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BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard University)
DTSTART:20210903T190000Z
DTEND:20210903T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/1
DESCRIPTION:Title: Factorization of the minimal model CFT and Langlands d
uality\nby Dennis Gaitsgory (Harvard University) as part of MIT Infini
te Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simon
s building.\n\nAbstract\nWe will suggest a conjectural picture\, which fol
lows from the quantum geometric Langlands theory\, according to which 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://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard)
DTSTART:20210910T190000Z
DTEND:20210910T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/2
DESCRIPTION:Title: Factorization of the minimal model CFT and Langlands d
uality\nby Dennis Gaitsgory (Harvard) as part of MIT Infinite Dimensio
nal Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.
\n\nAbstract\nWe will suggest a conjectural picture\, which follows from t
he quantum geometric Langlands theory\, according to which the minimal mod
el CFT factors into the tensor product of two copies of WZW CFT (for a pai
r of Langlands dual groups).\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milen Yakimov (Northeastern University)
DTSTART:20210917T190000Z
DTEND:20210917T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/3
DESCRIPTION:Title: Root of unity quantum cluster algebras: discriminants\
, Cayley-Hamilton algebras\, and Poisson orders\nby Milen Yakimov (Nor
theastern University) as part of MIT Infinite Dimensional Algebra Seminar\
n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract\nWe wil
l describe a theory of root of unity quantum cluster algebras\, which incl
udes various families of algebras from Lie theory and topology. All such a
lgebras will be shown to be maximal orders in central simple algebras. Ins
ide each of them\, we will construct a canonical central subalgebra which
is isomorphic to the underlying cluster algebra. It is a far-reaching gene
ralization of the De Concini-Kac-Procesi central subalgebras that play a f
undamental role in the representation theory of quantum groups at roots of
unity. An explicit formula for the corresponding discriminants will be pr
esented. We will also show that all root of unity quantum cluster algebras
have canonical structures of Cayley-Hamilton algebras (in the sense of Pr
ocesi) and Poisson orders (in the sense of De Concini-Kac-Procesi and Brow
n-Gordon). Their fully Azumaya loci will be shown to contain the underlyin
g cluster A varieties. This is a joint work with Shengnan Huang\, Thang Le
\, Bach Nguyen and Kurt Trampel.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Goncharov (Yale)
DTSTART:20210924T190000Z
DTEND:20210924T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/4
DESCRIPTION:Title: Spectral description of non-commutative local systems
on\nby Alexander Goncharov (Yale) as part of MIT Infinite Dimensional
Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.\n\n
Abstract\nI will explain a cluster description of moduli spaces of R-vecto
r bundles with flat connections over topological surfaces\, where R is a n
on-commutative field. Examples include moduli spaces of Stokes data\, whic
h appear in the study of differential equations with irregular singu
larities on Riemann surfaces. This is a joint work with Maxim Kontsevich.\
n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Finkelberg (HSE)
DTSTART:20211001T140000Z
DTEND:20211001T160000Z
DTSTAMP:20260422T225719Z
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 Algebra Semin
ar\n\n\nAbstract\nThis is a joint work with A.Braverman and H.Nakajima. We
give yet another proof (a geometric one) of the famous Kazhdan-Lusztig co
njecture on the characters of irreducible modules in the category O over a
complex semisimple Lie algebra (in the Koszul-dual formulation). The proo
f proceeds by analysis of fixed points in the zastava spaces.\n\nOur 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 will be on
line only\, at the following link (passcode "vertex"):\n\nhttps://mit.zoom
.us/j/94437991922?pwd=L2o4Njlubkk3Uk9Wc0EwQ1h6UjNQdz09\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugene Gorsky (UC Davis)
DTSTART:20211008T190000Z
DTEND:20211008T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/6
DESCRIPTION:Title: Tautological classes and symmetry in Khovanov-Rozansky
homology\nby Eugene Gorsky (UC Davis) as part of MIT Infinite Dimensi
onal Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons building
.\n\nAbstract\nWe define a new family of commuting operators F_k in Khovan
ov-Rozansky link homology\, similar to the action of tautological classes
in cohomology of character varieties. We prove that F_2 satisfies ``hard L
efshetz property" and hence exhibits the symmetry in Khovanov-Rozansky hom
ology conjectured by Dunfield\, Gukov and Rasmussen in 2005. This is a joi
nt work with Matt Hogancamp and Anton Mellit.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reimundo Heluani (IMPA)
DTSTART:20211015T190000Z
DTEND:20211015T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/7
DESCRIPTION:Title: Finite dimensionality of conformal blocks on the torus
\nby Reimundo Heluani (IMPA) as part of MIT Infinite Dimensional Algeb
ra Seminar\n\n\nAbstract\nWe will review conditions on a vertex algebra V
so that its space of conformal blocks on the torus is finite dimensional.
