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BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard University)
DTSTART:20210903T190000Z
DTEND:20210903T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/1
DESCRIPTION:Title: Factorization of the minimal model CFT and Lang
lands duality\nby Dennis Gaitsgory (Harvard University) as part of MIT
Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in th
e Simons building.\n\nAbstract\nWe will suggest a conjectural picture\, wh
ich follows from the quantum geometric Langlands theory\, according to whi
ch the minimal model CFT factors into the tensor product of two copies of
WZW CFT (for a pair of Langlands dual groups).\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard)
DTSTART:20210910T190000Z
DTEND:20210910T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/2
DESCRIPTION:Title: Factorization of the minimal model CFT and Lang
lands duality\nby Dennis Gaitsgory (Harvard) as part of MIT Infinite D
imensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons bu
ilding.\n\nAbstract\nWe will suggest a conjectural picture\, which follows
from the quantum geometric Langlands theory\, according to which the mini
mal model CFT factors into the tensor product of two copies of WZW CFT (fo
r a pair of Langlands dual groups).\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern University)
DTSTART:20210917T190000Z
DTEND:20210917T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/3
DESCRIPTION:Title: Root of unity quantum cluster algebras: discrim
inants\, Cayley-Hamilton algebras\, and Poisson orders\nby Milen Yakim
ov (Northeastern University) as part of MIT Infinite Dimensional Algebra S
eminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract\
nWe will describe a theory of root of unity quantum cluster algebras\, whi
ch includes various families of algebras from Lie theory and topology. All
such algebras will be shown to be maximal orders in central simple algebr
as. Inside each of them\, we will construct a canonical central subalgebra
which is isomorphic to the underlying cluster algebra. It is a far-reachi
ng generalization of the De Concini-Kac-Procesi central subalgebras that p
lay a fundamental role in the representation theory of quantum groups at r
oots of unity. An explicit formula for the corresponding discriminants wil
l be presented. We will also show that all root of unity quantum cluster a
lgebras have canonical structures of Cayley-Hamilton algebras (in the sens
e of Procesi) and Poisson orders (in the sense of De Concini-Kac-Procesi a
nd Brown-Gordon). Their fully Azumaya loci will be shown to contain the un
derlying cluster A varieties. This is a joint work with Shengnan Huang\, T
hang Le\, Bach Nguyen and Kurt Trampel.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale)
DTSTART:20210924T190000Z
DTEND:20210924T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/4
DESCRIPTION:Title: Spectral description of non-commutative local s
ystems on\nby Alexander Goncharov (Yale) as part of MIT Infinite Dimen
sional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons buildi
ng.\n\nAbstract\nI will explain a cluster description of moduli spaces of
R-vector bundles with flat connections over topological surfaces\, where R
is a non-commutative field. Examples include moduli spaces of Stokes data
\, which appear in the study of differential equations with irregula
r singularities on Riemann surfaces. This is a joint work with Maxim Konts
evich.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Finkelberg (HSE)
DTSTART:20211001T140000Z
DTEND:20211001T160000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/5
DESCRIPTION:Title: Kazhdan-Lusztig conjecture via zastava spaces\nby Michael Finkelberg (HSE) as part of MIT Infinite Dimensional Algebr
a Seminar\n\n\nAbstract\nThis is a joint work with A.Braverman and H.Nakaj
ima. We give yet another proof (a geometric one) of the famous Kazhdan-Lus
ztig conjecture on the characters of irreducible modules in the category O
over a complex semisimple Lie algebra (in the Koszul-dual formulation). T
he proof proceeds by analysis of fixed points in the zastava spaces.\n\nOu
r next speaker in the Infinite Dimensional Algebra Seminar (this Friday 10
-12 AM\, note special time) will be MICHAEL FINKELBERG\, who will speak to
us on:\n\n"Kazhdan-Lusztig conjecture via zastava spaces"\n\nThe talk wil
l be online only\, at the following link (passcode "vertex"):\n\nhttps://m
it.zoom.us/j/94437991922?pwd=L2o4Njlubkk3Uk9Wc0EwQ1h6UjNQdz09\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20211008T190000Z
DTEND:20211008T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/6
DESCRIPTION:Title: Tautological classes and symmetry in Khovanov-R
ozansky homology\nby Eugene Gorsky (UC Davis) as part of MIT Infinite
Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons b
uilding.\n\nAbstract\nWe define a new family of commuting operators F_k in
Khovanov-Rozansky link homology\, similar to the action of tautological c
lasses in cohomology of character varieties. We prove that F_2 satisfies `
