fourier analysis\nby Adeel Khan (colloquium) (Academia Sinic
a) as part of Algebra and Geometry Seminar @ HKUST\n\n\nAbstract\nI will d
iscuss incarnations of the Fourier transform in algebraic geometry and top
ology. Like its prototype\, these "sheafy" or categorified forms of Fouri
er analysis have proven unreasonably effective in applications. After giv
ing an overview of the sheaf-theoretic Fourier transform\, I will explain
a new "derived" version and some concrete problems in enumerative geometry
and number theory this abstract piece of machinery has proven useful for
so far.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Penghui Li (Tsinghua University)
DTSTART:20230927T070000Z
DTEND:20230927T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/22
DESCRIPTION:Title: Graded character sheaves\, HOMFLY-PT homology\, and Hilbert schemes of p
oints on $\\mathbb{C}^2$\nby Penghui Li (Tsinghua University) as part
of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4475.\n\nA
bstract\nUsing a geometric argument building on our new theory of graded s
heaves\, we compute the categorical trace and Drinfel'd center of the (gra
ded) finite Hecke category $\\mathsf{H}_W$ in terms of the category of (
graded) unipotent character sheaves\, upgrading results of Ben-Zvi-Nadler
and Bezrukavninov-Finkelberg-Ostrik. In type $A$\, we relate the categori
cal trace to the category of 2-periodic coherent sheaves on the Hilbert s
chemes of points on $\\mathbb{C}^2$ (equivariant with respect to the na
tural $\\mathbb{C}^* \\times \\mathbb{C}^*$ action)\, yielding a proof o
f a conjecture of Gorsky-Negut-Rasmussen which relates HOMFLY-PT link homo
logy and the spaces of global sections of certain coherent sheaves on Hil
bert schemes. As an important computational input\, we also establish a co
njecture of Gorsky-Hogancamp-Wedrich on the formality of the Hochschild ho
mology of $\\mathsf{H}_W$. This is a joint work with Quoc P. Ho.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aron Heleodoro (Hong Kong University)
DTSTART:20231030T070000Z
DTEND:20231030T083000Z
DTSTAMP:20260422T123036Z
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 Algebr
a and Geometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\n
Let $k$ be an algebraically closed field and $L=k((t))$\, for $G$ a connec
ted reductive algebraic group consider $\\breve G:= G(L)$. We establish a
semi-orthogonal decomposition indexed by Newton strata of $D(\\frac{\\brev
e G}{\\breve G})$\, the DG category of $\\breve G$-equivariant constructib
le etale sheaves on $\\breve G$. In this talk I will explain (1) how to co
nsider (ind-)constructible etale sheaves on such infinite-dimensional spac
es\, (2) what notion of semi-orthogonal decomposition we consider\, (3) th
e definiton of Newton strata and the geometric input about them we need fo
r the theory\, and (4) how this category relates to the affine Hecke categ
ory. This is joint work with Xuhua He.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kostiantyn Tolmachov (The University of Edinburgh)
DTSTART:20231011T070000Z
DTEND:20231011T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/24
DESCRIPTION:Title: Equivariant derived category of a reductive group as a categorical cente
r\nby Kostiantyn Tolmachov (The University of Edinburgh) as part of Al
gebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5566.\n\nAbstra
ct\nThere is a classical relationship between representations of the Iwaho
ri-Hecke algebra associated with a Weyl group of a split reductive group G
\, defined over a finite field\, and the (principal series) representation
s of the corresponding finite group of Lie type. I will discuss a categori
fication of this relationship in the context of various triangulated categ
ories of constructible sheaves on the group G. In particular\, I will pres
ent a new approach to connecting the categories of character sheaves to a
version of a categorical\ncenter of the constructible Hecke category. Base
d on a joint work with R. Bezrukavnikov\, A. Ionov\, and Y. Varshavsky.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamil Rychlewicz (Institute of Science and Technology Austria)
DTSTART:20231106T080000Z
DTEND:20231106T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/25
DESCRIPTION:Title: Cohomology theories and rings of functions\nby Kamil Rychlewicz (Ins
titute of Science and Technology Austria) as part of Algebra and Geometry
Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nExtending the c
lassical Poincare-Hopf theorem\, the work of Akyildiz\, Carrell\, Lieberma
nn\, Sommese shows how to recover the cohomology ring of a smooth projecti
ve variety from isolated zeros of a vector field. Thirty years later\, Bri
on and Carrell showed how to find the spectrum of the torus-equivariant co
homology as a geometrically defined scheme\, provided that the Borel of SL
_2 acts with a single fixed point of the regular unipotent. In a joint wor
k with Tamas Hausel we demonstrate how to see the spectrum of G-equivarian
t cohomology\, if G is a linear group acting with similar assumptions. Thi
s condition covers many interesting cases\, including flag varieties and B
ott–Samelson resolutions. I will present this work and also show how to
see the equivariant cohomology rings of spherical varieties as rings of fu
nctions on non-affine schemes. Besides\, there are a lot of new directions
and open questions I would like to advertise. This in particular concerns
general\, potentially singular varieties\, as well as other equivariant c
ohomology theories.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaoxiang Wen (Korea Institute For Advanced Study)
DTSTART:20231115T070000Z
DTEND:20231115T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/26
DESCRIPTION:Title: Mirror symmetries for parabolic Hitchin systems\, from classical to glob
al\, II\nby Yaoxiang Wen (Korea Institute For Advanced Study) as part
of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 3598.\n\nAbstra
ct\nIn the second talk\, I will focus on the moduli space of parabolic Hig
gs bundles of type B and C. With the mirror pair of parabolic structures (
or nilpotent orbits)\, I will briefly explain how to prove SYZ and topolog
ical mirror symmetries. The main ingredient here is the local parabolic Hi
ggs bundles\, which serve as a bridge between classical and global. This t
alk is based on the in-progress joint work with X. Su\, B. Wang\, and X. W
en.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaoxiang Wen (Korea Institute For Advanced Study)
DTSTART:20231113T070000Z
DTEND:20231113T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/27
DESCRIPTION:Title: Mirror symmetries for parabolic Hitchin systems\, from classical to glob
al\, I\nby Yaoxiang Wen (Korea Institute For Advanced Study) as part o
f Algebra and Geometry Seminar @ HKUST\n\nLecture held in 5510.\n\nAbstrac
t\nIn the first talk\, I will briefly review the Hitchin system's history
and mirror symmetries. Then\, mention our motivation for the parabolic Hit
chin system. I will explain how the parabolic structures connect to nilpot
ent orbits. In the rest of the talk\, I will explain the mirror symmetry f
or nilpotent orbit closures\, i.e.\, the classical mirror symmetry. This t
alk is mainly based on the joint work with B. Fu and Y. Ruan (arXiv:2207.1
0533).\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yibo Gao (Peking University)
DTSTART:20231127T070000Z
DTEND:20231127T083000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/28
DESCRIPTION:Title: Quantum Bruhat graphs and tilted Richardson varieties\nby Yibo Gao (
Peking University) as part of Algebra and Geometry Seminar @ HKUST\n\nLect
ure held in 3598.\n\nAbstract\nThe quantum Bruhat graph is introduced by B
renti-Fomin-Postnikov to study structure constants of the quantum cohomolo
gy ring of the flag variety\, with very rich combinatorial structures. In
this talk\, we provide an explicit formula for the minimal degree appearin
g 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 of tilte
