BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Chris Bowman (University of Kent)
DTSTART:20200915T073000Z
DTEND:20200915T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/1
DESCRIPTION:Title: Tautological p-Kazhdan–Lusztig Theory for cyclotomic Hecke algebr
as\nby Chris Bowman (University of Kent) as part of OIST representatio
n theory seminar\n\n\nAbstract\nWe discuss a new explicit isomorphism betw
een (truncations of) quiver Hecke algebras and Elias–Williamson’s diag
rammatic endomorphism algebras of Bott–Samelson bimodules. This allows u
s to deduce that the decomposition numbers of these algebras (including as
examples the symmetric groups and generalised blob algebras) are tautolog
ically 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 of the main theorem of Riche–W
illiamson’s recent monograph and extend their categorical equivalence to
cyclotomic Hecke algebras\, thus solving Libedinsky–Plaza’s categoric
al blob conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahir Can (Tulane University)
DTSTART:20200929T000000Z
DTEND:20200929T010000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/2
DESCRIPTION:Title: Spherical Varieties and Combinatorics\nby Mahir Can (Tulane Uni
versity) as part of OIST representation theory seminar\n\n\nAbstract\nLet
G be a reductive complex algebraic group with a Borel subgroup B. A spheri
cal G-variety is an irreducible normal G-variety X where B has an open orb
it. If X is affine\, or if it is projective but endowed with a G-linearize
d ample line bundle\, then the group action criteria for the sphericality
is in fact equivalent to the representation theoretic statement that a cer
tain space of functions (related to X) is multiplicity-free as a G-module.
In this talk\, we will discuss the following question about a class of sp
herical varieties: if X is a Schubert variety for G\, then when do we know
that X is a spherical L-variety\, where L is the stabilizer of X in G.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eoghan McDowell (Royal Holloway\, University of London)
DTSTART:20201013T073000Z
DTEND:20201013T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/3
DESCRIPTION:Title: The image of the Specht module under the inverse Schur functor\
nby Eoghan McDowell (Royal Holloway\, University of London) as part of OIS
T representation theory seminar\n\n\nAbstract\nThe Schur functor and its i
nverses give an important connection between the representation theories o
f the symmetric group and the general linear group. Kleshchev and Nakano p
roved in 2001 that when the characteristic of the field is at least 5\, th
e image of the Specht module under the inverse Schur functor is isomorphic
to the dual Weyl module. In this talk I will address what happens in char
acteristics 2 and 3: in characteristic 3\, the isomorphism holds\, and I w
ill give an elementary proof of this fact which covers also all characteri
stics other than 2\; in characteristic 2\, the isomorphism does not hold f
or all Specht modules\, and I will classify those for which it does. Our a
pproach is with Young tableaux\, tabloids and Garnir relations.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Washington and Jefferson College)
DTSTART:20201027T000000Z
DTEND:20201027T010000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/4
DESCRIPTION:Title: Specht modules and cuspidal ribbon tableaux\nby Rob Muth (Washi
ngton and Jefferson College) as part of OIST representation theory seminar
\n\n\nAbstract\nRepresentation theory of Khovanov-Lauda-Rouquier (KLR) alg
ebras in affine type A can be studied through the lens of Specht modules\,
associated with the cellular structure of cyclotomic KLR algebras\, or th
rough the lens of cuspidal modules\, associated with categorified PBW base
s for the quantum group of affine type A. Cuspidal ribbons provide a sort
of combinatorial bridge between these approaches. I will describe some rec
ent results on cuspidal ribbon tableaux\, and some implications in the wor
ld of KLR representation theory\, such as bounds on labels of simple facto
rs of Specht modules\, and the presentation of cuspidal modules. Portions
of this talk are joint work with Dina Abbasian\, Lena Difulvio\, Gabrielle
Pasternak\, Isabella Sholtes\, and Frances Sinclair.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jieru Zhu (Hausdorff Institute of Mathematics)
DTSTART:20201110T073000Z
DTEND:20201110T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/5
DESCRIPTION:Title: Double centralizer properties for the Drinfeld double of the Taft a
lgebras\nby Jieru Zhu (Hausdorff Institute of Mathematics) as part of
OIST representation theory seminar\n\n\nAbstract\nThe Drinfeld double of t
he taft algebra\, $D_n$\, whose ground field contains $n$-th roots of unit
y\, has a known list of 2-dimensional irreducible modules. For each of suc
h module $V$\, we show that there is a well-defined action of the Temperle
y-Lieb algebra $TL_k$ on the $k$-fold tensor product of $V$\, and this act
ion commutes with that of $D_n$. When $V$ is self-dual and when $k \\leq 2
(n-1)$\, we further establish a isomorphism between the centralizer algebr
a of $D_n$ on $V^{\\otimes k}$\, and $TL_k$. Our inductive argument uses
a rank function on the TL diagrams\, which is compatible with the nesting
function introduced by Russell-Tymoczko. This is joint work with Georgia B
enkart\, Rekha Biswal\, Ellen Kirkman and Van Nguyen.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Wang (Osaka University)
DTSTART:20201117T073000Z
DTEND:20201117T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/6
DESCRIPTION:Title: On $\\tau$-tilting finiteness of Schur algebras\nby Qi Wang (Os
aka University) as part of OIST representation theory seminar\n\n\nAbstrac
t\nSupport $\\tau$-tilting modules are introduced by Adachi\, Iyama and Re
iten in 2012 as a generalization of classical tilting modules. One of the
importance of these modules is that they are bijectively corresponding to
many other objects\, such as two-term silting complexes and left finite se
mibricks. Let $V$ be an $n$-dimensional vector space over an algebraically
closed field $\\mathbb{F}$ of characteristic $p$. Then\, the Schur algebr
a $S(n\,r)$ is defined as the endomorphism ring $\\mathsf{End}_{\\mathbb{F
}G_r}\\left ( V^{\\otimes r} \\right )$ over the group algebra $\\mathbb{
F}G_r$ of the symmetric group $G_r$. In this talk\, we discuss when the Sc
hur algebra $S(n\,r)$ has only finitely many pairwise non-isomorphic basic
support $\\tau$-tilting modules.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Jacon (University of Reims Champagne-Ardenne)
DTSTART:20201208T073000Z
DTEND:20201208T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/7
DESCRIPTION:Title: Cores of Ariki-Koike algebras\nby Nicolas Jacon (University of
Reims Champagne-Ardenne) as part of OIST representation theory seminar\n\n
\nAbstract\nWe study a natural generalization of the notion of cores for l
-partitions: the (e\, s)-cores. We relate this notion with the notion of w
eight as defined by Fayers and use it to describe the blocks of Ariki-Koik
e algebras.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Fayers (Queen Mary University of London)
DTSTART:20210112T073000Z
DTEND:20210112T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/8
DESCRIPTION:Title: The Mullineux map\nby Matthew Fayers (Queen Mary University of
London) as part of OIST representation theory seminar\n\n\nAbstract\nIn ch
aracteristic p\, the simple modules for the symmetric group \\(S_n\\) are
the James modules \\(D^\\lambda\\)\, labelled by p-regular partitions of n
. If we let \\(sgn\\) denote the 1-dimensional sign module\, then for any
p-regular \\(\\lambda\\)\, the module \\(D^\\lambda\\otimes sgn\\) is also
a simple module. So there is an involutory bijection \\(m_p\\) on the set
of p-regular partitions such that \\(D^\\lambda\\otimes sgn=D^{m_p(\\lamb
da)}\\). The map \\(m_p\\) is called the Mullineux map\, and an important
problem is to describe \\(m_p\\) combinatorially. There are now several kn
own solutions to this problem. I will describe the history of this problem
and explain the known combinatorial solutions\, and then give a new solut
ion based on crystals and regularisation.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Chung (Okinawa Institute of Science and Technology)