This leads to conditions of V related to C_2 cofiniteness: the zero-th Poi
sson homology of Zhu's C_2 algebra R_V is finite dimensional. We analyze a
nalogous conditions so that the higher chiral homology of V on the torus i
s finite dimensional\, this leads to the obvious condition on the Poisson
homology of Zhu's C_2 algebra\, as well as some extra conditions on the fu
ll classical limit of V. This is joint work with J. V. Ekeren.\n\nhttps://
math.mit.edu/infdim/\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne Moreau (Université de Lille)
DTSTART:20211022T140000Z
DTEND:20211022T160000Z
DTSTAMP:20260422T225719Z
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 Infini
te Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simon
s building.\n\nAbstract\nIn this talk\, I will give a simple description o
f the closure of the nilpotent orbits appearing as associated varieties of
admissible affine vertex algebras in terms of primitive ideals. I will al
so connect these varieties with the cohomology of the small quantum groups
associated with an l-th root of unity.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Mellit (University of Vienna)
DTSTART:20211029T190000Z
DTEND:20211029T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/9
DESCRIPTION:Title: Affine Springer fibers\, open Hessenberg varieties\, a
nd nabla positivity.\nby Anton Mellit (University of Vienna) as part o
f 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 o
f a certain affine Springer fiber studied by Goresky\, Kottwitz\, and MacP
herson\, and a certain interesting open subvariety. The Hilbert series of
their Borel-Moore homology turns out to be related to reproducing kernels
of the Bergeron-Garsia nabla operator. This operator is easy to define in
the basis of modified Macdonald polynomials\, but producing explicit combi
natorial evaluations of this operator is usually difficult and (conjectura
lly) relates to interesting Hilbert series associated to various moduli sp
aces. Our work is motivated by the nabla positivity conjecture of Bergeron
\, Garsia\, Haiman\, and Tesler that predicts that nabla evaluated on a Sc
hur function is sometimes positive\, sometimes negative. We categorify thi
s conjecture and reduce it to a vanishing conjecture for the interesting o
pen variety. It turns out\, each irreducible S_n representation mysterious
ly prefers to live in certain degrees and weights in the cohomology. This
is a joint work with Erik Carlsson.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Zhi Huang (Rutgers)
DTSTART:20211105T190000Z
DTEND:20211105T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/10
DESCRIPTION:Title: Vertex operator algebras and tensor categories\nb
y Yi-Zhi Huang (Rutgers) as part of MIT Infinite Dimensional Algebra Semin
ar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract\nIn
1988\, based on the fundamental conjectures on operator product expansion
and modular invariance\, Moore and Seiberg observed that there should be t
ensor categories with additional structures associated to rational conform
al field theories. Since then\, tensor category structures from conformal
field theories have been constructed\, studied and applied to solve mathem
atical problems. Mathematically\, conformal field theories can be construc
ted and studied using the representation theory of vertex operator algebra
s. In this talk\, I will give a survey on the constructions and studies of
various tensor category structures on module categories for vertex operat
or algebras.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (MIT)
DTSTART:20211112T200000Z
DTEND:20211112T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/11
DESCRIPTION:Title: Introduction to the analytic Langlands correspondence
\nby Pavel Etingof (MIT) as part of MIT Infinite Dimensional Algebra S
eminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract\
nI will review an analytic approach to the geometric Langlands corresponde
nce\, following my work with E. Frenkel and D. Kazhdan\, arXiv:1908.09677\
, arXiv:2103.01509\, arXiv:2106.05243. This approach was developed by us i
n the last couple of years and involves ideas from previous and ongoing wo
rks of a number of mathematicians and mathematical physicists -- Kontsevic
h\, Langlands\, Nekrasov\, Teschner\, Gaiotto-Witten and others. One of th