d Richardson varieties\, which provide geometrical interpretations of tilt
ed Bruhat orders. Tilted Richardson varieties are indexed by pairs of perm
utations and generalize Richardson varieties in the flag variety. Moreover
\, they equal the two-pointed curve neighborhoods of opposite Schubert var
ieties studied by Buch-Chaput-Mihalcea-Perrin. We establish several geomet
rical properties of tilted Richardson varieties including a Deodhar-like d
ecomposition. This is a joint work with Jiyang Gao and Shiliang Gao.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20240111T073000Z
DTEND:20240111T090000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/29
DESCRIPTION:Title: Okounkov's conjecture via BPS Lie algebras\nby Ben Davison (Universi
ty of Edinburgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLectur
e held in 4503.\n\nAbstract\nGiven an arbitrary finite quiver Q\, Maulik a
nd Okounkov defined a new Yangian-style quantum group. It is built via the
ir construction of R matrices on the cohomology of Nakajima quiver varieti
es\, which in turn is constructed via their construction of stable envelop
es. Just as in the case of ordinary Yangians\, there is a Lie algebra g_Q
inside their new algebra\, and the Yangian is a deformation of the current
algebra of this Lie algebra.\n\nOutside of extended ADE type\, numerous b
asic features of g_Q have remained mysterious since the outset of the subj
ect\, for example\, the dimensions of the graded pieces. A conjecture of O
kounkov predicts that these dimensions are given by the coefficients of Ka
c's polynomials\, which count isomorphism classes of absolutely indecompos
able 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 i
somorphic to a certain BPS Lie algebra constructed in my previous work wit
h Sven Meinhardt. This implies Okounkov's conjecture\, as well as essenti
ally determining g_Q\, thanks to recent joint work of myself with Hennecar
t and Schlegel Mejia.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/30
DESCRIPTION:Title: Wall-crossing formula I. Stable quasimaps and their wall-crossing formul
a\nby Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Uni
versity) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held i
n 1410.\n\nAbstract\nIn this lecture\, we will introduce the notion of qua
simaps and their stability conditions. We will establish the essential geo
metric properties of the moduli of epsilon-stable quasimaps. After definin
g the small I-function using quasimap graph space\, we will introduce the
quasi-map wall-crossing formula and explain its geometric meaning.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/31
DESCRIPTION:Title: Wall-crossing formula II. The master space technique and its application
to weighted pointed curves\nby Yang Zhou (Shanghai Center for Mathema
tical Sciences\, Fudan University) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in 1410.\n\nAbstract\nThe master space technique
is an important tool for proving the wall-crossing formula. In this lectur
e\, we will demonstrate this technique via a simple example\, namely\, the
moduli of weighted pointed curves.\n
LOCATION:https://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:20260422T123036Z
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\, Fudan Univ
ersity) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in
1410.\n\nAbstract\nIn this lecture\, we will introduce the notion of weig
hted prestable curves with entangled tails. Combining that with the master
space technique\, we will prove the quasimaps wall-crossing formula for a
general GIT quotient.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/33
DESCRIPTION:Title: Wall-crossing formula IV. Applications and generalizations\nby Yang
Zhou (Shanghai Center for Mathematical Sciences\, Fudan University) as par
t of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 1410.\n\nAbst
ract\nIn this lecture\, we will discuss some applications and generalizati
ons of the quasimaps wall-crossing formula. The applications include the g
enus 1 Lefschetz hyperplane principle and the genus 0 orbifold Gromov-Witt
en invariants for non-convex complete intersections. One generalization (o
f the idea of stable quasimaps) is a notion of Omega-stable Mixed-Spin-P f
ields for GIT quotients.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/34
DESCRIPTION:Title: Wall-crossing formula V. Applications and generalizations\nby Yang Z
hou (Shanghai Center for Mathematical Sciences\, Fudan University) as part
of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 2504.\n\nAbstr
act\nIn this lecture\, we will discuss some applications and generalizatio
ns of the quasimaps wall-crossing formula. The applications include the ge
nus 1 Lefschetz hyperplane principle and the genus 0 orbifold Gromov-Witte
n invariants for non-convex complete intersections. One generalization (of
the idea of stable quasimaps) is a notion of Omega-stable Mixed-Spin-P fi
elds for GIT quotients.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Jordan (The University of Edinburgh)
DTSTART:20240306T080000Z
DTEND:20240306T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/35
DESCRIPTION:Title: Quantum A-polynomial from TQFT\nby David Jordan (The University of E
dinburgh) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held
in 2405.\n\nAbstract\nThe classical A-polynomial of a knot encodes the "pe
ripheral map" from the fundamental group of the two-torus to the fundament
al group of the knot complement. Much work has gone into studying various
q-deformations of the A-polynomial\, known as the quantum A-polynomial\,
and its relationship to the Jones polynomial. In this talk\, I will repor
t on joint work with Jennifer Brown\, which constructs the quantum A-polyn
omial using skein modules with defects\, refining an earlier construction
of Dimofte involving cluster algebras.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaowei Wang (Rutgers University)
DTSTART:20240131T083000Z
DTEND:20240131T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/36
DESCRIPTION:Title: Moment map and convex function\nby Xiaowei Wang (Rutgers University)
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 study of H
amiltonian actions of compact Lie groups $K$ on symplectic manifolds $(Z\,
\\omega)$. In this talk\, we propose a theory of moment maps coupled with
an $Ad_K$-invariant convex function $f$ on $\\mathfrak{t}^*$\, the dual o
f Lie algebra of $K$\, and study the structure of the stabilizer of the cr
itical point of $f\\circ\\mu$ with moment map $\\mu: Z \\to \\mathfrak{t}^
*$. This work is motivated by the work of Donaldson on Ding functional\, w
hich is an example of infinite dimensional version of our setting. In part
icular\, we obtain a natural interpretation of Tian-Zhu's generalized Futa
ki-invariant and Calabi-decomposition.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaobo Liu (Peking University)
DTSTART:20240227T020000Z
DTEND:20240227T033000Z
DTSTAMP:20260422T123036Z
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\nLecture he
ld in 3598.\n\nAbstract\nRelations among tautological classes on moduli sp
aces of stable curves have important applications in cohomological field t
heory. For example\, relations among psi-classes and boundary classes give
universal equations for generating functions of Gromov-Witten invariants
of all compact symplectic manifolds. In this talk\, I will talk about such
relations and their applications to Gromov-Witten theory and integrable s
ystems.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaobo Liu (Peking University)
DTSTART:20240227T083000Z
DTEND:20240227T100000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/38
DESCRIPTION:Title: Intersection numbers and symmetric polynomials\nby Xiaobo Liu (Pekin
g University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture h
eld in 4503.\n\nAbstract\nGenerating functions of intersection numbers on
moduli spaces of curves provide geometric solutions to integrable systems.