`hard Lefshetz property" and hence exhibits the symmetry in Khovanov-Rozan
sky homology conjectured by Dunfield\, Gukov and Rasmussen in 2005. This i
s a joint work with Matt Hogancamp and Anton Mellit.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20211015T190000Z
DTEND:20211015T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/7
DESCRIPTION:Title: Finite dimensionality of conformal blocks on th
e torus\nby Reimundo Heluani (IMPA) as part of MIT Infinite Dimensiona
l Algebra Seminar\n\n\nAbstract\nWe will review conditions on a vertex alg
ebra V so that its space of conformal blocks on the torus is finite dimens
ional. This leads to conditions of V related to C_2 cofiniteness: the zero
-th Poisson homology of Zhu's C_2 algebra R_V is finite dimensional. We an
alyze analogous conditions so that the higher chiral homology of V on the
torus is finite dimensional\, this leads to the obvious condition on the P
oisson homology of Zhu's C_2 algebra\, as well as some extra conditions on
the full classical limit of V. This is joint work with J. V. Ekeren.\n\nh
ttps://math.mit.edu/infdim/\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Université de Lille)
DTSTART:20211022T140000Z
DTEND:20211022T160000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/8
DESCRIPTION:Title: Nilpotent orbits arising from admissible affine
vertex algebras\nby Anne Moreau (Université de Lille) as part of MIT
Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in th
e Simons building.\n\nAbstract\nIn this talk\, I will give a simple descri
ption of the closure of the nilpotent orbits appearing as associated varie
ties of admissible affine vertex algebras in terms of primitive ideals. I
will also connect these varieties with the cohomology of the small quantum
groups associated with an l-th root of unity.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20211029T190000Z
DTEND:20211029T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/9
DESCRIPTION:Title: Affine Springer fibers\, open Hessenberg variet
ies\, and nabla positivity.\nby Anton Mellit (University of Vienna) as
part of MIT Infinite Dimensional Algebra Seminar\n\nLecture held in Room:
2-135 in the Simons building.\n\nAbstract\nI will talk about the positive
part of a certain affine Springer fiber studied by Goresky\, Kottwitz\, a
nd MacPherson\, and a certain interesting open subvariety. The Hilbert ser
ies of their Borel-Moore homology turns out to be related to reproducing k
ernels of the Bergeron-Garsia nabla operator. This operator is easy to def
ine in the basis of modified Macdonald polynomials\, but producing explici
t combinatorial evaluations of this operator is usually difficult and (con
jecturally) relates to interesting Hilbert series associated to various mo
duli spaces. Our work is motivated by the nabla positivity conjecture of B
ergeron\, Garsia\, Haiman\, and Tesler that predicts that nabla evaluated
on a Schur function is sometimes positive\, sometimes negative. We categor
ify this conjecture and reduce it to a vanishing conjecture for the intere
sting open variety. It turns out\, each irreducible S_n representation mys
teriously prefers to live in certain degrees and weights in the cohomology
. This is a joint work with Erik Carlsson.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Zhi Huang (Rutgers)
DTSTART:20211105T190000Z
DTEND:20211105T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/10
DESCRIPTION:Title: Vertex operator algebras and tensor categories
\nby Yi-Zhi Huang (Rutgers) as part of MIT Infinite Dimensional Algebr
a Seminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstra
ct\nIn 1988\, based on the fundamental conjectures on operator product exp
ansion and modular invariance\, Moore and Seiberg observed that there shou
ld be tensor categories with additional structures associated to rational
conformal field theories. Since then\, tensor category structures from con
formal field theories have been constructed\, studied and applied to solve
mathematical problems. Mathematically\, conformal field theories can be c
onstructed and studied using the representation theory of vertex operator
algebras. In this talk\, I will give a survey on the constructions and stu
dies of various tensor category structures on module categories for vertex
operator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20211112T200000Z
DTEND:20211112T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/11
DESCRIPTION:Title: Introduction to the analytic Langlands corresp
ondence\nby Pavel Etingof (MIT) as part of MIT Infinite Dimensional Al
gebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAb
stract\nI will review an analytic approach to the geometric Langlands corr
espondence\, following my work with E. Frenkel and D. Kazhdan\, arXiv:1908
.09677\, arXiv:2103.01509\, arXiv:2106.05243. This approach was developed
by us in the last couple of years and involves ideas from previous and ong
oing works of a number of mathematicians and mathematical physicists -- Ko
ntsevich\, Langlands\, Nekrasov\, Teschner\, Gaiotto-Witten and others. On
e of the goals of this approach is to understand single-valued real analyt