DTSTART:20210126T073000Z
DTEND:20210126T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/9
DESCRIPTION:Title: \\(\\imath\\)Quantum Covering Groups: Serre presentation and canoni
cal basis\nby Chris Chung (Okinawa Institute of Science and Technology
) as part of OIST representation theory seminar\n\n\nAbstract\nIn 2016\, B
ao and Wang developed a general theory of canonical basis for quantum symm
etric pairs \\((\\mathbf{U}\, \\mathbf{U}^\\imath)\\)\, generalizing the c
anonical basis of Lusztig and Kashiwara for quantum groups and earning the
m the 2020 Chevalley Prize in Lie Theory. The \\(\\imath\\)divided powers
are polynomials in a single generator that generalize Lusztig's divided po
wers\, which are monomials. They can be similarly perceived as canonical b
asis in rank one\, and have closed form expansion formulas\, established b
y Berman and Wang\, that were used by Chen\, Lu and Wang to give a Serre p
resentation for coideal subalgebras \\(\\mathbf{U}^\\imath\\)\, featuring
novel \\(\\imath\\)Serre relations when \\(\\tau(i) = i\\).\n\nQuantum cov
ering groups\, developed by Clark\, Hill and Wang\, are a generalization t
hat `covers' both the Lusztig quantum group and quantum supergroups of ani
sotropic type. In this talk\, I will talk about how the results for \\(\\i
math\\)-divided powers and the Serre presentation can be extended to the q
uantum covering algebra setting\, and subsequently applications to canonic
al basis for \\(\\mathbf{U}^\\imath_\\pi\\)\, the quantum covering analogu
e of \\(\\mathbf{U}^\\imath\\)\, and quantum covering groups at roots of 1
.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Davidson (Reed College)
DTSTART:20210216T003000Z
DTEND:20210216T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/10
DESCRIPTION:Title: Type P Webs and Howe Duality\nby Nick Davidson (Reed College)
as part of OIST representation theory seminar\n\n\nAbstract\nWebs are comb
inatorially defined diagrams which encode homomorphisms between tensor pro
ducts of certain representations of Lie (super)algebras. I will describe
some recent work with Jon Kujawa and Rob Muth which defines webs for the t
ype P Lie superalgebra\, and then uses these webs to deduce an analog of H
owe duality for this Lie superalgebra.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Yi Rui Low (National University of Singapore)
DTSTART:20210302T073000Z
DTEND:20210302T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/11
DESCRIPTION:Title: Adjustment matrices\nby Aaron Yi Rui Low (National University
of Singapore) as part of OIST representation theory seminar\n\n\nAbstract\
nJames's Conjecture predicts that the adjustment matrix for weight $w$ blo
cks of the Iwahori-Hecke algebras $\\mathcal{H}_{n}$ and the $q$-Schur alg
ebras $\\mathcal{S}_{n}$ is the identity matrix when $w<\\textnormal{char}
(\\mathbb{F})$. Fayers has proved James's Conjecture for blocks of $\\math
cal{H}_{n}$ of weights 3 and 4. We shall discuss some results on adjustmen
t matrices that have been used to prove James's Conjecture for blocks of $
\\mathcal{S}_{n}$ of weights 3 and 4 in an upcoming paper. If time permits
\, we will look at a proof of the weight 3 case.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kleshchev (University of Oregon)
DTSTART:20210330T003000Z
DTEND:20210330T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/12
DESCRIPTION:Title: Irreducible restrictions from symmetric groups to subgroups\nb
y Alexander Kleshchev (University of Oregon) as part of OIST representatio
n theory seminar\n\n\nAbstract\nWe motivate\, discuss history of\, and pre
sent a solution to the following problem: describe pairs (G\,V) where V is
an irreducible representation of the symmetric group S_n of dimension >1
and G is a subgroup of S_n such that the restriction of V to G is irreduci
ble. We do the same with the alternating group A_n in place of S_n. \nThe
latest results on the problem are joint with Pham Huu Tiep and Lucia Morot
ti.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa)
DTSTART:20210202T003000Z
DTEND:20210202T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/13
DESCRIPTION:Title: Affinization of monoidal categories\nby Alistair Savage (Unive
rsity of Ottawa) as part of OIST representation theory seminar\n\n\nAbstra
ct\nWe define the affinization of an arbitrary monoidal category\, corresp
onding to the category of string diagrams on the cylinder. We also give a
n alternative characterization in terms of adjoining dot generators to the
category. The affinization formalizes and unifies many constructions app
earing in the literature. We describe a large number of examples coming f
rom Hecke-type algebras\, braids\, tangles\, and knot invariants.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (University of Bonn)
DTSTART:20210316T073000Z
DTEND:20210316T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/14
DESCRIPTION:Title: Verlinde rings and DAHA actions\nby Catharina Stroppel (Univer
sity of Bonn) as part of OIST representation theory seminar\n\n\nAbstract\
nIn this talk we will briefly recall how quantum groups at roots give rise
Verlinde algebras which can be realised as Grothendieck rings of certain
monoidal categories. The ring structure is quite interesting and was very
much studied in type A. I will try to explain how one gets a natural actio
n of certain double affine Hecke algebras and show how known properties of
these rings can be deduced from this action and in which sense modularity
of the tensor category is encoded.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Wildon (Royal Holloway\, University of London)
DTSTART:20210427T073000Z
DTEND:20210427T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/15
DESCRIPTION:Title: Plethysms\, polynomial representations of linear groups and Hermit
e reciprocity over an arbitrary field\nby Mark Wildon (Royal Holloway\
, University of London) as part of OIST representation theory seminar\n\n\
nAbstract\nLet \\(E\\) be a \\(2\\)-dimensional vector space. Over the com
plex numbers the irreducible polynomial representations of the special lin
ear group \\(SL(E)\\) are the symmetric powers \\(Sym^r E\\). Composing po
lynomial representations\, for example to form \\(Sym^4 Sym^2 E\\)\, corre
sponds to the plethysm product on symmetric functions. Expressing such a p
lethysm as a linear combination of Schur functions has been identified by
Richard Stanley as one of the fundamental open problems in algebraic combi
natorics. In my talk I will use symmetric functions to prove some classica
l isomorphisms\, such as Hermite reciprocity \\(Sym^m Sym^r E \\cong Sym^r
Sym^m E\\)\, and some others discovered only recently in joint work with
Rowena Paget. I will then give an overview of new results showing that\, p
rovided suitable dualities are introduced\, Hermite reciprocity holds over
arbitrary fields\; certain other isomorphisms (we can prove) have no modu
lar generalization. The final part is joint work with my Ph.D student Eogh
an McDowell.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stacey Law (University of Cambridge)
DTSTART:20210413T073000Z
DTEND:20210413T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/16
DESCRIPTION:Title: Sylow branching coefficients and a conjecture of Malle and Navarro
\nby Stacey Law (University of Cambridge) as part of OIST representati
on theory seminar\n\n\nAbstract\nThe relationship between the representati
on theory of a finite group and that of its Sylow subgroups is a key area
of interest. For example\, recent results of Malle–Navarro and Navarro
–Tiep–Vallejo have shown that important structural properties of a fin
ite group \\(G\\) are controlled by the permutation character \\(\\mathbb{
1}_P\\big\\uparrow^G\\)\, where \\(P\\) is a Sylow subgroup of \\(G\\) and
\\(\\mathbb{1}_P\\) denotes the trivial character of \\(P\\). We introduc
e so-called Sylow branching coefficients for symmetric groups to describe
multiplicities associated with these induced characters\, and as an applic
ation confirm a prediction of Malle and Navarro from 2012\, in joint work
with E. Giannelli\, J. Long and C. Vallejo.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Gurevich (Technion)
DTSTART:20210528T073000Z
DTEND:20210528T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/17