e goals of this approach is to understand single-valued real analytic eige
nfunctions of the quantum Hitchin integrable system. The main method of st
udying these functions is realizing them as the eigenbasis for certain com
pact normal commuting integral operators the Hilbert space of L2 half-dens
ities on the (complex points of) the moduli space $Bun(G\,X)$ of principal
G-bundles on a smooth projective curve X\, possibly with parabolic points
. These operators actually make sense over any local field\, and over non-
archimedian fields are a replacement for the quantum Hitchin system. We co
njecture them to be compact and prove this conjecture in the genus zero ca
se (with parabolic points) for $G=PGL(2)$.\n\nI will first discuss the sim
plest non-trivial example of Hecke operators over local fields\, namely $G
=PGL(2)$ and genus 0 curve with 4 parabolic points. In this case the modul
i space of semistable bundles $Bun(G\,X)^{ss}$ is $P^1$\, and the situatio
n is relatively well understood\; over C it is the theory of single-valued
eigenfunctions of the Lame operator with coupling parameter $-1/2$ (previ
ously studied by Beukers and later in a more functional-analytic sense in
our work with Frenkel and Kazhdan). I will consider the corresponding spec
tral theory and then explain its generalization to $N>4$ points and conjec
turally to higher genus curves.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kent Vashaw (LSU)
DTSTART:20211119T200000Z
DTEND:20211119T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/12
DESCRIPTION:Title: On the spectrum and support of a finite tensor catego
ry\nby Kent Vashaw (LSU) as part of MIT Infinite Dimensional Algebra S
eminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbstract\
nThe tools of support varieties (initiated by Carlson in 1983) and tensor
triangular geometry (initiated by Balmer in 2005) have played an important
role in the study of monoidal triangulated categories\, with stable categ
ories of finite tensor categories forming one of the principal classes of
examples. The relationship between support varieties and tensor triangular
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 noncom
mutative versions of Balmer's theory\, and will proceed to describe new me
thods for determining the Balmer spectrum and thick ideals of a monoidal t
riangulated category. This is joint work with Daniel Nakano and Milen Yaki
mov.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michela Varagnolo (Université de Cergy-Pontoise)
DTSTART:20211203T200000Z
DTEND:20211203T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/13
DESCRIPTION:Title: K theoretic Hall algebras and coherent categorificati
on of quantum groups\nby Michela Varagnolo (Université de Cergy-Ponto
ise) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture held i
n Room: 2-135 in the Simons building.\n\nAbstract\nI will explain an isomo
rphism between the positive half o a quantum toroidal group and the K-theo
retic 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 to propo
se a coherent categorification of the quantum affine sl(2). Surprisingly i
t may be computed using KLR algebras. The talk is based on two joint works
\, one with E. Vasserot\, the other with P. Shan and E. Vasserot\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (Mathematical Institute of the University of Bo
nn)
DTSTART:20220204T200000Z
DTEND:20220204T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/14
DESCRIPTION:Title: Motivic Springer theory\nby Catharina Stroppel (M
athematical Institute of the University of Bonn) as part of MIT Infinite D
imensional Algebra Seminar\n\n\nAbstract\nMany interesting algebras in (ge
ometric) representation theory arise as convolution algebras. Based on the
se examples we develop a general framework using Chow rings and Chow motiv
es. Chow motives are objects in a weights structure of the triangulated de
rived category of motives. I will explain weight structure and weight comp
lex functors and try to explain why it might be interesting for representa
tion theorists. We finally indicate formality results using motives inst
ead of perverse sheaves.\n\nMeeting Time: Fridays\, 3:00 PM - 5:00 PM | Lo
cation: 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 Zo
om link and password.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro van Ekeren (Instituto de Matematica Pura e Aplicada (IMPA))