ic eigenfunctions of the quantum Hitchin integrable system. The main metho
d of studying these functions is realizing them as the eigenbasis for cert
ain compact normal commuting integral operators the Hilbert space of L2 ha
lf-densities on the (complex points of) the moduli space $Bun(G\,X)$ of pr
incipal G-bundles on a smooth projective curve X\, possibly with parabolic
points. These operators actually make sense over any local field\, and ov
er non-archimedian fields are a replacement for the quantum Hitchin system
. We conjecture them to be compact and prove this conjecture in the genus
zero case (with parabolic points) for $G=PGL(2)$.\n\nI will first discuss
the simplest non-trivial example of Hecke operators over local fields\, na
mely $G=PGL(2)$ and genus 0 curve with 4 parabolic points. In this case th
e moduli space of semistable bundles $Bun(G\,X)^{ss}$ is $P^1$\, and the s
ituation is relatively well understood\; over C it is the theory of single
-valued eigenfunctions of the Lame operator with coupling parameter $-1/2$
(previously studied by Beukers and later in a more functional-analytic se
nse in our work with Frenkel and Kazhdan). I will consider the correspondi
ng spectral theory and then explain its generalization to $N>4$ points and
conjecturally to higher genus curves.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kent Vashaw (LSU)
DTSTART:20211119T200000Z
DTEND:20211119T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/12
DESCRIPTION:Title: On the spectrum and support of a finite tensor
category\nby Kent Vashaw (LSU) as part of MIT Infinite Dimensional Al
gebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAb
stract\nThe tools of support varieties (initiated by Carlson in 1983) and
tensor triangular geometry (initiated by Balmer in 2005) have played an im
portant role in the study of monoidal triangulated categories\, with stabl
e categories of finite tensor categories forming one of the principal clas
ses of examples. The relationship between support varieties and tensor tri
angular geometry has been used in many cases to classify the thick ideals
of the category in question\, a fundamental problem. We will discuss work
of Buan-Krause-Solberg and Nakano-V.-Yakimov\, which defined and developed
noncommutative versions of Balmer's theory\, and will proceed to describe
new methods for determining the Balmer spectrum and thick ideals of a mon
oidal triangulated category. This is joint work with Daniel Nakano and Mil
en Yakimov.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michela Varagnolo (Université de Cergy-Pontoise)
DTSTART:20211203T200000Z
DTEND:20211203T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/13
DESCRIPTION:Title: K theoretic Hall algebras and coherent categor
ification of quantum groups\nby Michela Varagnolo (Université de Cerg
y-Pontoise) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture
held in Room: 2-135 in the Simons building.\n\nAbstract\nI will explain a
n isomorphism between the positive half o a quantum toroidal group and the
K-theoretic Hall algebra of a preprojective algebra of affine type. There
is an analogue result in the finite type case. For type A_1 this allows t
o propose a coherent categorification of the quantum affine sl(2). Surpris
ingly it may be computed using KLR algebras. The talk is based on two join
t works\, one with E. Vasserot\, the other with P. Shan and E. Vasserot\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (Mathematical Institute of the University of Bo
nn)
DTSTART:20220204T200000Z
DTEND:20220204T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/14
DESCRIPTION:Title: Motivic Springer theory\nby Catharina Stro
ppel (Mathematical Institute of the University of Bonn) as part of MIT Inf
inite Dimensional Algebra Seminar\n\n\nAbstract\nMany interesting algebras
in (geometric) representation theory arise as convolution algebras. Based
on these examples we develop a general framework using Chow rings and Cho
w motives. Chow motives are objects in a weights structure of the triangul
ated derived category of motives. I will explain weight structure and weig
ht complex functors and try to explain why it might be interesting for rep
resentation theorists. We finally indicate formality results using motiv
es instead of perverse sheaves.\n\nMeeting Time: Fridays\, 3:00 PM - 5:00
PM | Location: Virtual on Zoom or on campus in Room 2-135\; please contact
Andrei Negut (anegut@mit.edu) to be placed on the mailing list and to rec
eive Zoom link and password.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro van Ekeren (Instituto de Matematica Pura e Aplicada (IMPA))
DTSTART:20220211T200000Z
DTEND:20220211T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/15
DESCRIPTION:Title: Chiral homology\, the Zhu algebra and identiti
es of Rogers-Ramanujan type\nby Jethro van Ekeren (Instituto de Matema
tica Pura e Aplicada (IMPA)) as part of MIT Infinite Dimensional Algebra S
eminar\n\n\nAbstract\nThe notion of chiral homology of a chiral algebra wa
s introduced by Beilinson and Drinfeld\, generalising conformal blocks.