DESCRIPTION:Title: New constructions for irreducible representations in monoidal cate
gories of type A\nby Max Gurevich (Technion) as part of OIST represent
ation theory seminar\n\n\nAbstract\nOne ever-recurring goal of Lie theory
is the quest for effective and elegant descriptions of collections of simp
le objects in categories of interest. A cornerstone feat achieved by Zelev
insky in that regard\, was the combinatorial explication of the Langlands
classification for smooth irreducible representations of p-adic GL_n. It w
as a forerunner for an exploration of similar classifications for various
categories of similar nature\, such as modules over affine Hecke algebras
or quantum affine algebras\, to name a few. \nA next step - reaching an ef
fective understanding of all reducible finite-length representations remai
ns largely a difficult task throughout these settings.\n\nRecently\, joint
with Erez Lapid\, we have revisited the original Zelevinsky setting by su
ggesting a refined construction of all irreducible representations\, with
the hope of shedding light on standing decomposition problems. This constr
uction applies the Robinson-Schensted-Knuth transform\, while categorifyin
g the determinantal Doubilet-Rota-Stein basis for matrix polynomial rings
appearing in invariant theory.\nIn this talk\, I would like to introduce t
he new construction into the setting of modules over quiver Hecke (KLR) al
gebras. In type A\, this category may be viewed as a quantization/gradatio
n of the category of representations of p-adic groups. I will explain how
adopting that point of view and exploiting recent developments in the subj
ect (such as the normal sequence notion of Kashiwara-Kim) brings some conj
ectural properties of the RSK construction (back in the p-adic setting) in
to resolution.\nTime permits\, I will discuss the relevance of the RSK con
struction to the representation theory of cyclotomic Hecke algebras.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow)
DTSTART:20210615T073000Z
DTEND:20210615T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/18
DESCRIPTION:Title: Grassmannians\, Cluster Algebras and Hypersurface Singularities\nby Sira Gratz (University of Glasgow) as part of OIST representation th
eory seminar\n\n\nAbstract\nGrassmannians are objects of great combinatori
al and geometric beauty\, which arise in myriad contexts. Their coordinate
rings serve as a classical example of cluster algebras\, as introduced by
Fomin and Zelevinsky at the start of the millennium\, and their combinato
rics is intimately related to algebraic and geometric concepts such as to
representations of algebras and hypersurface singularities. At the core li
es the idea of generating an object from a so-called “cluster” via the
concept of “mutation”. \n\nIn this talk\, we offer an overview of Gra
ssmannian combinatorics in a cluster theoretic framework\, and ultimately
take them to the limit to explore the a priori simple question: What happe
ns if we allow infinite clusters? We introduce the notion of a cluster alg
ebra of infinite rank (based on joint work with Grabowski)\, and of a Gras
smannian category of infinite rank (based on joint work with August\, Cheu
ng\, Faber and Schroll).\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Millan Berdasco (Queen Mary University of London)
DTSTART:20210706T073000Z
DTEND:20210706T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/19
DESCRIPTION:Title: On the computation of decomposition numbers of the symmetric group
\nby Diego Millan Berdasco (Queen Mary University of London) as part o
f OIST representation theory seminar\n\n\nAbstract\nThe most important ope
n problem in the modular representation theory of the symmetric group is f
inding the multiplicity of the simple modules as composition factors of th
e Specht modules. In characteristic 0 the Specht modules are just the simp
le modules of the symmetric group algebra\, but in positive characteristic
they may no longer be simple. We will survey the rich interplay between r
epresentation theory and combinatorics of integer partitions\, review a nu
mber of results in the literature which allow us to compute composition se
ries for certain infinite families of Specht modules from a finite subset
of them\, and discuss the extension of these techniques to other Specht mo
dules.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hankyung Ko (Uppsala University)
DTSTART:20210928T073000Z
DTEND:20210928T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/20
DESCRIPTION:Title: Bruhat orders and Verma modules\nby Hankyung Ko (Uppsala Unive
rsity) as part of OIST representation theory seminar\n\n\nAbstract\nThe Br
uhat order on a Weyl group has a representation theoretic interpretation i
n terms of Verma modules. The talk concerns resulting interactions between
combinatorics and homological algebra. I will present several questions a
round the above realization of the Bruhat order and answer them based on a
series of recent works\, partly joint with Volodymyr Mazorchuk and Rafael
Mrden.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich (University of Hamburg)
DTSTART:20211012T060000Z
DTEND:20211012T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/21
DESCRIPTION:Title: Knots and quivers\, HOMFLYPT and DT\nby Paul Wedrich (Universi
ty of Hamburg) as part of OIST representation theory seminar\n\n\nAbstract
\nI will describe a surprising connection between the colored HOMFLY-PT po
lynomials of knots and the motivic Donaldson-Thomas invariants of certain
symmetric quivers\, which was conjectured by Kucharski-Reineke-Stosic-Sulk
owski. I will outline a proof of this correspondence for arborescent links
via quivers associated with 4-ended tangles. Finally\, I will speculate a
bout how much of the HOMFLY-PT skein theory might carry over to the realm
of DT quiver invariants and what kind of geometric information about knots
might be encoded in these quivers. This is joint work with Marko Stosic.\
n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyuan Xu (University of Colorado at Boulder)
DTSTART:20211130T003000Z
DTEND:20211130T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/22
DESCRIPTION:Title: On Kazhdan–Lusztig cells of a-value 2\nby Tianyuan Xu (Unive
rsity of Colorado at Boulder) as part of OIST representation theory semina
r\n\n\nAbstract\nThe Kazhdan–Lusztig (KL) cells of a Coxeter group are s
ubsets of the group defined using the KL basis of the associated Iwahori
–Hecke algebra. The cells of symmetric groups can be computed via the Ro
binson–Schensted correspondence\, but for general Coxeter groups combina
torial descriptions of KL cells are largely unknown except for cells of a-
value 0 or 1\, where a refers to an N-valued function defined by Lusztig t
hat is constant on each cell. In this talk\, we will report some recent pr
ogress on KL cells of a-value 2. In particular\, we classify Coxeter group
s with finitely many elements of a-value 2\, and for such groups we charac
terize and count all cells of a-value 2 via certain posets called heaps. W
e will also mention some applications of these results for cell modules. T
his is joint work with Richard Green.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Seelinger (University of Michigan)
DTSTART:20211026T003000Z
DTEND:20211026T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/23
DESCRIPTION:Title: Diagonal harmonics and shuffle theorems\nby George Seelinger (
University of Michigan) as part of OIST representation theory seminar\n\n\
nAbstract\nThe Shuffle Theorem\, conjectured by Haglund\, Haiman\, Loehr\,
Remmel and Ulyanov\, and proved by Carlsson and Mellit\, describes the ch
aracteristic of the $S_n$-module of diagonal harmonics as a weight generat
ing function over labeled Dyck paths under a line with slope −1. The Shu
ffle Theorem has been generalized in many different directions\, producing
a number of theorems and conjectures. We provide a generalized shuffle th
eorem for paths under any line with negative slope using different methods
from previous proofs of the Shuffle Theorem. In particular\, our proof re
lies on showing a "stable" shuffle theorem in the ring of virtual GL_l-cha
racters. Furthermore\, we use our techniques to prove the Extended Delta C
onjecture\, yet another generalization of the original Shuffle Conjecture.