DTSTART:20220211T200000Z
DTEND:20220211T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/15
DESCRIPTION:Title: Chiral homology\, the Zhu algebra and identities of R
ogers-Ramanujan type\nby Jethro van Ekeren (Instituto de Matematica Pu
ra e Aplicada (IMPA)) as part of MIT Infinite Dimensional Algebra Seminar\
n\n\nAbstract\nThe notion of chiral homology of a chiral algebra was intro
duced by Beilinson and Drinfeld\, generalising conformal blocks. The con
struction of a chiral algebra from a conformal vertex algebra and a smooth
complex curve provides a large supply of interesting examples\, but in ge
neral the chiral homology of these examples seems not to be well understoo
d. Motivated by questions in the representation theory of vertex algebras\
, we study the behaviour of the chiral homology of families of elliptic c
urves degenerating to a nodal curve. After introducing chiral homology in
general\, I will explain how to develop explicit complexes to compute it
in the case of interest\, relate it to the Hochschild homology of the co
rresponding Zhu algebra\, and establish links with identities of Rogers-Ra
manujan type and their generalisations. (Joint work with R. Heluani)\n\nMe
eting 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://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sylvain Carpentier (Columbia University)
DTSTART:20220304T140000Z
DTEND:20220304T160000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/16
DESCRIPTION:Title: Quantization of integrable differential difference eq
uations\nby Sylvain Carpentier (Columbia University) as part of MIT In
finite Dimensional Algebra Seminar\n\n\nAbstract\nWe present a new approac
h to the problem of quantising integrable systems of differential-differen
ce equations. The main idea is to lift these systems to systems defined on
free associative algebras and look for the ideals there that are stabiliz
ed 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 hi
erarchy. Once these ideals are picked the challenge is to prove that the w
hole hierarchy of equations stabilizes them. We will discuss these ideas u
sing as a key example the hierarchy of the Bogoyavlensky equation. \n\nThi
s is a joint work with A. Mikhailov (Leeds) and J. P. Wang (U. of Kent). T
o 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 contact An
drei Negut (anegut@mit.edu) to be placed on the mailing list and to receiv
e Zoom link and password.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Negut (MIT Mathematics)
DTSTART:20220218T200000Z
DTEND:20220218T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/17
DESCRIPTION:Title: Generators and relations for quantum loop groups\
nby Andrei Negut (MIT Mathematics) as part of MIT Infinite Dimensional Alg
ebra Seminar\n\nLecture held in Room 2-135 in the Simons Building.\n\nAbst
ract\nI will describe a program that uses shuffle algebras to yield genera
tors-and-relations presentations for quantum loop groups. The main idea is
that the necessary relations are dual to the so-called wheel conditions t
hat describe the shuffle algebras in question\, and we will use this to ge
t a complete presentation of two interesting algebras that arise in geomet
ric representation theory: K-theoretic Hall algebras of quivers\, and Hall
algebras of coherent sheaves on curves over finite fields (the latter pro
ject joint work with Francesco Sala and Olivier Schiffmann).\n\nRegular Me
eting 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://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steven Sam (UC San Diego)
DTSTART:20220225T210000Z
DTEND:20220225T230000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/18
DESCRIPTION:Title: Curried Lie Algebras\nby Steven Sam (UC San Diego
) as part of MIT Infinite Dimensional Algebra Seminar\n\n\nAbstract\nA rep
resentation of $gl(V)$ is a map $V \\otimes V^* \\otimes M \\to M$ satisfy
ing 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 not exist
\, such as the category of sequences of symmetric group representations un
der the induction product. Several other families of Lie algebras have suc
h "curried" descriptions and their categories of representations have nice
compact descriptions as representations of diagram categories\, such as t
he (walled) Brauer category\, partition category\, and variants. I will ex