The construction of a chiral algebra from a conformal vertex algebra and a
smooth complex curve provides a large supply of interesting examples\, bu
t in general the chiral homology of these examples seems not to be well un
derstood. Motivated by questions in the representation theory of vertex al
gebras\, we study the behaviour of the chiral homology of families of ell
iptic curves degenerating to a nodal curve. After introducing chiral homol
ogy in general\, I will explain how to develop explicit complexes to comp
ute it in the case of interest\, relate it to the Hochschild homology of
the corresponding Zhu algebra\, and establish links with identities of Ro
gers-Ramanujan type and their generalisations. (Joint work with R. Heluani
)\n\nMeeting Time: Fridays\, 3:00 PM - 5:00 PM | Location: Virtual on Zoom
or on campus in Room 2-135\; please contact Andrei Negut (anegut@mit.edu)
to be placed on the mailing list and to receive Zoom link and password.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvain Carpentier (Columbia University)
DTSTART:20220304T140000Z
DTEND:20220304T160000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/16
DESCRIPTION:Title: Quantization of integrable differential differ
ence equations\nby Sylvain Carpentier (Columbia University) as part of
MIT Infinite Dimensional Algebra Seminar\n\n\nAbstract\nWe present a new
approach to the problem of quantising integrable systems of differential-d
ifference equations. The main idea is to lift these systems to systems def
ined on free associative algebras and look for the ideals there that are s
tabilized by the new dynamics. In a reasonable class of candidate ideals\,
there are typically very few that are invariant for the first equation in
the hierarchy. Once these ideals are picked the challenge is to prove tha
t the whole hierarchy of equations stabilizes them. We will discuss these
ideas using as a key example the hierarchy of the Bogoyavlensky equation.
\n\nThis is a joint work with A. Mikhailov (Leeds) and J. P. Wang (U. of K
ent). To be published soon.\n\nRegular Meeting Time: Fridays\, 3:00 PM - 5
:00 PM | Location: Virtual on Zoom or on campus in Room 2-135\; please con
tact Andrei Negut (anegut@mit.edu) to be placed on the mailing list and to
receive Zoom link and password.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT Mathematics)
DTSTART:20220218T200000Z
DTEND:20220218T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/17
DESCRIPTION:Title: Generators and relations for quantum loop grou
ps\nby Andrei Negut (MIT Mathematics) as part of MIT Infinite Dimensio
nal Algebra Seminar\n\nLecture held in Room 2-135 in the Simons Building.\
n\nAbstract\nI will describe a program that uses shuffle algebras to yield
generators-and-relations presentations for quantum loop groups. The main
idea is that the necessary relations are dual to the so-called wheel condi
tions that describe the shuffle algebras in question\, and we will use thi
s to get a complete presentation of two interesting algebras that arise in
geometric representation theory: K-theoretic Hall algebras of quivers\, a
nd Hall algebras of coherent sheaves on curves over finite fields (the lat
ter project joint work with Francesco Sala and Olivier Schiffmann).\n\nReg
ular Meeting Time: Fridays\, 3:00 PM - 5:00 PM | Location: Virtual on Zoom
or on campus in Room 2-135\; please contact Andrei Negut (anegut@mit.edu)
to be placed on the mailing list and to receive Zoom link and password.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Sam (UC San Diego)
DTSTART:20220225T210000Z
DTEND:20220225T230000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/18
DESCRIPTION:Title: Curried Lie Algebras\nby Steven Sam (UC Sa
n Diego) as part of MIT Infinite Dimensional Algebra Seminar\n\n\nAbstract
\nA representation of $gl(V)$ is a map $V \\otimes V^* \\otimes M \\to M$
satisfying some conditions\, or via currying\, it is a map $V \\otimes M \
\to V \\otimes M$ satisfying different conditions. The latter formulation
can be used in more general symmetric tensor categories where duals may no
t exist\, such as the category of sequences of symmetric group representat
ions under the induction product. Several other families of Lie algebras h
ave such "curried" descriptions and their categories of representations ha
ve nice compact descriptions as representations of diagram categories\, su
ch as the (walled) Brauer category\, partition category\, and variants. I
will explain a few examples in detail and how we came to this definition.