\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arik Wilbert (University of South Alabama)
DTSTART:20211109T003000Z
DTEND:20211109T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/24
DESCRIPTION:Title: Real Springer fibers and odd arc algebras\nby Arik Wilbert (Un
iversity of South Alabama) as part of OIST representation theory seminar\n
\n\nAbstract\nArc algebras were introduced by Khovanov in a successful att
empt to lift the quantum sl2 Reshetikhin-Turaev invariant for tangles to a
homological invariant. When restricted to knots and links\, Khovanov’s
homology theory categorifies the Jones polynomial. Ozsváth-Rasmussen-Szab
ó discovered a different categorification of the Jones polynomial called
odd Khovanov homology. Recently\, Naisse-Putyra were able to extend odd Kh
ovanov homology to tangles using so-called odd arc algebras which were ori
ginally constructed by Naisse-Vaz. The goal of this talk is to discuss a g
eometric approach to understanding odd arc algebras and odd Khovanov homol
ogy using Springer fibers over the real numbers. This is joint work with J
. N. Eberhardt and G. Naisse.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Creedon (City\, University of London)
DTSTART:20211116T073000Z
DTEND:20211116T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/25
DESCRIPTION:Title: Defining an Affine Partition Algebra\nby Samuel Creedon (City\
, University of London) as part of OIST representation theory seminar\n\n\
nAbstract\nIn this talk we motivate the construction of a new algebra call
ed the affine partition algebra. We summarise some of its basic properties
and describe an action which extends the Schur-Weyl duality between the s
ymmetric group and partition algebra. We establish connections to the affi
ne partition category defined recently by Brundan and Vargas and show that
such a category is a full subcategory of the Heisenberg category.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joanna Meinel (Federal Office for Information Security\, Bonn)
DTSTART:20211214T073000Z
DTEND:20211214T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/26
DESCRIPTION:Title: Decompositions of tensor products: Highest weight vectors from bra
nching\nby Joanna Meinel (Federal Office for Information Security\, Bo
nn) as part of OIST representation theory seminar\n\n\nAbstract\nWe consid
er tensor powers of the natural sl_n-representation\, and we look for desc
riptions of highest weight vectors therein: We discuss explicit formulas f
or n=2\, a recursion for n=3\, and for bigger n we demonstrate how Jucys-M
urphy elements allow us to compute highest weight vectors (both in theory
and in practice using sage). This is joint work with Pablo Zadunaisky.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tubbenhauer (University of Sydney)
DTSTART:20220201T073000Z
DTEND:20220201T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/27
DESCRIPTION:Title: On weighted KLRW algebras\nby Daniel Tubbenhauer (University o
f Sydney) as part of OIST representation theory seminar\n\n\nAbstract\nWei
ghted KLRW algebras are diagram algebras that depend on continuous \nparam
eters. Varying these parameters gives a way to interpolate between \nvario
us algebras that appear in (categorical) representation theory \nsuch as s
emisimple algebras\, KLR algebras\, quiver Schur algebras and diagrammatic
Cherednik algebras.\n\nThis talk is a friendly (and diagrammatic!) introd
uction explaining these algebras\, with no prior knowledge about any of th
ese assumed.\n\nBased on joint work A. Mathas.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Spencer (University of Cambridge)
DTSTART:20220301T073000Z
DTEND:20220301T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/28
DESCRIPTION:Title: (Some) Gram Determinants for \\(A_n\\) nets\nby Robert Spencer
(University of Cambridge) as part of OIST representation theory seminar\n
\n\nAbstract\nThe nets giving a diagrammatic description of the category o
f (tensor products of) fundamental representations of \\(sl_n\\) form a ce
llular category. We can then ask about the natural inner form on certain c
ell modules. In this talk\, we will calculate the determinant of some of t
hese forms in terms of certain traces of clasps or magic weave elements (f
or which there is a conjectured formula due to Elias). The method appears
moderately general and gives a result which is hopefully illuminating and
applicable to other monoidal\, cellular categories.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Murray (Maynooth University)
DTSTART:20220322T073000Z
DTEND:20220322T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/29
DESCRIPTION:Title: A Schur-positivity conjecture inspired by the Alperin-Mckay conjec
ture\nby John Murray (Maynooth University) as part of OIST representat
ion theory seminar\n\n\nAbstract\nThe McKay conjecture asserts that a fini
te group has the same number of odd degree irreducible characters as the n
ormalizer of a Sylow 2-subgroup. The Alperin-McKay (A-M) conjecture genera
lizes this to the height-zero characters in 2-blocks.\n\nIn his original p
aper\, McKay already showed that his conjecture holds for the finite symme
tric groups S_n. In 2016\, Giannelli\, Tent and the speaker established a
canonical bijection realising A-M for S_n\; the height-zero irreducible ch
aracters in a 2-block are naturally parametrized by tuples of hooks whose
lengths are certain powers of 2\, and this parametrization is compatible w
ith restriction to an appropriate 2-local subgroup.\n\nNow corresponding t
o a 2-block of the symmetric group S_n\, there is a 2-block of a maximal Y
oung subgroup of S_n of the same weight. An obvious question is whether ou
r canonical bijection is compatible with restriction of height-zero charac
ters between these blocks.\n\nAttempting to prove this compatibility lead
me to formulate a conjecture asserting the Schur-positivity of certain dif
ferences of skew-Schur functions. The corresponding skew-shapes have trian
gular inner-shape\, but otherwise do not refer to the 2-modular theory. I
will describe my conjecture and give positive evidence in its favour.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Doty (Loyola University Chicago)
DTSTART:20220215T003000Z
DTEND:20220215T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/30
DESCRIPTION:Title: Schur-Weyl duality for braid and twin groups via the Burau represe
ntation\nby Stephen Doty (Loyola University Chicago) as part of OIST r
epresentation theory seminar\n\n\nAbstract\nThe natural permutation repres
entation of the symmetric group admits a q-analogue known as the Burau rep
resentation. The symmetric group admits two natural covering groups: the b
raid group of Artin and the twin group of Khovanov\, obtained respectively
by forgetting the cubic and quadratic relations in the Coxeter presentati
on of the symmetric group. By computing centralizers of tensor powers of t
he Burau representation\, we obtain new instances of Schur-Weyl duality fo
r braid groups and twin groups\, in terms of the partial permutation and p
artial Brauer algebras. The method produces many representations of each g
roup that can be understood combinatorially. (This is joint work with Tony
Giaquinto.)\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kay Jin Lim (Nanyang Technological University)
DTSTART:20220420T073000Z
DTEND:20220420T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/31
DESCRIPTION:Title: Descent Algebra of Type A\nby Kay Jin Lim (Nanyang Technologic
al University) as part of OIST representation theory seminar\n\n\nAbstract
\nFor a finite Coxeter group W\, L. Solomon defined certain subalgebra of
the group algebra kW which is now commonly known as the Solomon’s descen
t algebra. As usual\, the type A and B cases have special interest for bot
h the algebraists and combinatorists. In this talk\, I will be particularl