plain 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 P
M - 5:00 PM | Location: Virtual on Zoom or on campus in Room 2-135\; pleas
e contact Andrei Negut (anegut@mit.edu) to be placed on the mailing list a
nd to receive Zoom link and password.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander "Sasha" Tsymbaliuk (Perdue)
DTSTART:20220318T190000Z
DTEND:20220318T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/19
DESCRIPTION:Title: Title to be announced\nby Alexander "Sasha" Tsymb
aliuk (Perdue) 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://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quoc Ho (Hong Kong University)
DTSTART:20220311T200000Z
DTEND:20220311T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/20
DESCRIPTION:Title: Title To Be Announced\nby Quoc Ho (Hong Kong Univ
ersity) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture hel
d in Room: 2-135 in the Simons building.\n\nAbstract\nAbstract to be share
d\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Köhl (University of Kiel)
DTSTART:20220401T190000Z
DTEND:20220401T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/21
DESCRIPTION:Title: Topological Kac-Moody groups -- Discussing the topolo
gy proposed by Kac and Peterson\nby Ralf Köhl (University of Kiel) as
part of MIT Infinite Dimensional Algebra Seminar\n\nLecture held in Room:
2-135 in the Simons building.\n\nAbstract\nGiven a (minimal) Kac-Moody gr
oup over a local field k (say of characteristic 0)\, for instance the subg
roup 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 fin
est group topology such that the embeddings of the Lie groups $(P)SL_2(k)$
become continuous.\n\nThis turns out to be a Hausdorff group topology\, a
nd actually equal to the group topology that Kac and Peterson suggested fo
r 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 actually i
s a finite-dimensional Lie group.\n\nThis topology induces the Lie topolog
y on the Levi factors of parabolics of spherical type\, in the indefinite
cases it provides new examples for Kramer's theory of topological twin bui
ldings (which he developed in 2002 for loop groups)\, and in the Archimedi
an case it is possible to determine their fundamental groups\, actually pr
oviding a structural explanation for the (known by classification) fundame
ntal groups of semisimple split real Lie groups.\n\nMoreover\, in the 2-sp
herical situation these topological groups turn out to satisfy Kazhdan's P
roperty (T)\, and allow Mostow-Margulis-type rigidity results for (S-)arit
hmetic subgroups.\n\nKac-Moody groups also admit symmetric spaces. In the
non-spherical situation\, these symmetric spaces have a causal structure w
ith the two halves of the twin building visible at infinity in the future\
, resp. past directions. One can prove that either time-travel is impossib
le on Kac-Moody symmetric spaces (i.e.\, there are no non-trivial closed c
ausal piecewise geodesic curves) or all points of the Kac-Moody symmetric
space are causally equivalent. It turns out that the question which of the
two cases occurs is equivalent to the question whether (global) Kostant c
onvexity holds for Kac-Moody groups\; it also seems\, by an observation th
at Hartnick and Damour pointed out to me\, that this question is closely r
elated to what physicists call "cosmological billards"\, so from a physica
l point of view one should expect Kostant convexity to hold and\, thus\, t
ime travel to be impossible on Kac-Moody symmetric spaces.\n\n(Global) Kos
tant convexity is the question how the A-part in the Iwasawa decomposition
KAN changes if one multiplies with an element in K from the wrong side. T
here is a local version concerning the adjoint action on the Kac-Moody alg
ebra\, and this holds by a result by Kac and Peterson from 1984.\n\nI star
ted thinking about Kac-Moody groups as a postdoc in 2005 (when together wi
th three peers at TU Darmstadt we founded what we then called the "anonymo
us Kac-Moody theorists")\, and this is a report on various things we encou
ntered along the way\; two of the three other anonymous Kac-Moody theorist
s became key collaborators of mine over the years. My collaborators and st
udents during various stages of my work will be mentioned explicitly as we