This is joint work with Andrew Snowden.\n\nRegular Meeting Time: Fridays\,
3:00 PM - 5:00 PM | Location: Virtual on Zoom or on campus in Room 2-135\
; please contact Andrei Negut (anegut@mit.edu) to be placed on the mailing
list and to receive Zoom link and password.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander "Sasha" Tsymbaliuk (Perdue)
DTSTART:20220318T190000Z
DTEND:20220318T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/19
DESCRIPTION:Title: Title to be announced\nby Alexander "Sasha
" Tsymbaliuk (Perdue) as part of MIT Infinite Dimensional Algebra Seminar\
n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract\nAbstra
ct to be shared\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quoc Ho (Hong Kong University)
DTSTART:20220311T200000Z
DTEND:20220311T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/20
DESCRIPTION:Title: Title To Be Announced\nby Quoc Ho (Hong Ko
ng University) as part of MIT Infinite Dimensional Algebra Seminar\n\nLect
ure held in Room: 2-135 in the Simons building.\n\nAbstract\nAbstract to b
e shared\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Köhl (University of Kiel)
DTSTART:20220401T190000Z
DTEND:20220401T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/21
DESCRIPTION:Title: Topological Kac-Moody groups -- Discussing the
topology proposed by Kac and Peterson\nby Ralf Köhl (University of K
iel) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture held i
n Room: 2-135 in the Simons building.\n\nAbstract\nGiven a (minimal) Kac-M
oody group over a local field k (say of characteristic 0)\, for instance t
he subgroup of $Aut(g)$\, g a Kac-Moody algebra over k\, generated by the
groups $(P)SL_2(k)$ belonging to the simple roots\, one can endow it with
the finest group topology such that the embeddings of the Lie groups $(P)S
L_2(k)$ become continuous.\n\nThis turns out to be a Hausdorff group topol
ogy\, and actually equal to the group topology that Kac and Peterson sugge
sted for such Kac-Moody groups in the 1980s.\n\nThis topology is always $k
_omega$\, and it is locally compact if and only if the Kac-Moody group act
ually is a finite-dimensional Lie group.\n\nThis topology induces the Lie
topology on the Levi factors of parabolics of spherical type\, in the inde
finite cases it provides new examples for Kramer's theory of topological t
win buildings (which he developed in 2002 for loop groups)\, and in the Ar
chimedian case it is possible to determine their fundamental groups\, actu
ally providing a structural explanation for the (known by classification)
fundamental groups of semisimple split real Lie groups.\n\nMoreover\, in t
he 2-spherical situation these topological groups turn out to satisfy Kazh
dan's Property (T)\, and allow Mostow-Margulis-type rigidity results for (
S-)arithmetic subgroups.\n\nKac-Moody groups also admit symmetric spaces.
In the non-spherical situation\, these symmetric spaces have a causal stru
cture with the two halves of the twin building visible at infinity in the
future\, resp. past directions. One can prove that either time-travel is i
mpossible on Kac-Moody symmetric spaces (i.e.\, there are no non-trivial c
losed causal piecewise geodesic curves) or all points of the Kac-Moody sym
metric space are causally equivalent. It turns out that the question which
of the two cases occurs is equivalent to the question whether (global) Ko
stant convexity holds for Kac-Moody groups\; it also seems\, by an observa
tion that Hartnick and Damour pointed out to me\, that this question is cl
osely related to what physicists call "cosmological billards"\, so from a
physical point of view one should expect Kostant convexity to hold and\, t
hus\, time travel to be impossible on Kac-Moody symmetric spaces.\n\n(Glob
al) Kostant convexity is the question how the A-part in the Iwasawa decomp
osition KAN changes if one multiplies with an element in K from the wrong
side. There is a local version concerning the adjoint action on the Kac-Mo
ody algebra\, and this holds by a result by Kac and Peterson from 1984.\n\
nI started thinking about Kac-Moody groups as a postdoc in 2005 (when toge
ther with three peers at TU Darmstadt we founded what we then called the "
anonymous Kac-Moody theorists")\, and this is a report on various things w
e encountered along the way\; two of the three other anonymous Kac-Moody t
heorists became key collaborators of mine over the years. My collaborators
and students during various stages of my work will be mentioned explicitl
y as we make our way through the various observations.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT Mathematics)
DTSTART:20220415T190000Z
DTEND:20220415T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/22
DESCRIPTION:Title: Conjugacy classes in the Weyl group and nilpot
ent orbits\nby Zhiwei Yun (MIT Mathematics) as part of MIT Infinite Di
mensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons bui
lding.\n\nAbstract\nThe Weyl group and the nilpotent orbits are two basic