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 will then
discuss possible extensions for more general geometric models using Hall-L
ittlewood polynomials. This talk is based on joint works with Chenglang Ya
ng.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/39
DESCRIPTION:Title: Torsors on loop groups\nby Alexis Bouthier (Sorbonne Université –
Campus Pierre et Marie Curie) as part of Algebra and Geometry Seminar @ H
KUST\n\nLecture held in 2303.\n\nAbstract\nFor various applications in geo
metric representation theory\, such as affine Springer theory or the more
recent Ben-Zvi--Sakellaridis--Venkatesh program\, it has become necessary
to develop a set of foundational results on loop space and torsors on loop
groups. We will survey different techniques on them and explain how they
can be applied to explicit situations.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yucheng Liu (Chongqing University)
DTSTART:20240229T080000Z
DTEND:20240229T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/40
DESCRIPTION:Title: Continuum envelopes on Fargues-Fontaine curve and elliptic curves\nb
y Yucheng Liu (Chongqing University) as part of Algebra and Geometry Semin
ar @ HKUST\n\nLecture held in 4472.\n\nAbstract\nAbstract: In this talk\,
I will discuss some of the applications of Bridgeland stability conditions
\, which was originated from string theory\, on Fargues-Fontaine curve. Th
is leads us to the notion of continuum \nenvelope on the curve and SL(2\,Z
) variants of Colmez-Fontaine‘s division algebra. Fargues-Fontaine curve
presents strong similarity to elliptic curves and noncommutative tori in
this perspective.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (Università degli Studi di Milano)
DTSTART:20240305T083000Z
DTEND:20240305T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/41
DESCRIPTION:Title: Stability conditions: from curve to hyperkaehler manifolds (I)\nby P
aolo Stellari (Università degli Studi di Milano) as part of Algebra and
Geometry Seminar @ HKUST\n\nLecture held in 4503.\n\nAbstract\nIn these le
ctures we will review the basic material about stability conditions and fo
cus on examples. We will start reviewing the simplest example given by alg
ebraic curves and illustrate how this allows us to move to higher dimensio
ns passing through the case of noncommutative surfaces. The goal is to ill
ustrate how to construct stability conditions on special hyperkaehler mani
folds which are Hilbert schemes of points on special K3 surfaces and to ap
ply this to the geometry of hyperkaehler manifolds. The new results are a
joint work in progress with Chunyi Li\, Emanuele Macri'\, Alex Perry and X
iaolei Zhao.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Stellari (Università degli Studi di Milano)
DTSTART:20240307T083000Z
DTEND:20240307T093000Z
DTSTAMP:20260422T123036Z
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 Algebra and
Geometry Seminar @ HKUST\n\nLecture held in 5510.\n\nAbstract\nIn these l
ectures we will review the basic material about stability conditions and f
ocus on examples. We will start reviewing the simplest example given by al
gebraic curves and illustrate how this allows us to move to higher dimensi
ons passing through the case of noncommutative surfaces. The goal is to il
lustrate how to construct stability conditions on special hyperkaehler man
ifolds which are Hilbert schemes of points on special K3 surfaces and to a
pply this to the geometry of hyperkaehler manifolds. The new results are a
joint work in progress with Chunyi Li\, Emanuele Macri'\, Alex Perry and
Xiaolei Zhao.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (Academia Sinica)
DTSTART:20240430T083000Z
DTEND:20240430T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/43
DESCRIPTION:Title: Universal Virasoro constraints for quivers with relations\nby Arkadi
j Bojko (Academia Sinica) as part of Algebra and Geometry Seminar @ HKUST\
n\nLecture held in 3598.\n\nAbstract\nThe recent reformulation of sheaf-th
eoretic Virasoro constraints opens many doors for future research. In part
icular\, one may consider its analog for quivers. After phrasing a univers
al approach to Virasoro constraints for moduli of quiver-representations\,
I will sketch their proof for any finite quiver with relations\, with fro
zen vertices\, but without cycles. I will use partial flag varieties which
are a special case of moduli of framed representations as a guiding examp
le throughout. Using derived equivalences to quivers with relations\, I g
ive self-contained proofs of Virasoro constraints for all Gieseker semista
ble sheaves on $S = \\mathbb{P}^2\,\\mathbb{P}^1 \\times \\mathbb{P}^1$\,
and $\\mathrm{Bl}_\\mathrm{pt}\\mathbb{P}^2$. Combined with an existing u
niversality argument for Virasoro constraints on Hilbert schemes of points
of surface\, this leads to a proof for any $S$ which is independent of th
e previous results in GW theory.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadij Bojko (Academia Sinica)
DTSTART:20240502T083000Z
DTEND:20240502T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/44
DESCRIPTION:Title: Wall-crossing for Calabi-Yau fourfolds and applications\nby Arkadij
Bojko (Academia Sinica) as part of Algebra and Geometry Seminar @ HKUST\n\
nLecture held in 3598.\n\nAbstract\nMy work focuses on proving wall-crossi
ng for sheaves and pairs on Calabi-Yau fourfolds. It is desirable that the
end result can have many concrete applications to existing conjectures. F
or this purpose\, I introduce a new structure into the picture - formal fa
milies of vertex algebras. Apart from being a natural extension of the ver
tex algebras introduced by Joyce\, they allow to wall-cross with insertion
s instead of the plain virtual fundamental classes. Many fundamental hurd
les needed to be overcome to prove wall-crossing in this setting. They inc
luded constructing Calabi-Yau four obstruction theories on (enhanced) mast
er spaces and showing that the invariants counting semistable torsion-free
sheaves are well-defined. At the end\, I will use the complete package to
address existing conjectures with applications to 3-fold DT/PT correspond
ences.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cailan Li (Columbia University)
DTSTART:20240410T060000Z
DTEND:20240410T073000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/45
DESCRIPTION:Title: Ext enhanced Soergel bimodules\, link homology\, and Gomi's trace\nb
y Cailan Li (Columbia University) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in 2126D.\n\nAbstract\nSoergel Bimodules began as
an alternative approach to proving the illustrious Kazhdan-Lusztig conject
ures and have since become a cornerstone of representation theory and link
homology. In this talk\, we will give a diagrammatic presentation for Ext
groups between Soergel Bimodules in rank 2 à la Elias-Khovanov and Elias
-Williamson. We then use our results to (1) show how it helps with computi
ng triply graded link homology for braids on 3 strands (2) show how Ext gr
oups of Soergel Bimodules in rank 2 categorifies Gomi's Trace\, a generali
zation of Markov's trace to the Hecke algebra of any finite Coxeter group.
\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240501T083000Z
DTEND:20240501T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/46
DESCRIPTION:Title: Higher Segal spaces and algebraic structures\nby Walker Stern (Bilke
nt University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in 3598.\n\nAbstract\nIn this talk\, I will introduce the 2-Segal con
ditions of Dyckerhoff and Kapranov\, describing both the algebraic and geo
metric intuitions which lead to the 2-Segal conditions. I will then give a
n overview of how the algebraic intuition can be extended to classify vari
ous algebraic structures in (higher) categories of spans. I will additiona
lly explain how the geometric intuition can be used to provide state-sum-s
tyle invariants of surfaces. Time permitting\, I will then discuss work in
progress on higher cyclic operads\, inspired by intuitions which arise fr
om the algebraic characterization of 2-Segal objects.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuai Guo (Peking University)
DTSTART:20240417T083000Z
DTEND:20240417T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/47
DESCRIPTION:Title: Conjectural structures for Calabi-Yau threefolds\nby Shuai Guo (Peki
ng University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in 4472.\n\nAbstract\nIn this talk\, I will review the conjectural st
ructures for the Calabi-Yau threefold proposed by physists. And explain ho
w they solve the generating function by using these conjectures for one-pa
rameter models\, especially for the quintic threefold.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuai Guo (Peking University)
DTSTART:20240418T083000Z
DTEND:20240418T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/48
DESCRIPTION:Title: Mathematical approaches to the BCOV’s conjectures\nby Shuai Guo (P
eking University) as part of Algebra and Geometry Seminar @ HKUST\n\nLectu
re held in 3598.\n\nAbstract\nIn this talk\, I will try to explain the mat
hematical approaches to the BCOV’s conjectures. I will review the defini
tion of NMSP theory\, and how to use it to calculate the Gromov-Witten pot
ential for the quintic threefold and the Calabi-Yau hypersurface in P2 x P
2.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Chen (Rutgers University)
DTSTART:20240514T083000Z
DTEND:20240514T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/49
DESCRIPTION:Title: Symmetric polynomials and interpolation polynomials\nby Hong Chen (R
utgers University) as part of Algebra and Geometry Seminar @ HKUST\n\nLect
ure held in 4504.\n\nAbstract\nSymmetric polynomials---for example\, Schur
\, Jack\, and Macdonald polynomials---are classical objects in the study o
f algebra\, representation theory\, and combinatorics. Interpolation polyn
omials are certain inhomogeneous versions of Jack and Macdonald polynomial
s. In this talk\, after reviewing some basics on symmetric polynomials\, I
will introduce interpolation polynomials and discuss our recent work on t
heir properties. As an application\, I will give a characterization of the
containment partial order in terms of Schur positivity or Jack positivity
. This result parallels the works of Cuttler--Greene--Skandera\, Sra\, and
Khare--Tao\, which characterize two other partial orders in terms of Schu
r positivity. This work is joint with Siddhartha Sahi.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20240507T083000Z
DTEND:20240507T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/50
DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, and alge
braic cycles I\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 talks\, wher
e we will focus on geometry and topology of abelian fibrations --- these a
re maps whose general fibers are complex tori but special fibers may be hi
ghly singular and complicated. The decomposition theorem of Beilinson\, Be
rnstein\, Deligne\, and Gabber (BBDG) provides powerful tools for studying
these maps\; Corti-Hanamura further conjectured that the sheaf-theoretic
BBDG decomposition is governed by algebraic cycles. In my talks\, I will e