make our way through the various observations.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiwei Yun (MIT Mathematics)
DTSTART:20220415T190000Z
DTEND:20220415T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/22
DESCRIPTION:Title: Conjugacy classes in the Weyl group and nilpotent orb
its\nby Zhiwei Yun (MIT Mathematics) as part of MIT Infinite Dimension
al Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.\
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 ve
ry different geometric constructions relating these two objects\, due to K
azhdan-Lusztig\, Lusztig\, and myself.\n\nThe main result is that these tw
o constructions give the same maps between conjugacy classes in the Weyl g
roup and the set of nilpotent orbits. It confirms a conjecture of Kazhdan
and Lusztig in the 80s. The proof uses affine Springer fibers\, and leads
to more open questions about them.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Bezrukavnikov (MIT Mathematics)
DTSTART:20220506T190000Z
DTEND:20220506T210000Z
DTSTAMP:20260422T225719Z
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 Infinite Dimen
sional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons buildi
ng.\n\nAbstract\nI will talk about relations between modules over the smal
l 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 $u_q$\, whi
le (Koszul dual of) the category of $u_q$ modules is related to microlocal
sheaves on F.Based on joint project with Pablo Boixeda Alvarez\, Peng Sha
n and Eric Vasserot\, and with Boixeda Alvarez\, Michael McBreen and Zhiwe
i Yun.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Gaitsgory (Harvard University)
DTSTART:20220408T190000Z
DTEND:20220408T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/24
DESCRIPTION:Title: Screening operators revisited\nby Dennis Gaitsgor
y (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 screening oper
ators that act between Wakimoto modules satisfy quantum Serre relations. W
e’ll use this to giving an alternative construction of (the Iwahori) var
iant of Kazhdan-Lusztig equivalence.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandra Utiralova (MIT Mathematics)
DTSTART:20220422T190000Z
DTEND:20220422T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/25
DESCRIPTION:Title: Harish-Chandra bimodules in complex rank\nby Alek
sandra Utiralova (MIT Mathematics) as part of MIT Infinite Dimensional Alg
ebra Seminar\n\nLecture held in Room: 2-135 in the Simons building.\n\nAbs
tract\nThe Deligne tensor categories are defined as an interpolation of th
e 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 classica
l representation-theoretic notions and constructions to this context. Thes
e complex rank analogs of classical objects provide insights into their st
able behavior patterns as n goes to infinity. \n\nI will talk about some o
f my results on Harish-Chandra bimodules in the Deligne categories. It is
known that in the classical case simple Harish-Chandra bimodules admit a c
lassification in terms of W-orbits of certain pairs of weights. However\,
the notion of weight is not well-defined in the setting of the Deligne cat
egories. I will explain how in complex rank the above-mentioned classifica
tion translates to a condition on the corresponding (left and right) centr
al characters.\n\nAnother interesting phenomenon arising in complex rank i
s that there are two ways to define Harish-Chandra bimodules. That is\, on
e can either require that the center acts locally finitely on a bimodule M
or that M has a finite K-type. The two conditions are known to be equival
ent for a semi-simple Lie algebra in the classical setting\, however\, in
the Deligne categories\, it is no longer the case. I will talk about a way
to construct examples of Harish-Chandra bimodules of finite K-type using
the ultraproduct realization of the Deligne categories.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Webster (University of Waterloo + Perimeter Institute)
DTSTART:20220429T190000Z
DTEND:20220429T200000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/26
DESCRIPTION:Title: Noncommutative resolutions and Coulomb branches\n
by Ben Webster (University of Waterloo + Perimeter Institute) as part of M
IT Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in
the Simons building.\n\nAbstract\nCoulomb branches are a new construction
of symplectic singularities based in 3-dimensional N=4 supersymmetric quan