y focusing on the type A and modular case. It is closely related to the re
presentation theory of the symmetric group and the (higher) Lie representa
tions.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dean Yates (Queen Mary University of London)
DTSTART:20220405T073000Z
DTEND:20220405T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/32
DESCRIPTION:Title: Spin representations of the symmetric group\nby Dean Yates (Qu
een Mary University of London) as part of OIST representation theory semin
ar\n\n\nAbstract\nSpin representations of the symmetric group S_n can be t
hought of equivalently as either projective representations of S_n\, or as
linear representations of a double cover S_n+ of S_n. Whilst t
he linear representation theory of S_n is dictated by removing ‘rim-hook
s’ from (the Young diagrams of) partitions of n\, the projective represe
ntation theory of S_n is controlled by removing ‘bars’ from bar partit
ions of n (i.e. partitions of n into distinct parts). We will look at some
combinatorial results on bar partitions from a recent paper of the author
before discussing methods for determining the modular decomposition of sp
in representations over fields of positive characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinsuke Tsuchioka (Tokyo Institute of Technology)
DTSTART:20220614T073000Z
DTEND:20220614T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/33
DESCRIPTION:Title: An example of A2 Rogers-Ramanujan bipartition identities of level
3\nby Shinsuke Tsuchioka (Tokyo Institute of Technology) as part of OI
ST representation theory seminar\n\n\nAbstract\nIn the 1970s\, Lepowsky-Mi
lne discovered a similarity between the infinite products of the Rogers-Ra
manujan identities (RR identities\, for short) and the principal character
s of the level 3 standard modules of the affine Lie algebra of type \\(A^{
(1)}_{1}\\). Subsequently\, Lepowsky-Wilson gave a Lie-theoretic interpret
ation and a proof of the RR identities with the vertex operators. In this
talk\, I will present some results (arXiv:2205.04811) for the level 3 case
of type \\(A^{(1)}_{2}\\).\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Duquesne University)
DTSTART:20220705T073000Z
DTEND:20220705T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/34
DESCRIPTION:Title: Superalgebra deformations of web categories\nby Rob Muth (Duqu
esne University) as part of OIST representation theory seminar\n\n\nAbstra
ct\nFor a superalgebra A\, and even subalgebra a\, one may define an assoc
iated diagrammatic monoidal supercategory Web(A\,a)\, which generalizes a
number of symmetric web category constructions. In this talk\, I will defi
ne and discuss Web(A\,a)\, focusing on two interesting applications: First
ly\, Web(A\,a) is equipped with an asymptotically faithful functor to the
category of gl_n(A)-modules generated by symmetric powers of the natural m
odule\, and may be used to establish Howe dualities between gl_n(A) and gl
_m(A) in some cases. Secondly\, Web(A\,a) yields a diagrammatic presentati
on for the ‘Schurification' T^A_a(n\,d). For various choices of A/a\, th
ese Schurifications have proven connections to RoCK blocks of Hecke algebr
as\, and conjectural connections to RoCK blocks of Schur algebras and Serg
eev superalgebras. This is joint work with Nicholas Davidson\, Jonathan Ku
jawa\, and Jieru Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Mathas (University of Sydney)
DTSTART:20220810T060000Z
DTEND:20220810T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/35
DESCRIPTION:Title: Content systems and KLR algebras\nby Andrew Mathas (University
of Sydney) as part of OIST representation theory seminar\n\n\nAbstract\nI
n 1901 Young gave an explicit construction of the ordinary irreducible rep
resentations of the symmetric groups. In doing this\, he introduced conten
t functions for partitions\, which are now a key statistic in the semisimp
le representation theory of the symmetric groups. In this talk I will desc
ribe a generalisation of Young's ideas to the cyclotomic KLR algebras of a
ffine types A and C. This is quite surprising because Young's seminormal f
orms are creatures from the semisimple world whereas the cyclotomic KLR al
gebras are rarely semisimple. As an application\, we show that these algeb
ras are cellular and construct their irreducible representations. A specia
l case of these results gives new information about the symmetric groups i
n characteristic p>0. If time permits\, I will describe how these results
lead to an explicit categorification of the corresponding integrable highe
st weight modules.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (University of East Anglia)
DTSTART:20220719T073000Z
DTEND:20220719T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/36
DESCRIPTION:Title: Scopes equivalence for blocks of Ariki-Koike algebras\nby Alic
e Dell'Arciprete (University of East Anglia) as part of OIST representatio
n theory seminar\n\n\nAbstract\nWe consider representations of the Ariki-K
oike algebra\, a $q$-deformation of the group algebra of the complex refle
ction group $C_r \\wr S_n$. The representations of this algebra are natura
lly indexed by multipartitions of $n$. We examine blocks of the Ariki-Koik
e algebra\, in an attempt to generalise the combinatorial representation t
heory of the Iwahori-Hecke algebra. In particular\, we prove a sufficient
condition such that restriction of modules leads to a natural corresponden
ce between the multipartitions of $n$ whose Specht modules belong to a blo
ck $B$ and those of $n-\\delta_i(B)$ whose Specht modules belong to the bl
ock $B'$\, obtained from $B$ applying a Scopes' equivalence.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinéad Lyle (University of East Anglia)
DTSTART:20220721T073000Z
DTEND:20220721T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/37
DESCRIPTION:Title: Rouquier blocks for Ariki-Koike algebras\nby Sinéad Lyle (Uni
versity of East Anglia) as part of OIST representation theory seminar\n\n\
nAbstract\nThe Rouquier blocks\, also known as the RoCK blocks\, are impor
tant blocks of the symmetric groups algebras and the Hecke algebras of typ
e $A$\, with the partitions labelling the Specht modules that belong to th
ese blocks having a particular abacus configuration. We generalise the def
inition of Rouquier blocks to the Ariki-Koike algebras\, where the Specht
modules are indexed by multipartitions\, and explore the properties of the
se blocks.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Meng Tan (National University of Singapore)
DTSTART:20220920T073000Z
DTEND:20220920T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/38
DESCRIPTION:Title: Young’s seminormal basis vectors and their denominators\nby
Kai Meng Tan (National University of Singapore) as part of OIST representa
tion theory seminar\n\n\nAbstract\nThe dual Specht module of the symmetric
group algebra over $\\mathbb{Q}$ has two distinguished bases\, namely the
standard basis and Young’s seminormal basis. We study how the Young’s
seminormal basis vectors are expressed in terms of the standard basis\, a
s well as the denominators of the coefficients in these expressions. We ob
tain closed formula for some Young’s seminormal basis vectors\, as well
as partial results for the denominators in general. This is a joint work w
ith Ming Fang (Chinese Academy of Sciences) and Kay Jin Lim (Nanyang Techn
ological University).\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giada Volpato (University of Florence)
DTSTART:20221115T073000Z
DTEND:20221115T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/39
DESCRIPTION:Title: On the restriction of a character of \\(\\mathfrak{S}_n\\) to a Sy
low \\(p\\)-subgroup\nby Giada Volpato (University of Florence) as par
t of OIST representation theory seminar\n\n\nAbstract\nThe relevance of th