objects attached to a semisimple Lie group. In this talk\, I will describe
two very different geometric constructions relating these two objects\, d
ue to Kazhdan-Lusztig\, Lusztig\, and myself.\n\nThe main result is that t
hese two constructions give the same maps between conjugacy classes in the
Weyl group and the set of nilpotent orbits. It confirms a conjecture of K
azhdan and Lusztig in the 80s. The proof uses affine Springer fibers\, and
leads to more open questions about them.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT Mathematics)
DTSTART:20220506T190000Z
DTEND:20220506T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/23
DESCRIPTION:Title: New geometric approaches to the small quantum
group\nby Roman Bezrukavnikov (MIT Mathematics) as part of MIT Infinit
e Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons
building.\n\nAbstract\nI will talk about relations between modules over t
he small quantum group $u_q$ at a root of unity and geometry of a specific
affine Springer fiber F. Cohomology of F is related to the center of $u_q
$\, while (Koszul dual of) the category of $u_q$ modules is related to mic
rolocal sheaves on F.Based on joint project with Pablo Boixeda Alvarez\, P
eng Shan and Eric Vasserot\, and with Boixeda Alvarez\, Michael McBreen an
d Zhiwei Yun.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard University)
DTSTART:20220408T190000Z
DTEND:20220408T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/24
DESCRIPTION:Title: Screening operators revisited\nby Dennis G
aitsgory (Harvard University) as part of MIT Infinite Dimensional Algebra
Seminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract
\nWe’ll revisit the theorem of Feigin and Frenkel that says that screeni
ng operators that act between Wakimoto modules satisfy quantum Serre relat
ions. We’ll use this to giving an alternative construction of (the Iwaho
ri) variant of Kazhdan-Lusztig equivalence.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandra Utiralova (MIT Mathematics)
DTSTART:20220422T190000Z
DTEND:20220422T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/25
DESCRIPTION:Title: Harish-Chandra bimodules in complex rank\n
by Aleksandra Utiralova (MIT Mathematics) as part of MIT Infinite Dimensio
nal Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.
\n\nAbstract\nThe Deligne tensor categories are defined as an interpolatio
n of the categories of representations of groups $GL_n$\, $O_n$\, $Sp_{2n}
$ or $S_n$ to the complex values of the parameter n. One can extend many c
lassical representation-theoretic notions and constructions to this contex
t. These complex rank analogs of classical objects provide insights into t
heir stable behavior patterns as n goes to infinity. \n\nI will talk about
some of my results on Harish-Chandra bimodules in the Deligne categories.
It is known that in the classical case simple Harish-Chandra bimodules ad
mit a classification in terms of W-orbits of certain pairs of weights. How
ever\, the notion of weight is not well-defined in the setting of the Deli
gne categories. I will explain how in complex rank the above-mentioned cla
ssification translates to a condition on the corresponding (left and right
) central characters.\n\nAnother interesting phenomenon arising in complex
rank is that there are two ways to define Harish-Chandra bimodules. That
is\, one can either require that the center acts locally finitely on a bim
odule M or that M has a finite K-type. The two conditions are known to be
equivalent for a semi-simple Lie algebra in the classical setting\, howeve
r\, in the Deligne categories\, it is no longer the case. I will talk abou
t a way to construct examples of Harish-Chandra bimodules of finite K-type
using the ultraproduct realization of the Deligne categories.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (University of Waterloo + Perimeter Institute)
DTSTART:20220429T190000Z
DTEND:20220429T200000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/26
DESCRIPTION:Title: Noncommutative resolutions and Coulomb branche
s\nby Ben Webster (University of Waterloo + Perimeter Institute) as pa
rt of MIT Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-
135 in the Simons building.\n\nAbstract\nCoulomb branches are a new constr
uction of symplectic singularities based in 3-dimensional N=4 supersymmetr
ic quantum field theory. Even in the case where these recover well-known
singularities such as nilcones and symmetric powers of $C^2$\, they still
shed new light on these varieties. In particular\, they are a presentatio
n which is much better adapted to the construction of tilting generators u
sing the approach of Bezrukavnikov and Kaledin. I'll discuss how this lea
ds to interesting noncommutative symplectic resolutions of Coulomb branche
s\, and a description of the wall-crossing functors for the categories of
coherent sheaves on resolutions.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nate Harman (Institute of Advanced Study)
DTSTART:20220513T190000Z
DTEND:20220513T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/27