tum field theory. Even in the case where these recover well-known singula
rities such as nilcones and symmetric powers of $C^2$\, they still shed ne
w light on these varieties. In particular\, they are a presentation which
is much better adapted to the construction of tilting generators using th
e approach of Bezrukavnikov and Kaledin. I'll discuss how this leads to i
nteresting noncommutative symplectic resolutions of Coulomb branches\, and
a description of the wall-crossing functors for the categories of coheren
t sheaves on resolutions.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nate Harman (Institute of Advanced Study)
DTSTART:20220513T190000Z
DTEND:20220513T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/27
DESCRIPTION:Title: Oligomorphic Groups and Pre-Tannakian Categories\
nby Nate Harman (Institute of Advanced Study) as part of MIT Infinite Dime
nsional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons build
ing.\n\nAbstract\nI will discuss a new construction of pre-Tannakian categ
ories associated to oligomorphic groups -- a class of groups arising in mo
del theory. This gives a new concrete realization of Deligne's interpolati
on categories Rep $(S_t)$\, as well as new examples of pre-Tannakian categ
ories in characteristic zero which are not interpolations or ultraproducts
of Tannakian categories.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Gorelik and Vladimir Hinich (UC Berkeley)
DTSTART:20221014T190000Z
DTEND:20221014T210000Z
DTSTAMP:20260422T225719Z
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 Infinite Di
mensional Algebra Seminar\n\nLecture held in Room: 2-135 in the Simons bui
lding.\n\nAbstract\nThis talk in based on a joint work with V. Serganova a
nd V. Hinich\, arXiv:2209.06253 [1].\n\nWe introduce a notion of a root gr
oupoid as a replacement of the notion of Weyl group for (Kac-Moody) Lie su
peralgebras. The objects of the root groupoid classify certain root data\
, the arrows are defined by generators and relations. As an abstract group
oid the root groupoid has many connected components and we show that to so
me of them one can associate an interesting family of Lie superalgebras wh
ich we call root superalgebras. Classical Kac-Moody Lie superalgebras appe
ar as minimal root superalgebras in fully reflectable components. We class
ify all root superalgebras in these components.\n\nTo each connected compo
nent we associate a graph (called skeleton) generalizing the Cayley graph
of the Weyl group. The skeleton satisfies a version of Coxeter property ge
neralizing the fact that the Weyl group of a Kac-Moody Lie algebra is Coxe
ter.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Davison (University of Edinburgh)
DTSTART:20221021T190000Z
DTEND:20221021T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/29
DESCRIPTION:Title: Title to be announced\nby Ben Davison (University
of Edinburgh) as part of MIT Infinite Dimensional Algebra Seminar\n\nLect
ure held in Room: 2-135 in the Simons building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arun Kanaan (MIT Mathematics)
DTSTART:20221028T190000Z
DTEND:20221028T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/30
DESCRIPTION:Title: Symmetric Tensor Categories and New Constructions of
Exceptional Simple Lie\nby Arun Kanaan (MIT Mathematics) as part of MI
T Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in t
he Simons building.\n\nAbstract\n\\noindent I will present new constructio
ns of several of the exceptional simple Lie super- algebras with integer C
artan 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
additive group scheme $\\mathbb{G}_{a}$ over an algebraically closed field
of characteristic p. The Verlinde category Verp is the semisimplification
of the representation category Rep αp\, and Verp contains the category o
f super vector spaces as a full subcategory. Each exceptional Lie superalg
ebra we construct is realized as the image of an exceptional Lie algebra e
quipped with a nilpotent derivation of order at most p under the semisimpl
ification 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\\noinden
t Keywords: modular Lie superalgebras\, symmetric tensor categories Mathem
atics Subject Classification 2020: 17B\, 18M20\n\n\\vspace{2ex}\n\n\\noind
ent References \\\\\n\\noindent {[1]} S. Bouarroudj\, P. Grozman\, and D.