e McKay Conjecture in the representation theory of finite groups has led t
o investigate how irreducible characters decompose when restricted to Sylo
w \\(p\\)-subgroups. In this talk we will focus on the symmetric groups. S
ince the linear constituents of the restriction to a Sylow \\(p\\)-subgrou
p has been studied a lot by E. Giannelli and S. Law\, we will concentrate
on constituents of higher degree. In particular\, we will describe the set
of the irreducible characters which allow a constituent of a fixed degree
\, separating the cases of \\(p\\) being odd and \\(p=2\\). This is a join
t work with Eugenio Giannelli.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haralampos Geranios (University of York)
DTSTART:20221011T073000Z
DTEND:20221011T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/40
DESCRIPTION:Title: On self-extensions of irreducible modules for symmetric groups
\nby Haralampos Geranios (University of York) as part of OIST representati
on theory seminar\n\n\nAbstract\nWe work in the context of the modular rep
resentation theory of the symmetric groups. A long-standing conjecture\, f
rom the late 80s\, suggests that there are no (non-trivial) self-extension
s of irreducible modules over fields of odd characteristic. In this talk w
e will highlight several new positive results on this conjecture. This is
a joint work with S. Kleshchev and L. Morotti.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chun-Ju Lai (Academia Sinica)
DTSTART:20221025T003000Z
DTEND:20221025T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/41
DESCRIPTION:Title: Quasi-hereditary covers\, Hecke subalgebras and quantum wreath pro
duct\nby Chun-Ju Lai (Academia Sinica) as part of OIST representation
theory seminar\n\n\nAbstract\nThe Hecke algebra is in general not quasi-he
reditary\, meaning that its module category is not a highest weight catego
ry\; while it admits a quasi-hereditary cover via category O for certain r
ational Cherednik algebras due to Ginzburg-Guay-Opdam-Rouquier. It was pro
ved in type A that this category O can be realized using q-Schur algebra\,
but this realization problem remains open beyond types A/B/C. An essentia
l step for type D is to study Hu's Hecke subalgebra\, which deforms from a
wreath product that is not a Coxeter group. In this talk\, I'll talk abou
t a new theory allowing us to take the ``quantum wreath product'' of an al
gebra by a Hecke algebra. Our wreath product produces the Ariki-Koike alge
bra as a special case\, as well as new ``Hecke algebras'' of wreath produc
ts between symmetric groups. We expect them to play a role in answering th
e realization problem for complex reflection groups. This is a joint work
with Dan Nakano and Ziqing Xiang.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loïc Poulain d'Andecy (University of Reims Champagne-Ardenne)
DTSTART:20221101T073000Z
DTEND:20221101T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/42
DESCRIPTION:Title: KLR-type presentation of affine Hecke algebras of type B\nby L
oïc Poulain d'Andecy (University of Reims Champagne-Ardenne) as part of O
IST representation theory seminar\n\n\nAbstract\nKLR algebras of type A ha
ve been a revolution in the representation theory of Hecke algebras of a t
ype A flavour\, thanks to the the Brundan-Kleshchev-Rouquier isomorphism r
elating them explicitly to the affine Hecke algebra of type A. KLR algebra
s of other types exist but are not related to affine Hecke algebras of oth
er types. In this talk I will present a generalisation of the KLR presenta
tion for the affine Hecke algebra of type B and I will discuss some applic
ations. This talk is based on joint works with Salim Rostam and Ruari Walk
er.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (UC Berkeley)
DTSTART:20221129T003000Z
DTEND:20221129T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/44
DESCRIPTION:Title: Higher Rank Rational (q\,t)-Catalan Polynomials and a Finite Shuff
le Theorem\nby Nicolle González (UC Berkeley) as part of OIST represe
ntation theory seminar\n\n\nAbstract\nThe classical shuffle theorem states
that the Frobenius character of the space of diagonal harmonics is given
by a certain combinatorial sum indexed by parking functions on square latt
ice paths. The rational shuffle theorem\, conjectured by Gorsky-Negut and
proven by Mellit\, states that the geometric action on symmetric functions
(described by Schiffmmann-Vasserot) of certain elliptic Hall algebra elem
ents $P_{(m\,n)}$ yield the bigraded Frobenius character of a certain Sn r
epresentation. This character is known as the Hikita polynomial. In this t
alk I will introduce the higher rank rational (q\,t)-Catalan polynomials a
nd show these are equal to finite truncations of the Hikita polynomial. By
generalizing results of Gorsky-Mazin-Vazirani and constructing an explici
t bijection between rational semistandard parking functions and affine com
positions\, I will derive a finite analog of the rational shuffle theorem
in the context of spherical double affine Hecke algebras.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Turek (Royal Holloway\, University of London)
DTSTART:20230124T073000Z
DTEND:20230124T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/45
DESCRIPTION:Title: On stable modular plethysms of the natural module of $\\textrm{SL}
_2(\\mathbb{F}_p)$ in characteristic $p$\nby Pavel Turek (Royal Hollow
ay\, University of London) as part of OIST representation theory seminar\n
\n\nAbstract\nTo study polynomial representations of general and special l
inear groups in characteristic zero one can use formal characters to work
with symmetric functions instead. The situation gets more complicated when
working over a field $k$ of non-zero characteristic. However\, by describ
ing the representation ring of $k\\textrm{SL}_2(\\mathbb{F}_p)$ modulo pro
jective modules appropriately we are able to use symmetric functions with
a suitable specialisation to study a family of polynomial representations
of $k\\textrm{SL}_2(\\mathbb{F}_p)$ in the stable category. In this talk w
e describe how this introduction of symmetric functions works and how to c
ompute various modular plethysms of the natural $k\\textrm{SL}_2(\\mathbb{
F}_p)$-module in the stable category. As an application we classify which
of these modular plethysms are projective and which are `close' to being p
rojective. If time permits\, we describe how to generalise these classific
ations using a rule for exchanging Schur functors and tensoring with an en
dotrivial module.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rowena Paget (University of Kent)
DTSTART:20230110T073000Z
DTEND:20230110T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/46
DESCRIPTION:Title: Plethysm and the Partition Algebra\nby Rowena Paget (Universit
y of Kent) as part of OIST representation theory seminar\n\n\nAbstract\nTh
e symmetric group $S_{mn}$ acts naturally on the collection of set partiti
ons of a set of size mn into n sets each of size m. The irreducible const
ituents of the associated ordinary character are largely unknown\; in part
icular\, they are the subject of the longstanding Foulkes Conjecture. Ther
e are equivalent reformulations using polynomial representations of infini
te general linear groups or using plethysms of symmetric functions. I wi
ll review plethysm from these three perspectives before presenting a new a
pproach to studying plethysm: using the Schur-Weyl duality between the sym
metric group and the partition algebra. This method allows us to study sta
bility properties of certain plethysm coefficients. This is joint work wit
h Chris Bowman. If time permits\, I will also discuss some new results wit
h Chris Bowman and Mark Wildon.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soichi Okada (Nagoya University)
DTSTART:20230314T013000Z
