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BEGIN:VEVENT
SUMMARY:Raphael Rouquier (University of California\, Los Angeles)
DTSTART:20201130T160000Z
DTEND:20201130T170000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/1
DESCRIPTION:Title: Affinizations and modular representations of finite groups\
nby Raphael Rouquier (University of California\, Los Angeles) as part of M
onoidal and 2-categories in representation theory and categorification\n\n
\nAbstract\nWe will discuss affinizations of 2-Kac-Moody algebras and thei
r role in degenerations of categories of modular representations of finite
groups of Lie type.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bowman (University of Kent)
DTSTART:20201130T180000Z
DTEND:20201130T190000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/2
DESCRIPTION:Title: Tautological p-Kazhdan-Lusztig Theory for cyclotomic Hecke alge
bras\nby Chris Bowman (University of Kent) as part of Monoidal and 2-c
ategories in representation theory and categorification\n\n\nAbstract\nWe
discuss a new explicit isomorphism between (truncations of) quiver Hecke a
lgebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-
Samelson bimodules. This allows us to deduce that the decomposition number
s of these algebras (including as examples the symmetric groups and genera
lised blob algebras) are tautologically equal to the associated p-Kazhdan-
Lusztig polynomials\, provided that the characteristic is greater than the
Coxeter number. This allows us to give an elementary and explicit proof o
f the main theorem of Riche-Williamson's recent monograph and extend their
categorical equivalence to cyclotomic Hecke algebras\, thus solving Libed
insky-Plaza's categorical blob conjecture.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thorsten Heidersdorf (Universität Bonn)
DTSTART:20201130T191500Z
DTEND:20201130T201500Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/3
DESCRIPTION:Title: On fusion rules for supergroups\nby Thorsten Heidersdorf (U
niversität Bonn) as part of Monoidal and 2-categories in representation t
heory and categorification\n\n\nAbstract\nI will report on some recent pro
gress to understand the indecomposable summands in tensor products of irre
ducible representations of an algebraic supergroup. I will focus on the $G
L(m|n)$ and $OSp(m|2n)$-case.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Thorge Jensen (University of Clermont Auvergne)
DTSTART:20201201T160000Z
DTEND:20201201T170000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/4
DESCRIPTION:Title: Cellularity of the p-Kazhdan-Lusztig Basis for Symmetric Groups
\nby Lars Thorge Jensen (University of Clermont Auvergne) as part of M
onoidal and 2-categories in representation theory and categorification\n\n
\nAbstract\nAfter recalling the most important results about Kazhdan-Luszt
ig cells\nfor symmetric groups\, I will introduce the p-Kazhdan-Lusztig ba
sis and\ngive a complete description of p-cells for symmetric groups.\nAft
er that I will mention important consequences of the Perron-Frobenius\nthe
orem for p-cells which provide one of the last missing ingredients\nfor th
e proof of the cellularity of the p-canonical basis\nin finite type A.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iva Halacheva (Northeastern University)
DTSTART:20201201T180000Z
DTEND:20201201T190000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/5
DESCRIPTION:Title: The cactus group\, crystals\, and perverse equivalences\nby
Iva Halacheva (Northeastern University) as part of Monoidal and 2-categor
ies in representation theory and categorification\n\n\nAbstract\nSuppose C
is a category equipped with a categorical action of a (simply-laced) semi
simple Lie algebra g. Chuang and Rouquier construct equivalences on its de
rived category $D^b(C)$ via the so called Rickard complexes\, one for each
simple root of g. These complexes satisfy the braid relations for g\, as
shown by Cautis and Kamnitzer\, and hence give an action of the braid grou
p. We show that the complex corresponding to the positive lift of the long
est Weyl group element (of any parabolic in g) is a perverse equivalence o
n $D^b(C)$. Hence\, it induces a bijection on the irreducible objects of C
\, and recovers the cactus group action on the corresponding g-crystal. Th
is is joint work in progress with Tony Licata\, Ivan Losev\, and Oded Yaco
bi.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Vazirani (University of California\, Davis)
DTSTART:20201201T191500Z