xplain how to find these algebraic cycles for certain geometries. I will s
tart with the case of an abelian scheme (i.e.\, an abelian fibration witho
ut singular fiber)\, where the desired cycles have been found by Beauville
and Deninger-Murre more than 30 years ago. Then I will discuss the case w
ith singular fibers. Our ultimate goal for this lecture series is to expla
in how to find the cycles for Hitchin’s integrable system. If time permi
ts\, I will discuss how/why these cycles can help us to understand various
cohomological and sheaf-theoretic questions/conjectures for the Hitchin s
ystem. Based on joint work (in progress) with Davesh Maulik and Qizheng Yi
n.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20240508T083000Z
DTEND:20240508T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/51
DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, and alge
braic cycles II\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 talks\, whe
re we will focus on geometry and topology of abelian fibrations --- these
are maps whose general fibers are complex tori but special fibers may be h
ighly singular and complicated. The decomposition theorem of Beilinson\, B
ernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for studyin
g these maps\; Corti-Hanamura further conjectured that the sheaf-theoretic
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 fibration with
out singular fiber)\, where the desired cycles have been found by Beauvill
e 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 to expl
ain how to find the cycles for Hitchin’s integrable system. If time perm
its\, I will discuss how/why these cycles can help us to understand variou
s cohomological and sheaf-theoretic questions/conjectures for the Hitchin
system. Based on joint work (in progress) with Davesh Maulik and Qizheng Y
in.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20240509T083000Z
DTEND:20240509T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/52
DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, and alge
braic cycles III\nby Junliang Shen (Yale University) as part of Algebr
a 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\, wh
ere 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 Beilinson\,
Bernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for studyi
ng these maps\; Corti-Hanamura further conjectured that the sheaf-theoreti
c 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 fibration wit
hout singular fiber)\, where the desired cycles have been found by Beauvil
le 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 to exp
lain how to find the cycles for Hitchin’s integrable system. If time per
mits\, I will discuss how/why these cycles can help us to understand vario
us cohomological and sheaf-theoretic questions/conjectures for the Hitchin
system. Based on joint work (in progress) with Davesh Maulik and Qizheng
Yin.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Huang (Texas A&M University)
DTSTART:20240730T083000Z
DTEND:20240730T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/53
DESCRIPTION:Title: Syzygies of determinantal thickenings and gl(m|n) representations\nb
y 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\nThe coord
inate ring $S = \\mathbb{C}[x_{i\,j}]$ of space of $m \\times n$ matrices
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 any $\\ma
thrm{GL}_m \\times \\mathrm{GL}_n$-invariant ideal $I$ in $S$\, the syzygy
modules $\\mathrm{Tor}_i(I\,\\mathbb{C})$ will carry a natural action of
$\\mathrm{GL}_m \\times \\mathrm{GL}_n$. Via BGG correspondence\, they als
o carry an action of $\\bigwedge^{\\bullet} (\\mathbb{C}^m \\otimes \\math
bb{C}^n)$. It is a result by Raicu and Weyman that we can combine these ac
tions together and make them modules over the general linear Lie superalge
bra $\\mathfrak{gl}(m|n)$. We will explain how this works and how it enabl
es us to compute all Betti numbers of any $\\mathrm{GL}_m \\times \\mathrm
{GL}_n$-invariant ideal $I$.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanze Chen (University of Alberta)
DTSTART:20240906T083000Z
DTEND:20240906T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/54
DESCRIPTION:Title: Whittaker coefficients of metaplectic Eisenstein series and multiple Dir
ichlet series\nby Yanze Chen (University of Alberta) as part of Algebr
a and Geometry Seminar @ HKUST\n\nLecture held in 4472.\n\nAbstract\nWe in
vestigate the Whittaker coefficients of an Eisenstein series on a global m
etaplectic cover of a semisimple algebraic group induced from the Borel su
bgroup and establish the relation with Weyl group multiple Dirichlet serie
s\, verifying a conjecture of Brubaker-Bump-Friedberg. This is a joint wor
k with Manish Patnaik.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gufang Zhao (University of Melbourne)
DTSTART:20240911T080000Z
DTEND:20240911T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/55
DESCRIPTION:Title: Cousins of relative Donaldson-Thomas theory in dimension 4\nby Gufan
g Zhao (University of Melbourne) as part of Algebra and Geometry Seminar @
HKUST\n\nLecture held in 4472.\n\nAbstract\nThe goal of this talk is to g
ive a few examples of moduli spaces originated from relative Donaldson-Tho
mas theory in dimension 4. Attempts in finding numerical invariants via th
ese moduli spaces lead to a question of functoriality of the cohomology or
K-theory of these moduli spaces. Invariants arising from the functorialit
y in examples will be given. The original parts of the talk are based on a
project joint with Cao\, and partially with Zhou.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaping Yang (University of Melbourne)
DTSTART:20240913T080000Z
DTEND:20240913T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/56
DESCRIPTION:Title: Higher spin representations of the Yangian of sl_2 and R-matrices\nb
y Yaping Yang (University of Melbourne) as part of Algebra and Geometry Se
minar @ HKUST\n\nLecture held in 4472.\nAbstract: TBA\n\nFor the Yangian o
f sl_2\, higher spin representations are tensor products of the evaluation
pullback of the $\\ell_i+1$-dimensional irreducible representations of sl
_2\, where $\\ell_i$ are the highest weights. In my talk\, I will give a g
eometric realization of the higher spin representations in terms of the cr
itical cohomology of representations of the quiver with potential of Bykov
and Zinn-Justin. I will also talk about the construction of R-matrices v
ia the lattice model and the weight functions.\n\nThis is based on my join
t work with Paul Zinn-Justin.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Kivinen (Aalto University)
DTSTART:20241030T080000Z
DTEND:20241030T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/58
DESCRIPTION:Title: A Lie-theoretic generalization of some Hilbert schemes\nby Oscar Kiv
inen (Aalto University) as part of Algebra and Geometry Seminar @ HKUST\n\
nLecture held in Room 4475 (Lifts 25/26).\n\nAbstract\nI will introduce se
veral varieties attached to a complex reductive group\, generalizing for e
xample $\\mathsf{Hilb}^n(\\mathbb{C}^2)$ and Haiman’s isospectral Hilber
t scheme\, which pertain to the $\\mathsf{GL}_n$-case. I will then explain
what is currently known about these varieties (including some low-rank ex
amples) and what else one would like to know about them.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yau Wing Li (The University of Melbourne)
DTSTART:20240919T083000Z
DTEND:20240919T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/59
DESCRIPTION:Title: Endoscopy for affine Hecke category\nby Yau Wing Li (The University
of Melbourne) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture h
eld in 5506.\n\nAbstract\nAffine Hecke categories are categorifications of
Iwahori-Hecke algebras\, which are essential in the classification of irr
educible representations of loop group LG with Iwahori-fixed vectors. The
affine Hecke category has a monodromic counterpart\, which contains sheave
s with prescribed monodromy under the left and right actions of the maxima
l torus. We show that the neutral block of this monoidal category is equiv
alent to the neutral block of the affine Hecke category (with trivial toru
s monodromy) for the endoscopic group H. It is consistent with the Langlan
ds functoriality conjecture.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241113T084500Z
DTEND:20241113T094500Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/61
DESCRIPTION:Title: On the theory of double $\\infty$-categories I\nby Jaco Ruit (Utrech
t University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture h
eld in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three talks ai
ms to give a detailed introduction to double $\\infty$-categories. Double
$\\infty$-categories can be viewed as generalizations of $(\\infty\,2)$-ca
tegories that admit two directions for morphisms. The series starts by mot
ivating these categorical constructions\, and we will see how these appear
in mathematics. We will discuss their definitions\, including different c
ompleteness assumptions. Moreover\, we will see how double $\\infty$-categ
ories can be used to model $(\\infty\,2)$-categories. We highlight some i
mportant examples of double $\\infty$-categories throughout.\n\nWe will th
en continue to study the notions of companionships and conjunctions in dou
ble $\\infty$-categories. These are important and useful concepts that can
be used to describe the universal property of so-called squares construct
ions\, as we will see. Moreover\, we will study functors between double $\
\infty$-categories and show that they assemble into double $\\infty$-categ
ories of functors with vertical and horizontal natural transformations. We
present a new result that characterizes the companions and conjoints in t
hese functor double $\\infty$-categories. On the way\, we will see how thi
s double categorical machinery can be specialized to prove results in $(\\
infty\,2)$-category theory.\n\nDuring the first talk\, we will recall 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://researchseminars.org/talk/HKUST-AG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241120T084500Z
DTEND:20241120T094500Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/63
DESCRIPTION:Title: On the theory of double $\\infty$-categories III\nby Jaco Ruit (Utre
cht University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three talks
aims to give a detailed introduction to double $\\infty$-categories. Doubl
e $\\infty$-categories can be viewed as generalizations of $(\\infty\,2)$-
categories that admit two directions for morphisms. The series starts by m
otivating these categorical constructions\, and we will see how these appe
ar in mathematics. We will discuss their definitions\, including different
completeness assumptions. Moreover\, we will see how double $\\infty$-cat
egories 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 d
ouble $\\infty$-categories. These are important and useful concepts that c
an be used to describe the universal property of so-called squares constru
ctions\, as we will see. Moreover\, we will study functors between double
$\\infty$-categories and show that they assemble into double $\\infty$-cat
egories of functors with vertical and horizontal natural transformations.
