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BEGIN:VEVENT
SUMMARY:Harrison Chen (Academia Sinica)
DTSTART;VALUE=DATE-TIME:20230224T070000Z
DTEND;VALUE=DATE-TIME:20230224T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230303T070000Z
DTEND;VALUE=DATE-TIME:20230303T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230315T070000Z
DTEND;VALUE=DATE-TIME:20230315T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230419T070000Z
DTEND;VALUE=DATE-TIME:20230419T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230322T070000Z
DTEND;VALUE=DATE-TIME:20230322T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230405T070000Z
DTEND;VALUE=DATE-TIME:20230405T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230426T070000Z
DTEND;VALUE=DATE-TIME:20230426T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230412T070000Z
DTEND;VALUE=DATE-TIME:20230412T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230426T083000Z
DTEND;VALUE=DATE-TIME:20230426T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230510T030000Z
DTEND;VALUE=DATE-TIME:20230510T043000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230816T070000Z
DTEND;VALUE=DATE-TIME:20230816T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230811T060000Z
DTEND;VALUE=DATE-TIME:20230811T070000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230814T060000Z
DTEND;VALUE=DATE-TIME:20230814T070000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230815T060000Z
DTEND;VALUE=DATE-TIME:20230815T070000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230817T060000Z
DTEND;VALUE=DATE-TIME:20230817T070000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230818T060000Z
DTEND;VALUE=DATE-TIME:20230818T070000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231009T070000Z
DTEND;VALUE=DATE-TIME:20231009T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231016T070000Z
DTEND;VALUE=DATE-TIME:20231016T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230925T070000Z
DTEND;VALUE=DATE-TIME:20230925T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231025T070000Z
DTEND;VALUE=DATE-TIME:20231025T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231027T070000Z
DTEND;VALUE=DATE-TIME:20231027T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20230927T070000Z
DTEND;VALUE=DATE-TIME:20230927T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231030T070000Z
DTEND;VALUE=DATE-TIME:20231030T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231011T070000Z
DTEND;VALUE=DATE-TIME:20231011T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231106T080000Z
DTEND;VALUE=DATE-TIME:20231106T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231115T070000Z
DTEND;VALUE=DATE-TIME:20231115T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231113T070000Z
DTEND;VALUE=DATE-TIME:20231113T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20231127T070000Z
DTEND;VALUE=DATE-TIME:20231127T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240111T073000Z
DTEND;VALUE=DATE-TIME:20240111T090000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240115T070000Z
DTEND;VALUE=DATE-TIME:20240115T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240117T080000Z
DTEND;VALUE=DATE-TIME:20240117T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240122T070000Z
DTEND;VALUE=DATE-TIME:20240122T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240124T070000Z
DTEND;VALUE=DATE-TIME:20240124T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240125T070000Z
DTEND;VALUE=DATE-TIME:20240125T083000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240306T080000Z
DTEND;VALUE=DATE-TIME:20240306T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240131T083000Z
DTEND;VALUE=DATE-TIME:20240131T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240227T020000Z
DTEND;VALUE=DATE-TIME:20240227T033000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240227T083000Z
DTEND;VALUE=DATE-TIME:20240227T100000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240228T083000Z
DTEND;VALUE=DATE-TIME:20240228T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240229T080000Z
DTEND;VALUE=DATE-TIME:20240229T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240305T083000Z
DTEND;VALUE=DATE-TIME:20240305T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240307T083000Z
DTEND;VALUE=DATE-TIME:20240307T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240430T083000Z
DTEND;VALUE=DATE-TIME:20240430T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240502T083000Z
DTEND;VALUE=DATE-TIME:20240502T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240410T060000Z
DTEND;VALUE=DATE-TIME:20240410T073000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240501T083000Z
DTEND;VALUE=DATE-TIME:20240501T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240417T083000Z
DTEND;VALUE=DATE-TIME:20240417T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240418T083000Z
DTEND;VALUE=DATE-TIME:20240418T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240514T083000Z
DTEND;VALUE=DATE-TIME:20240514T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240507T083000Z
DTEND;VALUE=DATE-TIME:20240507T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240508T083000Z
DTEND;VALUE=DATE-TIME:20240508T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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;VALUE=DATE-TIME:20240509T083000Z
DTEND;VALUE=DATE-TIME:20240509T093000Z
DTSTAMP;VALUE=DATE-TIME:20240715T183004Z
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
END:VCALENDAR