DESCRIPTION:Title: Oligomorphic Groups and Pre-Tannakian Categori
es\nby Nate Harman (Institute of Advanced Study) as part of MIT Infini
te Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simon
s building.\n\nAbstract\nI will discuss a new construction of pre-Tannakia
n categories associated to oligomorphic groups -- a class of groups arisin
g in model theory. This gives a new concrete realization of Deligne's inte
rpolation categories Rep $(S_t)$\, as well as new examples of pre-Tannakia
n categories in characteristic zero which are not interpolations or ultrap
roducts of Tannakian categories.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik and Vladimir Hinich (UC Berkeley)
DTSTART:20221014T190000Z
DTEND:20221014T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/28
DESCRIPTION:Title: Root groupoid and related Lie superalgebras.\nby Maria Gorelik and Vladimir Hinich (UC Berkeley) as part of MIT Infi
nite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Sim
ons building.\n\nAbstract\nThis talk in based on a joint work with V. Serg
anova and V. Hinich\, arXiv:2209.06253 [1].\n\nWe introduce a notion of a
root groupoid as a replacement of the notion of Weyl group for (Kac-Moody)
Lie superalgebras. The objects of the root groupoid classify certain roo
t data\, the arrows are defined by generators and relations. As an abstrac
t groupoid the root groupoid has many connected components and we show tha
t to some of them one can associate an interesting family of Lie superalge
bras which we call root superalgebras. Classical Kac-Moody Lie superalgebr
as appear as minimal root superalgebras in fully reflectable components. W
e classify all root superalgebras in these components.\n\nTo each connecte
d component we associate a graph (called skeleton) generalizing the Cayley
graph of the Weyl group. The skeleton satisfies a version of Coxeter prop
erty generalizing the fact that the Weyl group of a Kac-Moody Lie algebra
is Coxeter.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20221021T190000Z
DTEND:20221021T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/29
DESCRIPTION:Title: Title to be announced\nby Ben Davison (Uni
versity of Edinburgh) as part of MIT Infinite Dimensional Algebra Seminar\
n\nLecture held in Room: 2-135 in the Simons building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arun Kanaan (MIT Mathematics)
DTSTART:20221028T190000Z
DTEND:20221028T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/30
DESCRIPTION:Title: Symmetric Tensor Categories and New Constructi
ons of Exceptional Simple Lie\nby Arun Kanaan (MIT Mathematics) as par
t of MIT Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-1
35 in the Simons building.\n\nAbstract\n\\noindent I will present new cons
tructions of several of the exceptional simple Lie super- algebras with in
teger Cartan matrix in characteristic p = 3 and p = 5\, which were classif
ied in [1]. These include the Elduque and Cunha Lie superalgebras. Specifi
cally\, let $\\alpha_{p}$ denote the kernel of the Frobenius endomorphism
on the additive group scheme $\\mathbb{G}_{a}$ over an algebraically close
d field of characteristic p. The Verlinde category Verp is the semisimplif
ication of the representation category Rep αp\, and Verp contains the cat
egory of super vector spaces as a full subcategory. Each exceptional Lie s
uperalgebra we construct is realized as the image of an exceptional Lie al
gebra equipped with a nilpotent derivation of order at most p under the se
misimplification functor from Rep $\\alpha_{p}$ to $Ver_{p}$. The content
of this talk can primarily be found in [2] and [3].\n\n\\vspace{2ex}\n\n\\
noindent Keywords: modular Lie superalgebras\, symmetric tensor categories
Mathematics Subject Classification 2020: 17B\, 18M20\n\n\\vspace{2ex}\n\n
\\noindent References \\\\\n\\noindent {[1]} S. Bouarroudj\, P. Grozman\,
and D. Leites\, Classification of simple finite- dimensional modular Lie s
uperalgebras with Cartan matrix\, Symmetry\, Inte- grability and Geometry:
Methods and Applications (SIGMA) v. 5 (2009)\, no. 060\, 63 pages. \\\\\n
\\noindent {[2]} A.S. Kannan\, New Constructions of Exceptional Simple Lie
Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via T
ensor Categories\, Trans- formation Groups (2022). \\\\\n\\noindent {[3]}
P. Etingof\, and A.S. Kannan\, Lectures On Symmetric Tensor Categories\, a
rXiv:2103.04878 (2021).\\\\\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Williams (Boston University)
DTSTART:20221104T190000Z
DTEND:20221104T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/31
DESCRIPTION:Title: Dolbeault AGT and infinite dimensional excepti
onal super Lie algebras\nby Brian Williams (Boston University) as part
of MIT Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-13
5 in the Simons building.\n\nAbstract\nI will present new constructions of
several of the exceptional simple Lie super- algebras with integer Cartan
matrix in characteristic p = 3 and p = 5\, which were classified in [1].