We present a new result that characterizes the companions and conjoints in
these functor double $\\infty$-categories. On the way\, we will see how t
his double categorical machinery can be specialized to prove results in $(
\\infty\,2)$-category theory.\n \nDuring the first talk\, we will recall s
ome relevant background material on $\\infty$-categories that will be need
ed to follow the series. No knowledge of $(\\infty\,2)$-categories is assu
med.\n\nLecture series: On the theory of double $\\infty$-categories\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241115T090000Z
DTEND:20241115T103000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/64
DESCRIPTION:Title: On the theory of double $\\infty$-categories II\nby Jaco Ruit (Utrec
ht University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture
held in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three talks a
ims to give a detailed introduction to double $\\infty$-categories. Double
$\\infty$-categories can be viewed as generalizations of $(\\infty\,2)$-c
ategories that admit two directions for morphisms. The series starts by mo
tivating these categorical constructions\, and we will see how these appea
r in mathematics. We will discuss their definitions\, including different
completeness assumptions. Moreover\, we will see how double $\\infty$-cate
gories can be used to model $(\\infty\,2)$-categories. We highlight some
important examples of double $\\infty$-categories throughout.\n\nWe will t
hen continue to study the notions of companionships and conjunctions in do
uble $\\infty$-categories. These are important and useful concepts that ca
n be used to describe the universal property of so-called squares construc
tions\, as we will see. Moreover\, we will study functors between double $
\\infty$-categories and show that they assemble into double $\\infty$-cate
gories of functors with vertical and horizontal natural transformations. W
e present a new result that characterizes the companions and conjoints in
these functor double $\\infty$-categories. On the way\, we will see how th
is double categorical machinery can be specialized to prove results in $(\
\infty\,2)$-category theory.\n\nDuring the first talk\, we will recall som
e relevant background material on $\\infty$-categories that will be needed
to follow the series. No knowledge of $(\\infty\,2)$-categories is assume
d.\n\nLecture series: On the theory of double $\\infty$-categories\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael McBreen (The Chinese University of Hong Kong)
DTSTART:20241023T080000Z
DTEND:20241023T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/65
DESCRIPTION:Title: The Hamiltonian reduction of hypertoric mirror symmetry\nby Michael
McBreen (The Chinese University of Hong Kong) as part of Algebra and Geome
try Seminar @ HKUST\n\nLecture held in 4475.\n\nAbstract\nI will describe
recent work with Vivek Shende and Peng Zhou\, which relates the Fukaya cat
egory of a multiplicative hypertoric variety to the Fukaya category of its
associated toric arrangement. This provides evidence for a general conjec
ture which describes the `hamiltonian reduction' of a Fukaya category at s
ingular values of the moment parameter. Despite the subject\, the talk sho
uld be accessible to someone unfamiliar with the Fukaya category.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/66
DESCRIPTION:Title: Nilpotent orbits for classical groups\nby Hiraku Nakajima (Kavli Ins
titute for the Physics and Mathematics of the Universe) as part of Algebra
and Geometry Seminar @ HKUST\n\nLecture held in Room 4475 (Lifts 25/26).\
n\nAbstract\nKraft-Procesi realized nilpotent orbits for classical groups
as orthosymplectic quiver varieties\, which are defined as quiver varietie
s\, but replacing products of GL by products of O and Sp. Motivated by stu
dy of Coulomb branches\, we introduce variants of these\, which remove `ba
d' behavior of nilpotent orbit closures\, such as non-irreducibility\, non
-normality\, etc. This talk is based on on-going project with Finkelberg a
nd Hanany.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tudor Pădurariu (CNRS\, IMJ-PRG\, Sorbonne Université)
DTSTART:20241220T030000Z
DTEND:20241220T043000Z
DTSTAMP:20260422T123036Z
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 Algebr
a and Geometry Seminar @ HKUST\n\nLecture held in Room 6580 (lift 27/28).\
n\nAbstract\nI will report on joint work with Yukinobu Toda (partially in
progress) about the derived category of coherent sheaves of semistable Hig
gs bundles on a curve. \n\nThese categories have semiorthogonal decomposit
ions in certain categories analogous to the ``window categories” of Halp
ern-Leistner\, Ballard-Favero-Katzarkov\, Špenko-Van den Bergh. In the fi
rst half of the talk\, I will discuss the general theory of ``window categ
ories”.\n\nNext\, I will focus on two conjectural dualities. The first i
s between semistable Higgs bundles of degree zero and a "limit" category.