DTEND:20230314T023000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/47
DESCRIPTION:Title: Intermediate symplectic characters and enumeration of shifted plan
e partitions\nby Soichi Okada (Nagoya University) as part of OIST repr
esentation theory seminar\n\n\nAbstract\nThe intermediate symplectic chara
cters\, introduced by R. Proctor\, interpolate between Schur functions and
symplectic characters. They arise as the characters of indecomposable rep
resentations of the intermediate symplectic group\, which is defined as th
e group of linear transformations fixing a (not necessarily non-degenerate
) skew-symmetric bilinear form. In this talk\, we present Jacobi-Trudi-typ
e determinant formulas and bialternant formulas for intermediate symplecti
c characters. By using the bialternant formula\, we can derive factorizati
on formulas for sums of intermediate symplectic characters\, which allow u
s to give a proof and variations of Hopkins' conjecture on the number of s
hifted plane partitions of double-staircase shape with bounded entries.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Lancaster University)
DTSTART:20230829T073000Z
DTEND:20230829T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/48
DESCRIPTION:Title: Higher-dimensional cluster combinatorics and representation theory
\nby Nicholas Williams (Lancaster University) as part of OIST represen
tation theory seminar\n\n\nAbstract\nPerhaps the most prominent example of
a cluster algebra is the type A cluster algebra\, where clusters are in b
ijection with triangulations of a convex polygon\, as observed by Fomin an
d Zelevinsky. A categorical version of this relationship is that triangula
tions of a convex polygon are in bijection with cluster-tilting objects in
the cluster category of the path algebra of the type A quiver. In each ca
se\, mutating the cluster or cluster-tilting object corresponds to flippin
g a diagonal inside a quadrilateral. It is natural to wonder whether any s
imilar relationship exists for triangulations of higher-dimensional polyto
pes. Indeed\, in a beautiful paper Oppermann and Thomas show that triangul
ations of even-dimensional cyclic polytopes are in bijection with cluster-
tilting objects in the cluster categories of the higher Auslander algebras
of type A\, which were introduced by Iyama. Mutating the cluster-tilting
objects corresponds to bistellar flips of triangulations\, which are the h
igher-dimensional analogues of flipping a diagonal inside a quadrilateral.
In this talk\, we will outline the work of Oppermann and Thomas\, and exp
lain the odd-dimensional half of the picture too. Indeed\, the speaker has
shown that triangulations of odd-dimensional cyclic polytopes are in bije
ction with equivalence classes of maximal green sequences for the higher A
uslander algebras of type A\, where maximal green sequences are maximal ch
ains of cluster-tilting objects.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Sambale (Leibniz Universität Hannover)
DTSTART:20231010T073000Z
DTEND:20231010T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/49
DESCRIPTION:Title: Groups of p-central type\nby Benjamin Sambale (Leibniz Univers
ität Hannover) as part of OIST representation theory seminar\n\n\nAbstrac
t\nA finite group \\(G\\) with center \\(Z\\) is of central type if there exists an irre
ducible character \\(\\chi\\) such that \\(\\chi(1)^2=|G:Z|\\). Howlett–Isaacs have sh
own that such groups are solvable. A corresponding theorem for \\(p\\)-Brauer characters was proved by Navarro–Spät
h–Tiep under the assumption that \;\\(p\\ne 5
\\). I have shown that there are no exceptions for \\(p=5\\). Moreover\, I give some applications to \;\\(p\\)-blocks with a unique Brauer character.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Norton (University of Kent)
DTSTART:20231024T073000Z
DTEND:20231024T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/50
DESCRIPTION:Title: Decomposition numbers for unipotent blocks with small $sl_2$-weigh
t in finite classical groups\nby Emily Norton (University of Kent) as
part of OIST representation theory seminar\n\n\nAbstract\nThere are many f
amiliar module categories admitting a categorical action of a Lie algebra.
The combinatorial shadow of such an action often yields answers to module
-theoretic questions\, for instance via crystals. In proving a conjecture
of Gerber\, Hiss\, and Jacon\, it was shown by Dudas\, Varagnolo\, and Vas
serot that the category of unipotent representations of a finite classical
group has such a categorical action. In this talk I will explain how we c
an use the categorical action to deduce closed formulas for certain famili
es of decomposition numbers of these groups. This is joint work in progres
s with Olivier Dudas.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Thiel (University of Kaiserslautern-Landau)
DTSTART:20231107T073000Z
DTEND:20231107T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/51
DESCRIPTION:Title: The rank one property for free Frobenius extensions\nby Ulrich
Thiel (University of Kaiserslautern-Landau) as part of OIST representatio
n theory seminar\n\n\nAbstract\nThe Cartan matrix of a finite-dimensional
algebra is the matrix of multiplicities of simple modules in indecomposabl
e projective modules. This is crucial information about the representation
theory of the algebra. In my talk I will present a general setting includ
ing several important examples from Lie theory\, such as restricted quanti
zed enveloping algebras at roots of unity\, in which we could prove that t
he Cartan matrix has the remarkable property of being blockwise of rank on
e. This is joint work with Gwyn Bellamy.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Yong (University of Illinois at Urbana-Champaign)
DTSTART:20231128T003000Z
DTEND:20231128T013000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/52
DESCRIPTION:Title: Newell-Littlewood numbers\nby Alexander Yong (University of Il
linois at Urbana-Champaign) as part of OIST representation theory seminar\
n\n\nAbstract\nThe Newell-Littlewood numbers are defined in terms of the L
ittlewood-Richardson coefficients from algebraic combinatorics. Both appea
r in representation theory as tensor product multiplicities for a classica
l Lie group. This talk concerns the question: Which multiplicities are non
zero? In 1998\, Klyachko established common linear inequalities defining b
oth the eigencone for sums of Hermitian matrices and the saturated Littlew
ood-Richardson cone. We prove some analogues of Klyachko's nonvanishing re
sults for the Newell-Littlewood numbers. This is joint work with Shiliang
Gao\, Gidon Orelowitz\, and Nicolas Ressayre. The presentation is based on
arXiv:2005.09012\, arXiv:2009.09904\, and arXiv:2107.03152.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand (OIST)
DTSTART:20231212T073000Z
DTEND:20231212T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/53
DESCRIPTION:Title: Some applications of bricks in classical and modern problems in re
presentation theory\nby Kaveh Mousavand (OIST) as part of OIST represe
ntation theory seminar\n\n\nAbstract\nBricks (also known as Schur represen
tations) form a special subfamily of indecomposable modules\, and they are
used in the algebraic and geometric study of representation theory of alg
ebras. We start by looking at some classical results on bricks\, including
a characterization of locally representation-directed algebras (due to Dr
äxler). Then\, we consider some new directions of research in which brick
s have played crucial roles. More specifically\, we briefly recall an eleg
ant correspondence between bricks and indecomposable $\\tau$-rigid-modules
(due to Demonet-Iyama-Jasso)\, which has many applications in $\\tau$-til
ting theory. We use the notion of $\\tau$-rigidity to give a new character