These include the Elduque and Cunha Lie superalgebras. Specifically\, let
$\\alpha_{p}$ denote the kernel of the Frobenius endomorphism on the addit
ive group scheme $\\mathbb{G}_{a}$ over an algebraically closed field of c
haracteristic p. The Verlinde category Verp is the semisimplification of t
he representation category Rep αp\, and Verp contains the category of sup
er vector spaces as a full subcategory. Each exceptional Lie superalgebra
we construct is realized as the image of an exceptional Lie algebra equipp
ed with a nilpotent derivation of order at most p under the semisimplifica
tion functor from Rep $\\alpha_{p}$ to $Ver_{p}$. The content of this talk
can primarily be found in [2] and [3].\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (The University of Melbourne)
DTSTART:20221118T200000Z
DTEND:20221118T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/32
DESCRIPTION:Title: Cotangent Schubert calculus and Lagrangian cor
respondences\nby Iva Halacheva (The University of Melbourne) as part o
f MIT Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135
in the Simons building.\n\nAbstract\nIn recent work\, the study of partial
flag varieties and the Schubert bases of their equivariant cohomology has
been extended to cotangent bundles and Segre-Schwartz-MacPherson classes.
I will discuss the behavior of these bases in the restriction in cohomolo
gy from type A to type C Grassmannians. When considering their cotangent b
undles\, this behavior has a further geometric interpretation in terms of
Maulik-Okounkov stable envelopes and Lagrangian correspondences. Both sett
ings can be considered from the combinatorial perspective of puzzle rules\
, which in turn are interpreted as quantum integrable systems via R-matric
es for the sl(3) Yangian. This is joint work with Allen Knutson and Paul Z
inn-Justin.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumansky (MIT Mathematics)
DTSTART:20221202T200000Z
DTEND:20221202T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/33
DESCRIPTION:Title: Title to be announced\nby Ilya Dumansky (M
IT Mathematics) as part of MIT Infinite Dimensional Algebra Seminar\n\nLec
ture held in Room: 2-135 in the Simons building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Borodin (MIT Mathematics)
DTSTART:20221209T200000Z
DTEND:20221209T220000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/34
DESCRIPTION:Title: Title to be announced\nby Alexey Borodin (
MIT Mathematics) as part of MIT Infinite Dimensional Algebra Seminar\n\nLe
cture held in Room: 2-135 in the Simons building.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Krylov (MIT Mathematics)
DTSTART:20221007T190000Z
DTEND:20221007T210000Z
DTSTAMP:20260404T131159Z
UID:MIT_Inf_Dim_Algebra_Seminar/35
DESCRIPTION:Title: Subregular nilpotent orbits and explicit chara
cter formulas for modules over affine Lie algebras.\nby Vasily Krylov
(MIT Mathematics) as part of MIT Infinite Dimensional Algebra Seminar\n\nL
ecture held in Room: 2-135 in the Simons building.\n\nAbstract\nThe talk i
s based on the joint work with Roman Bezrukavnikov and Victor Kac (arXiv:2
209.08865). Let g be a simple Lie algebra and let $\\hat{g}$ be the corres
ponding affine Lie algebra. It is known that characters of irreducible (hi
ghest weight) representations of $\\hat{g}$ can be computed in terms of va
lues at q=1 of affine (inverse) Kazhdan-Lusztig polynomials. These values
can be computed recursively but there are no explicit formulas for them in
general. The goal of this talk is to describe certain cases when we can c
ompute the values above explicitly resulting in explicit formulas for char
acters of certain irreducible $\\hat{g}$-modules (partly generalizing resu
lts of Kac and Wakimoto). The calculation relies on the description of the
corresponding module over the affine Hecke algebra in terms of the equiva
riant $K$-theory of the Springer resolution. Time permitting we will discu
ss possible generalizations.\n
LOCATION:https://stable.researchseminars.org/talk/MIT_Inf_Dim_Algebra_Semi
nar/35/
END:VEVENT
END:VCALENDAR