Leites\, Classification of simple finite- dimensional modular Lie superalg
ebras with Cartan matrix\, Symmetry\, Inte- grability and Geometry: Method
s and Applications (SIGMA) v. 5 (2009)\, no. 060\, 63 pages. \\\\\n\\noind
ent {[2]} A.S. Kannan\, New Constructions of Exceptional Simple Lie Supera
lgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor C
ategories\, Trans- formation Groups (2022). \\\\\n\\noindent {[3]} P. Etin
gof\, and A.S. Kannan\, Lectures On Symmetric Tensor Categories\, arXiv:21
03.04878 (2021).\\\\\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Williams (Boston University)
DTSTART:20221104T190000Z
DTEND:20221104T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/31
DESCRIPTION:Title: Dolbeault AGT and infinite dimensional exceptional su
per Lie algebras\nby Brian Williams (Boston University) as part of MIT
Infinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in th
e Simons building.\n\nAbstract\nI will present new constructions of severa
l of the exceptional simple Lie super- algebras with integer Cartan matrix
in characteristic p = 3 and p = 5\, which were classified in [1]. These i
nclude the Elduque and Cunha Lie superalgebras. Specifically\, let $\\alph
a_{p}$ denote the kernel of the Frobenius endomorphism on the additive gro
up scheme $\\mathbb{G}_{a}$ over an algebraically closed field of characte
ristic p. The Verlinde category Verp is the semisimplification of the repr
esentation category Rep αp\, and Verp contains the category of super vect
or spaces as a full subcategory. Each exceptional Lie superalgebra we cons
truct is realized as the image of an exceptional Lie algebra equipped with
a nilpotent derivation of order at most p under the semisimplification fu
nctor from Rep $\\alpha_{p}$ to $Ver_{p}$. The content of this talk can pr
imarily be found in [2] and [3].\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (The University of Melbourne)
DTSTART:20221118T200000Z
DTEND:20221118T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/32
DESCRIPTION:Title: Cotangent Schubert calculus and Lagrangian correspond
ences\nby Iva Halacheva (The University of Melbourne) as part of MIT I
nfinite Dimensional Algebra Seminar\n\nLecture held in Room: 2-135 in the
Simons building.\n\nAbstract\nIn recent work\, the study of partial flag v
arieties and the Schubert bases of their equivariant cohomology has been e
xtended to cotangent bundles and Segre-Schwartz-MacPherson classes. I will
discuss the behavior of these bases in the restriction in cohomology from
type A to type C Grassmannians. When considering their cotangent bundles\
, this behavior has a further geometric interpretation in terms of Maulik-
Okounkov stable envelopes and Lagrangian correspondences. Both settings ca
n be considered from the combinatorial perspective of puzzle rules\, which
in turn are interpreted as quantum integrable systems via R-matrices for
the sl(3) Yangian. This is joint work with Allen Knutson and Paul Zinn-Jus
tin.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Dumansky (MIT Mathematics)
DTSTART:20221202T200000Z
DTEND:20221202T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/33
DESCRIPTION:Title: Title to be announced\nby Ilya Dumansky (MIT Math
ematics) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture he
ld in Room: 2-135 in the Simons building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Borodin (MIT Mathematics)
DTSTART:20221209T200000Z
DTEND:20221209T220000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/34
DESCRIPTION:Title: Title to be announced\nby Alexey Borodin (MIT Mat
hematics) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture h
eld in Room: 2-135 in the Simons building.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasily Krylov (MIT Mathematics)
DTSTART:20221007T190000Z
DTEND:20221007T210000Z
DTSTAMP:20260422T225719Z
UID:MIT_Inf_Dim_Algebra_Seminar/35
DESCRIPTION:Title: Subregular nilpotent orbits and explicit character fo
rmulas for modules over affine Lie algebras.\nby Vasily Krylov (MIT Ma
thematics) as part of MIT Infinite Dimensional Algebra Seminar\n\nLecture
held in Room: 2-135 in the Simons building.\n\nAbstract\nThe talk is based
on the joint work with Roman Bezrukavnikov and Victor Kac (arXiv:2209.088
65). Let g be a simple Lie algebra and let $\\hat{g}$ be the corresponding
affine Lie algebra. It is known that characters of irreducible (highest w
eight) representations of $\\hat{g}$ can be computed in terms of values at
q=1 of affine (inverse) Kazhdan-Lusztig polynomials. These values can be
computed recursively but there are no explicit formulas for them in genera
l. The goal of this talk is to describe certain cases when we can compute
the values above explicitly resulting in explicit formulas for characters
of certain irreducible $\\hat{g}$-modules (partly generalizing results of
Kac and Wakimoto). The calculation relies on the description of the corres
ponding module over the affine Hecke algebra in terms of the equivariant $
K$-theory of the Springer resolution. Time permitting we will discuss poss
ible generalizations.\n
LOCATION:https://researchseminars.org/talk/MIT_Inf_Dim_Algebra_Seminar/35/
END:VEVENT
END:VCALENDAR