This equivalence aims to make precise the proposal of Donagi-Pantev of con
sidering the classical limit of the de Rham Langlands equivalence. The sec
ond is a primitive version of the first\, and it relates categories of she
aves on moduli of semistable Higgs bundles (for various degrees). This equ
ivalence may be regarded as a version of the D-equivalence conjecture / SY
Z mirror symmetry. We can prove (partial) versions of these conjectures fo
r topological K-theory of these categories.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/69
DESCRIPTION:Title: q-characters for quantum loop groups\nby Andrei Neguț (Swiss Federa
l Technology Institute of Lausanne (EPFL)) as part of Algebra and Geometry
Seminar @ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nq
-characters are a mainstay of the representation theory of quantum affine
algebras. We generalize this theory to all quantum loop algebras\, that un
derlie arbitrary Kac-Moody Lie algebras instead of just semisimple Lie alg
ebras\, as well as introduce new techniques for the computation of q-chara
cters.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Lauda (The University of Southern California)
DTSTART:20250226T080000Z
DTEND:20250226T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/70
DESCRIPTION:Title: Nonsemisimple Topological Quantum Computation\nby Aaron Lauda (The U
niversity of Southern California) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 4472 (Lifts 25/26).\n\nAbstract\nSince the
foundational work of Freedman\, Kitaev\, Larsen\, and Wang\, it has been
understood that 3-dimensional topological quantum field theories (TQFTs)\,
described via modular tensor categories\, provide a universal model for f
ault-tolerant topological quantum computation. These TQFTs\, derived from
quantum groups at roots of unity\, achieve modularity by semisimplifying t
heir representation categories—discarding objects with quantum trace zer
o. The resulting semisimple categories describe anyons whose braiding enab
les robust quantum computation.\n\nThis talk explores recent advances in l
ow-dimensional topology\, focusing on the use of nonsemisimple categories
that retain quantum trace zero objects to construct new TQFTs. These nonse
misimple TQFTs surpass their semisimple counterparts\, distinguishing topo
logical features inaccessible to the latter. For physical applications\, u
nitarity is essential\, ensuring Hom spaces form Hilbert spaces. We presen
t joint work with Nathan Geer\, Bertrand Patureau-Mirand\, and Joshua Suss
an\, where nonsemisimple TQFTs are equipped with a Hermitian structure. Th
is framework introduces Hilbert spaces with possibly indefinite metrics\,
presenting new challenges.\n\nWe further discuss collaborative work with S
ung Kim\, Filippo Iulianelli\, and Sussan\, demonstrating that nonsemisimp
le TQFTs enable universal quantum computation at roots of unity where semi
simple theories fail. Specifically\, we show how Ising anyons within this
framework achieve universality through braiding alone. The resulting braid
ing operations are deeply connected to the Lawrence-Krammer-Bigelow repres
entations\, with the Hermitian structure providing a nondegenerate inner p
roduct grounded in quantum algebra.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Sala (University of Pisa)
DTSTART:20250319T080000Z
DTEND:20250319T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/71
DESCRIPTION:Title: Cohomological Hall algebras of 1-dimensional sheaves and Yangians\nb
y Francesco Sala (University of Pisa) as part of Algebra and Geometry Semi
nar @ HKUST\n\nLecture held in Room 3598 (Lift 27-28).\n\nAbstract\nThe fi
rst part of this talk provides a brief and gentle introduction to the theo
ry of 2-dimensional cohomological Hall algebras. The second part focuses o
n the introduction of the nilpotent cohomological Hall algebra COHA(S\, Z)
of coherent sheaves on a smooth quasi-projective complex surface S set-th
eoretically supported on a closed subscheme Z. When S is the minimal resol
ution of an ADE singularity and Z is the exceptional divisor\, I will desc
ribe how to characterize COHA(S\, Z) via the Yangian of the corresponding
affine ADE quiver. This is a joint project with Emanuel Diaconescu\, Mauro
Porta\, Oliver Schiffmann\, and Eric Vasserot.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonte Gödicke (Universität Hamburg)
DTSTART:20250326T080000Z
DTEND:20250326T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/72
DESCRIPTION:Title: Multi-fusion categories from 2-Segal spaces\nby Jonte Gödicke (Univ
ersität Hamburg) as part of Algebra and Geometry Seminar @ HKUST\n\nLectu
re held in Room 3598 (Lift 27/28).\n\nAbstract\nIn the study of 3-dimensio
nal Topological Quantum Field Theories (short TQFTs)\, certain monoidal ca
tegories called multi-fusion categories are of fundamental importance. Wel
l-known examples of these arise from finite groups through a linearization
construction. However\, it is less well-known that the same construction
can produce more interesting examples of monoidal structures from any 2-Se
gal space. These include so-called Hall monoidal structures\, which are an
ticipated to have interesting connections to quantum topology and TQFTs.\n
\nIn this talk\, I will classify those 2-Segal spaces that induce multi-fu
sion categories. For this\, I will introduce a 2-categorical characterizat
ion of multi-fusion categories to translate questions about these monoidal
structures to questions about homotopy coherent algebra in span categorie
s. Afterwards\, I will discuss extensions of this to the context of derive
d categories and derived TQFTs.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhao (Beijing Institute of Technology)
DTSTART:20250218T020000Z
DTEND:20250218T033000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/73
DESCRIPTION:Title: Grassmannian of two term complexes and instantons on the blow ups\nb
y Yu Zhao (Beijing Institute of Technology) as part of Algebra and Geometr
y Seminar @ HKUST\n\nLecture held in Room 2303 (Lift 17-18).\n\nAbstract\n
The semi-orthogonal decomposition of the cohomological theory of Grassmann
ian of two-term complexes is studied by a series paper of Jiang. In this t
alk\, we will reinterpret it as a representation of the Clifford algebra.\
n\n As an application\, we will explain a relation between the basic repre
sentation of the affine Lie algebra and the moduli space of the instanton
spaces on the blow up of a point in a surface. It verifies the predictions
of Li-Qin and Feigin-Gukov. Based on joint work with Qingyuan Jiang and W
ei-ping Li.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Rozenblyum (University of Toronto)
DTSTART:20250423T080000Z
DTEND:20250423T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/74
DESCRIPTION:Title: Higher traces and characters of finite groups of Lie type\nby Nick R
ozenblyum (University of Toronto) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 2128B (Lift 19).\n\nAbstract\nI will give
a brief overview of the theory of traces in higher categories and explain
how this gives a new approach to the study of representation of finite gro
ups of Lie type. Given an algebraic group $G$ over a finite field $\\mathb
b{F}_q$\, I will explain how representations of $G(\\mathbb{F}_q)$ arise a
s traces of categorical representations of $G$. Moreover\, I will explain
the higher categorical origin of Deligne-Lusztig representations and give
a new conceptual computation of their characters which explains their regu
larity as a function of $q$. This is joint work with Gaitsgory and Varshav
sky.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adeel Khan (Academia Sinica)
DTSTART:20250514T080000Z
DTEND:20250514T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/75
DESCRIPTION:Title: Microlocal categorical sheaves on shifted symplectic spaces\nby Adee
l 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 describ
e a ladder of conjectural $(n+1)$-categorical invariants associated to $n$
-shifted symplectic derived stacks. For $n=0$ these generalize categories
of microsheaves on smooth symplectic schemes (closely related to Fukaya c
ategories). For $n=-1$ and $-2$ they should recover (categorifications of
) Donaldson-Thomas invariants of Calabi-Yau three- and four-folds\, respec
tively\, thus giving a microlocal perspective on Donaldson-Thomas invarian
ts.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Khoa Bang Pham (University of Rennes)
DTSTART:20250528T080000Z
DTEND:20250528T093000Z
DTSTAMP:20260422T123036Z
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 @ HKUST\n\n\
nAbstract\nIn the quest for discovering exotic spheres\, Milnor studied th
e topology of complex hypersurface singularities\, which eventually led to
the notion of Milnor fibers. Around the same time\, Grothendieck and Deli
gne globalized this concept to define the nearby and vanishing cycles func
tors\, which later played a crucial role in the proof of the Weil conjectu
res. These foundational ideas\, introduced over half a century ago\, have
since evolved in various directions. In motivic homotopy theory\, a notabl
e descendant is the motivic nearby functor\, originally constructed by J.