DTEND:20201201T201500Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/6
DESCRIPTION:Title: Representations of the affine BMW category\nby Monica Vazir
ani (University of California\, Davis) as part of Monoidal and 2-categorie
s in representation theory and categorification\n\n\nAbstract\nThe BMW alg
ebra is a deformation of the Brauer algebra\, and has the Hecke algebra of
type A as a quotient. Its specializations play a role in types B\, C\, D
akin to that of the symmetric group in Schur-Weyl duality. I will discuss
Walker’s TQFT-motivated 1-handle construction of a family of representat
ions of the affine BMW category and the resulting representations of the a
ffine BMW algebra. These representations are “integral” and X-semisimp
le\, or calibrated. While the construction is topological\, the resulting
representation has a straightforward combinatorial description. This is jo
int work with Kevin Walker.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vanessa Miemietz (University of East Anglia)
DTSTART:20201202T160000Z
DTEND:20201202T170000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/7
DESCRIPTION:Title: A categorified double centraliser theorem and applications to S
oergel bimodules\nby Vanessa Miemietz (University of East Anglia) as p
art of Monoidal and 2-categories in representation theory and categorifica
tion\n\n\nAbstract\nI will explain how notions from classical representati
on theory\, including a double centraliser theorem\, lift to finitary 2-re
presentation theory\, and how this helps in classifying simple 2-represent
ations of Soergel bimodules of finite Coxeter type in characteristic zero.
\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Hogancamp (Northeastern University)
DTSTART:20201202T180000Z
DTEND:20201202T190000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/8
DESCRIPTION:Title: Soergel bimodules and the Carlsson-Mellit algebra\nby Matt
Hogancamp (Northeastern University) as part of Monoidal and 2-categories i
n representation theory and categorification\n\n\nAbstract\nThe dg cocente
r of the category of Soergel bimodules in type A\, morally speaking\, can
be thought of as a categorical analogue of the ring of symmetric functions
\, as in joint work of myself\, Eugene Gorsky\, and Paul Wedrich. Meanwhil
e\, the ring of symmetric functions is the recipient of actions of various
interesting algebras (affine Lie algebras in type A\, Heisenberg algebra\
, elliptic hall algebra\, etc). It is therefore natural to wonder if the a
ctions of such algebras have categorical analogues acting on the cocenter
of SBim. In this talk we give precisely such a Soergel bimodule interpreta
tion to the action of the Carlsson-Mellit algebra $e_0 A_{q\,t} e_0$ on sy
mmetric functions. By considering in addition various ``dg cocentralizers'
' of SBim we obtain a categorical analogue of the full polynomial represen
tation of the Carlsson-Mellit algebra $A_{q\,t}$. A key component in this
work is a skein theoretic interpretation of the polynomial representation
of $A_{q\,t}$. This is joint work with Nicolle Sandoval Gonzalez.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Rider (University of Georgia)
DTSTART:20201202T191500Z
DTEND:20201202T201500Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/9
DESCRIPTION:Title: Modular Perverse Sheaves on the affine Flag Variety\nby Lau
ra Rider (University of Georgia) as part of Monoidal and 2-categories in r
epresentation theory and categorification\n\n\nAbstract\nThere are two cat
egorical realizations of the affine Hecke algebra: constructible sheaves o
n the affine flag variety and coherent sheaves on the Langlands dual Stein
berg variety. A fundamental problem in geometric representation theory is
to relate these two categories by a category equivalence. This was achieve
d by Bezrukavnikov in characteristic 0 about a decade ago. In this talk\,
I will discuss a first step toward solving this problem in the modular cas
e joint with R. Bezrukavnikov and S. Riche.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juliet Cooke (Université catholique de Louvain)
DTSTART:20201203T160000Z
DTEND:20201203T170000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/10
DESCRIPTION:Title: Skein categories\nby Juliet Cooke (Université catholique
de Louvain) as part of Monoidal and 2-categories in representation theory
and categorification\n\n\nAbstract\nIn this talk we will talk about skein
categories which are a categorical analogue of skein algebras based on col