Ayoub. This functor can be regarded as the ``seventh operation'' in the yo
ga of six-functor formalism developed by Grothendieck’s school\, and it
exhibits many remarkable properties. In this talk\, I will introduce the t
heory of motivic nearby functors and discuss some recent developments.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yifeng Huang (The University of Southern California)
DTSTART:20250618T020000Z
DTEND:20250618T030000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/77
DESCRIPTION:Title: High-rank motivic degree-zero Donaldson--Thomas theory on singular curve
s\, and q-series\nby Yifeng Huang (The University of Southern Californ
ia) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in 450
2 (Lifts 25/26).\n\nAbstract\nMy main point is that high-rank motivic degr
ee-zero DT invariants on singular curves appear to give infinite products
of Rogers--Ramanujan type. This is based on explicit computation of certai
n Quot schemes\, which is where the new ideas and results lie\, but this s
eems to be a new phenomenon that I cannot explain from physics or other co
nceptual connection. For context\, the rank-1 case has been observed to re
late to knot theory and Catalan combinatorics in the last decade (keyword:
Oblomkov--Rasmussen--Shende conjecture). \n\nA down-to-earth statement th
at captures all the essence is the following (stated for the singular curv
e $y^2=x^3$): For a random $n\\times n$ matrix $A$ over a finite field $\\
mathbb{F}_q$\, what is the expected number of matrices $B$ such that $AB=B
A$ and $A^3=B^2$? It turns out that as $n\\to \\infty$\, the limiting answ
er is $\\prod (1-q^{-i})$ over all positive $i$ congruent to $1\,4$ mod $5
$\, the famous Rogers--Ramanujan infinite product. \n\nThe reported result
s contain joint work with Ruofan Jiang (on the $y^2=x^n$ case) and joint w
ork in progress with RJ and Alexei Oblomkov (on the $y^m=x^n$ case with $m
\,n$ coprime).\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaif Hilman (University of Bonn)
DTSTART:20250903T080000Z
DTEND:20250903T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/78
DESCRIPTION:Title: Atiyah-Bott's fixed point theorem via categorification\nby Kaif Hilm
an (University of Bonn) as part of Algebra and Geometry Seminar @ HKUST\n\
nLecture held in Room 4472 (Lift 25/26).\n\nAbstract\nA famous result of A
tiyah 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 the Atiya
h-Singer index theorem. In this talk\, I will explain a different\, purely
homotopical\, proof which in particular exhibits that the theorem is real
ly a consequence of ``global'' homotopical reasons rather than ``local'' g
eometric ones. To this end\, I will introduce a theory of Poincare duality
for arbitrary topoi together with a suite of ``basechange'' principles. I
will then sketch how this abstract theory reduces the theorem to an eleme
ntary Tate cohomology calculation by working with an equivariant topos. Th
is is based on joint work with D. Kirstein and C. Kremer from arXiv:2405.1
7641.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Zhao (Beijing Institute of Technology)
DTSTART:20251001T080000Z
DTEND:20251001T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/80
DESCRIPTION:Title: The affine super Yangian of $\\mathfrak{gl}(1|1)$\nby Yu Zhao (Beiji
ng Institute of Technology) as part of Algebra and Geometry Seminar @ HKUS
T\n\nLecture held in Room 4504 (Lifts 25/26).\n\nAbstract\nNakajima and Va
fa-Witten noticed that the blow up formulae for the partition functions of
Euler numbers on the instanton moduli space is the character of affine ve
rtex algebra at level 1\, and asked the CFT explanation. Together with Jia
ng and Li\, we answered this question. However\, our proof leaves more que
stions: 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 discuss
how to solve the above problems through a larger algebra action.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sasha Minets (Max Planck Institute for Mathematics)
DTSTART:20251119T080000Z
DTEND:20251119T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/81
DESCRIPTION:Title: Ersatz parity sheaves and stratifications of algebras\nby Sasha Mine
ts (Max Planck Institute for Mathematics) as part of Algebra and Geometry
Seminar @ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nMa
ny important algebras\, notably quiver Hecke algebras\, can be realized as
Ext-algebras of constructible sheaves on a given space. Since representat
ion theorists like highest weight categories\, they want to know when such
algebras are quasi-hereditary (or polynomially quasi-hereditary\, or prop
erly stratified\, etc). In characteristic 0\, Kato proved a rather general
result of this sort\, under the assumption that the space has finitely ma
ny orbits under the action of an algebraic group. This was extended to cha
racteristic p by McNamara\, substituting perverse sheaves techniques for p
arity sheaves of Juteau-Mautner-Williamson. Unfortunately\, this approach
do not apply to quiver Hecke algebras beyond Dynkin type. I will explain h
ow to extend the theory of parity sheaves to cover the first non-trivial c
ase of Kronecker quiver\, and speculate about how to approach other affine
types. Based on arXiv:2504.17430\, joint with R. Maksimau.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/82
DESCRIPTION:Title: An introduction to (infinitesimal) categorical torelli\nby Xun Lin (
Hong Kong University of Science and Technology) as part of Algebra and Geo
metry Seminar @ HKUST\n\nLecture held in Room 2405 (Lifts 17/18).\n\nAbstr
act\nIn the first part\, I will talk about the categorical torelli. We pro
ve the Kuznetsov components of a series of hypersurface in projective spac
e reconstruct the hypersurfaces. Our method allow us to work for hypersurf
aces in weighted projective space\, and prove the reconstruction theorem f
or veronese double cone\, which is a long-time open case. Joint with J. Re
nnemo and Shizhuo Zhang. In the second part\, I will talk about the infini
tesimal categorical torelli for Fano 3-folds. I will prove the classical
infinitesimal torelli for Fano 3-folds using the infinitesimal categorical
torelli\, especially for special Gushel-Mukai 3-folds. Joint with Shizhuo
Zhang and Zheng Zhang.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaolei Zhao (University of California\, Santa Barbara)
DTSTART:20251203T080000Z
DTEND:20251203T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/83
DESCRIPTION:Title: Non-commutative abelian surfaces and Kummer type hyperkähler manifolds<
/a>\nby Xiaolei Zhao (University of California\, Santa Barbara) as part of
Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4504 (Lift 2
5/26).\n\nAbstract\nExamples of non-commutative K3 surfaces arise from sem
iorthogonal decompositions of the bounded derived category of certain Fano
varieties. The most interesting cases are those of cubic fourfolds and Gu
shel-Mukai varieties of even dimension. Using the deep theory of families
of stability conditions\, locally complete families of hyperkähler manifo
lds deformation equivalent to Hilbert schemes of points on a K3 surface ha
ve been constructed from moduli spaces of stable objects in these non-comm
utative K3 surfaces. On the other hand\, an explicit description of a loca
lly complete family of hyperkähler manifolds deformation equivalent to a
generalized Kummer variety is not yet available.\n\nIn this talk we will c
onstruct families of non-commutative abelian surfaces as equivariant categ
ories of the derived category of K3 surfaces which specialize to Kummer K3
surfaces. Then we will explain how to induce stability conditions on them
and produce examples of locally complete families of hyperkähler manifol
ds of generalized Kummer deformation type. Applications to abelian fourfol
ds of Weil type will be discussed.\n\nThis is joint work in preparation wi
th Arend Bayer\, Alex Perry and Laura Pertusi.\n
LOCATION:https://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:20260422T123036Z
UID:HKUST-AG/84
DESCRIPTION:Title: Quantization of symmetric pairs\nby Jinfeng Song (The Hong Kong Univ
ersity of Science and Technology) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 1104 (Lift 19).\n\nAbstract\nChevalley gro
up schemes are group schemes defined over the integers that parametrize co
nnected reductive groups over algebraically closed fields as geometric fib
ers. Symmetric subgroups are fixed point subgroups of reductive groups und
er an involutions. In this talk\, we construct closed subgroup schemes of
Chevalley group schemes that parametrize symmetric subgroups of reductive
groups as geometric fibers. Our construction relies crucially on the theor
y of quantum symmetric pairs and thus naturally admits a quantization. As
applications\, we obtain deeper insights into the structures of symmetric
spaces and their embeddings\, yielding applications to their dual canonica
l basis\, good filtrations\, integral models\, etc. This is based on joint
works with Huanchen Bao (NUS).\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Heidersdorf (Newcastle University)
DTSTART:20260401T080000Z
DTEND:20260401T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/85
DESCRIPTION:Title: Koszulity for semi-infinite highest weight categories\nby Thorsten H
eidersdorf (Newcastle University) as part of Algebra and Geometry Seminar
@ HKUST\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nKoszul alg
ebras are positively graded algebras with very amenable homological proper
ties. Typical examples are the polynomial ring over a field or the exterio
r and symmetric algebra of a vector space. A category is called Koszul if
it has a grading with which it is equivalent to the category of graded mod
ules over a Koszul algebra. A famous example (due to Soergel) is the princ
ipal block of category $\\mathcal{O}$ for a semisimple Lie algebra. Koszul
ity is a very nice property but often very difficult to check. I will give
a criterion which allows to check Koszulity in case the category is a gra
ded semi-infinite highest weight category (which is a structure that appea
rs often in representation theory). This is joint work with Jonas Nehme \n
and Catharina Stroppel.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Germán Stefanich (Max Planck Institute for Mathematics)
DTSTART:20260422T080000Z
DTEND:20260422T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/86
DESCRIPTION:Title: Higher algebraic geometry\nby Germán Stefanich (Max Planck Institut
e for Mathematics) as part of Algebra and Geometry Seminar @ HKUST\n\nLect
ure held in Room 5562 (Lift 27/28).\n\nAbstract\nThe goal of this talk is
to explain joint work with Scholze where we study a version of algebraic g
eometry which is built\, not out of spectra of commutative rings\, but out
of spectra of symmetric monoidal higher categories. The resulting higher
geometry contains the usual category of qcqs schemes\, but also provides a
home to new and interesting objects which cannot be studied with more cla
ssical means. In particular\, I hope to explain the role that some of thes
e objects play in ongoing work with Ben-Zvi and Nadler on various Langland
s duality statements in the context of three dimensional topological field
theory.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonte Gödicke (Max-Plank-Institute for Mathematics)
DTSTART:20260311T080000Z
DTEND:20260311T093000Z
DTSTAMP:20260422T123036Z
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 diff
erent incarnations\, Hall algebras play an important role in classical rep
resentation theory. Broadly speaking\, the Hall algebra construction assoc
iates to an abelian category $A$ an algebra of functions on the moduli of
objects $M(A)$ of $A$.\n\nThe goal of this talk is to describe a twofold c
ategorification of the Hall algebra construction. This new construction as
sociates to an abelian category $A$ a lax-braided monoidal 2-category of 2
-sheaves on $M(A)$. Even in the simplest case of the abelian category of v
ector spaces\, this construction yields a rich and highly structured objec
t. Focusing on this example\, I will explain the construction in detail an
d describe why it is desirable from the perspective of categorified repres
entation theory.\n\nThis is joint work with Quoc Ho\, Yang Hu\, and Walker
Stern.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Technical University of Munich)
DTSTART:20260318T080000Z
DTEND:20260318T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/88
DESCRIPTION:Title: More about spans than you ever wanted to know\nby Walker Stern (Tech
nical University of Munich) as part of Algebra and Geometry Seminar @ HKUS
T\n\nLecture held in Room 3598 (Lift 27/28).\n\nAbstract\nHigher categorie
s of spans\, also called correspondences\, play a key role in many algebra
ic and algebro-geometric constructions --- from six functor formalisms to
the constructions of Hall algebras. In this talk\, I will describe the fun
damental categorical structures which underpin ongoing research (joint wit
h Jonte Gödicke\, Quoc Ho\, and Yang Hu) aimed at constructing braided mo
noidal categories using higher categories of spans. In particular\, I will
explain a new approach to $(\\infty\,n)$-categories of spans and deduce f
rom it a new universal property which allows us to construct the $E_2$ (br
aided) algebras described in last week's talk by Jonte Gödicke.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Liu (Kavli IPMU)
DTSTART:20260429T080000Z
DTEND:20260429T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/90
DESCRIPTION:Title: Wall-crossing for invariants of equivariant 3CY categories (overview)\nby Henry Liu (Kavli IPMU) as part of Algebra and Geometry Seminar @ HKU
ST\n\nLecture held in Room 5562 (Lift 27/28).\n\nAbstract\nI will give an
overview of: what is wall-crossing\; geometric techniques for producing wa
ll-crossing formulas\; recent advances in such techniques for enumerative
invariants\, particularly those of ``3-Calabi-Yau type''\, in various equi
variant cohomology theories like K-theory or elliptic cohomology. This inc
ludes joint work with N. Kuhn and F. Thimm which can be thought of as a re
finement and generalization of results of Joyce-Song and Kontsevich-Soibel
man. Applications include the Donaldson-Thomas/Pandharipande-Thomas vertex
correspondence (related to the topological vertex) and the study of refin
ed Vafa-Witten invariants.\n\nLecture series: Wall-crossing for invariants
of equivariant 3CY categories\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bohan Fang (BICMR\, Peking University)
DTSTART:20260422T063000Z
DTEND:20260422T080000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/91
DESCRIPTION:Title: Conic bundle and the mirror hypersurface for a toric Calabi-Yau n-folds<
/a>\nby Bohan Fang (BICMR\, Peking University) as part of Algebra and Geom
etry Seminar @ HKUST\n\nLecture held in Room 5562 (Lift 27/28).\n\nAbstrac
t\nWe study the Hori-Vafa mirror Calabi-Yau n-fold to a toric Calabi-Yau n
-orbifold. One version of homological mirror symmetry expects that the wra
pped Fukaya category on the Hori-Vafa mirror is equivalent to the toric Ca
labi-Yau with a hypersurface removed. We use a microlocal sheaf model of t
his Fukaya category\, and in this setting prove the statement by descent p
roperty and Orlov's semi-orthogonal decomposition. Moreover\, we expect th
e object-level correspondence when interpreted in terms of some reasonably
defined characteristic cycles\, matches the integral structure correspond
ence from the Gamma classes. This talk is based on the joint work with Yuz
e Sun and Peng Zhou.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bohan Fang (BICMR\, Peking University)
DTSTART:20260423T080000Z
DTEND:20260423T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/92
DESCRIPTION:Title: Remodeling conjecture with primaries\, descendants\, and multiple branes
\nby Bohan Fang (BICMR\, Peking University) as part of Algebra and Geo
metry Seminar @ HKUST\n\nLecture held in Room 2126D (Lift 19).\n\nAbstract
\nThe remodeling conjecture equates the topological recursion and all-genu
s Gromov-Witten theory of a toric Calabi-Yau 3-fold. I will report our ser
ies of works on the remodeling conjecture involving the open-closed Gromov
-Witten invariants on multiple inner and outer branes\, with primary and d
escendant insertions. This talk is based on works with Chiu-Chu Melissa Li
u\, Song Yu\, and Zhengyu Zong.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Liu (Kavli IPMU)
DTSTART:20260430T080000Z
DTEND:20260430T093000Z
DTSTAMP:20260422T123036Z
UID:HKUST-AG/93
DESCRIPTION:Title: Wall-crossing for invariants of equivariant 3CY categories (a user guide
)\nby Henry Liu (Kavli IPMU) as part of Algebra and Geometry Seminar @
HKUST\n\nLecture held in Room 2126D (Lift 19).\n\nAbstract\nIn practice\,
in order to apply the Joyce-style wall-crossing formulas from my previous
talk\, some control over the wall-crossing term is needed. I will explain
how this wall-crossing term\, in K-theory\, is governed by a certain ``ve
rtex coproduct'' arising from a multiplicative vertex (co)algebra. This ve
rtex coproduct is compatible with K-theoretic Hall operations --- which fo
rm positive halves of quantum loop algebras --- whenever they exist. I wil
l present formulas for this coproduct in the easiest cases in 3-fold and 4
-fold Donaldson-Thomas theory. Applications include an explicit descendent
Donaldson-Thomas/Pandharipande-Thomas vertex correspondence.\n\nLecture s
eries: Wall-crossing for invariants of equivariant 3CY categories\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/93/
END:VEVENT
END:VCALENDAR