oured ribbon tangles. We shall then see how these skein categories satisfy
excision and therefore fit within the framework of factorisation homology
as k-linear factorisation homology theories of surfaces. We shall conclud
e by discussing how to relate them to Alekseev's moduli algebras and state
d skein algebras.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Lanini (Università degli studi di Roma Tor Vergata)
DTSTART:20201203T180000Z
DTEND:20201203T190000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/11
DESCRIPTION:Title: Attractive forests and torus actions\nby Martina Lanini (U
niversità degli studi di Roma Tor Vergata) as part of Monoidal and 2-cate
gories in representation theory and categorification\n\n\nAbstract\nAttrac
tive forests are well behaved quiver representations\, examples of which a
re nilpotent representations of the equioriented cycle. In ongoing joint w
ork with Alexander Puetz\, we define and investigate torus actions on qui
ver Grassmannians of attractive forests. In the case of nilpotent represen
tations of the equioriented cycle\, our torus action equips the quiver Gra
ssmannian with a structure of an equivariantly formal space\, the correspo
nding moment graph can be combinatorially described and exploited to compu
te equivariant cohomology. We expect the same results to hold true for any
attractive forest. Our construction generalises the very much investigate
d (maximal) torus actions on type A flag varieties.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ostrik (University of Oregon)
DTSTART:20201203T191500Z
DTEND:20201203T201500Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/12
DESCRIPTION:Title: Two dimensional topological field theories and partial fractio
ns\nby Victor Ostrik (University of Oregon) as part of Monoidal and 2-
categories in representation theory and categorification\n\n\nAbstract\nTh
is talk is based on joint work with M.Khovanov and Y.Kononov. By evaluatin
g a topological field theory in dimension 2 on surfaces of genus 0\,1\,2 e
tc we get a sequence. We investigate which sequences occur in this way dep
ending on the assumptions on the target category.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Inna Entova-Aizenbud (Ben Gurion University)
DTSTART:20201204T160000Z
DTEND:20201204T170000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/13
DESCRIPTION:Title: Jacobson-Morozov Lemma for Lie superalgebras using semisimplif
ication\nby Inna Entova-Aizenbud (Ben Gurion University) as part of Mo
noidal and 2-categories in representation theory and categorification\n\n\
nAbstract\nI will present a generalization of the Jacobson-Morozov Lemma f
or quasi-reductive algebraic supergroups (respectively\, Lie superalgebras
)\, based on the idea of semisimplification of tensor categories\, which w
ill be explained during the talk. This is a joint project with V. Serganov
a.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Khovanov (Columbia University)
DTSTART:20201204T180000Z
DTEND:20201204T190000Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/14
DESCRIPTION:Title: Universal construction in ultra low dimensions\nby Mikhail
Khovanov (Columbia University) as part of Monoidal and 2-categories in re
presentation theory and categorification\n\n\nAbstract\nWe'll explain the
notion of the universal construction\, which can be viewed as a weakening
of the TQFT axioms\, and demonstrate how it works in dimensions one and tw
o.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Elias (University of Oregon)
DTSTART:20201204T191500Z
DTEND:20201204T201500Z
DTSTAMP:20260418T132502Z
UID:HIM-Workshop-Dec20/15
DESCRIPTION:Title: Categorifying Hecke algebras at prime roots of unity\nby B
en Elias (University of Oregon) as part of Monoidal and 2-categories in re
presentation theory and categorification\n\n\nAbstract\nThirty years ago\,
Soergel changed the paradigm with his algebraic construction of the Hecke
category. This is a categorification of the Hecke algebra at a generic pa
rameter\, where the parameter is categorified by a grading shift. One key
open problem in categorification is to categorify Hecke algebras not at a
generic parameter\, but at a root of unity. In this talk I will explain ho
w one can utilize the technology of p-DG categories to provide such a conj
ectural categorification. This is joint work with Y. Qi.\n
LOCATION:https://researchseminars.org/talk/HIM-Workshop-Dec20/15/
END:VEVENT
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