ization of locally representation-directed algebras\, and to further gener
alize this family. If time permits\, we also report on some new results on
an open conjecture (so-called the 2nd brick-Brauer-Thrall conjecture) whi
ch I posed in 2019. Part of this talk is based on my recent joint work wit
h Charles Paquette.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Marberg (The Hong Kong University of Science and Technology (
HKUST))
DTSTART:20231205T073000Z
DTEND:20231205T083000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/54
DESCRIPTION:Title: From Klyachko models to perfect models\nby Eric Marberg (The H
ong Kong University of Science and Technology (HKUST)) as part of OIST rep
resentation theory seminar\n\n\nAbstract\nIn this talk a "model" of a fini
te group or semisimple algebra means a representation containing a unique
irreducible subrepresentation from each isomorphism class. In the 1980s Kl
yachko identified an elegant model for the general linear group over a fin
ite field with $q$ elements. There is an informal sense in which taking th
e $q \\to 1$ limit of Klyachko's construction gives a model for the symmet
ric group\, which can be extended to its Iwahori-Hecke algebra. The result
ing Hecke algebra representation is a special case of a "perfect model"\,
which is a more flexible construction that can be considered for any finit
e Coxeter group. In this talk\, I will classify exactly which Coxeter grou
ps have perfect models\, and discuss some notable features of this classif
ication. For example\, each perfect model gives rise to a pair of related
W-graphs\, which are dual in types B and D but not in type A. Various inte
resting questions about these W-graphs remain open. This is joint work wit
h Yifeng Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Scrimshaw (Hokkaido University)
DTSTART:20240119T050000Z
DTEND:20240119T060000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/55
DESCRIPTION:Title: An Overview of Kirillov-Reshtikhin Modules and Crystals\nby Tr
avis Scrimshaw (Hokkaido University) as part of OIST representation theory
seminar\n\n\nAbstract\nKirillov-Reshetikhin (KR) modules are an important
class of finite dimensional representations associated to an affine Lie a
lgebra and the associated Yangian and quantum group. KR modules are known
to appear in many integrable systems and govern the dynamics. In this talk
\, we will give an overview of the role KR modules play in the category of
finite dimensional representations\, R-matrices and the fusion constructi
on\, their (conjectural) crystal bases\, and how they relate to Demazure m
odules. In particular\, we will focus on how to construct their crystal ba
ses combinatorially and the different types of character theories. As time
permits\, we will discuss some of the relations with (quantum) integrable
systems.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (Nagoya University)
DTSTART:20240131T043000Z
DTEND:20240131T053000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/56
DESCRIPTION:Title: Bongartz co-completions in cluster algebras and its applications\nby Peigen Cao (Nagoya University) as part of OIST representation theor
y seminar\n\n\nAbstract\nA cluster algebra is a Z-subalgebra of a rational
function field generated by a special set of generators called cluster va
riables\, which are grouped into overlapping subsets of fixed size\, calle
d clusters. One can travel from one cluster to the others by a recursive p
rocess called mutation. In this talk I will introduce Bongartz co-completi
ons in cluster algebras and give its applications to Fomin-Zelevinsky’s
conjectures on denominator vectors and exchange graphs of cluster algebras
.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (Osaka Metropolitan University)
DTSTART:20240228T043000Z
DTEND:20240228T053000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/57
DESCRIPTION:Title: Classifying torsion classes of Noetherian algebras\nby Yuta Ki
mura (Osaka Metropolitan University) as part of OIST representation theory
seminar\n\n\nAbstract\nLet R be a commutative Noetherian ring and A a Noe
therian R-algebra. In this talk\, we study classification of torsion class
es\, torsion free classes and Serre subcategories of modA. In the case whe
re A=R\, such subcategories were classified by Gabriel\, Takahashi and Sta
nley-Wang by using prime ideals of R. If R is a field\, then A is a finite
dimensional algebra\, and there are many studies of such subcategories re
lating with tilting theory. For a Noetherian algebra case\, localization o
f A at a prime ideal of R plays an important role. We see that classificat
ion can be reduced to finite dimensional algebras. If A is commutative\, o
ur results cover cases of commutative rings. This is joint work with Osamu
Iyama.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eoghan McDowell (OIST)
DTSTART:20240416T060000Z
DTEND:20240416T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/58
DESCRIPTION:Title: Spin representations of the symmetric group which reduce modulo 2
to Specht modules\nby Eoghan McDowell (OIST) as part of OIST represent
ation theory seminar\n\n\nAbstract\nWhen do two ordinary irreducible repre
sentations of a group have the same p-modular reduction? In this talk I wi
ll address this question for the double cover of the symmetric group\, and
more generally give a necessary and sufficient condition for a spin repre
sentation of the symmetric group to reduce modulo 2 to a multiple of a Spe
cht module (in the sense of Brauer characters or in the Grothendieck group
). I will explain some of the techniques used in the proof\, including des
cribing a function which swaps adjacent runners in an abacus display for t
he labelling partition of a character. This is joint work with Matthew Fay
ers.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kay Jin Lim (Nanyang Technological University)
DTSTART:20241001T060000Z
DTEND:20241001T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/59
DESCRIPTION:Title: Integral Basic Algebras\nby Kay Jin Lim (Nanyang Technological
University) as part of OIST representation theory seminar\n\nAbstract: TB
A\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Meng Tan (National University of Singapore)
DTSTART:20241015T060000Z
DTEND:20241015T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/60
DESCRIPTION:Title: Cores and core blocks of Ariki-Koike algebras\nby Kai Meng Tan
(National University of Singapore) as part of OIST representation theory
seminar\n\n\nAbstract\nThis talk will consist of two parts. In the first p
art\, we will see how certain results (such as the Nakayama 'Conjecture')
for the symmetric groups and Iwahori-Hecke algebras of type A can be gener
alised to Ariki-Koike algebras using the map from the set of multipartitio
ns to that of (single) partitions first defined by Uglov. In the second pa
rt\, we look at Fayers's core blocks\, and see how these blocks may be cla
ssified using the notation of moving vectors first introduced by Yanbo Li
and Xiangyu Qi. If time allows\, we will discuss Scopes equivalences betwe
en these blocks arising as a consequence of this classification.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (OIST)
DTSTART:20240917T060000Z
DTEND:20240917T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/61
DESCRIPTION:Title: Application of (K-theoretic) Peterson isomorphism\nby Duc-Khan
h Nguyen (OIST) as part of OIST representation theory seminar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rongwei Yang (University at Albany\, SUNY)
DTSTART:20241029T060000Z
DTEND:20241029T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/62
DESCRIPTION:Title: Linear algebra in several variables\nby Rongwei Yang (Universi
ty at Albany\, SUNY) as part of OIST representation theory seminar\n\n\nAb
stract\nMany mathematical and scientific problems concern systems of linea
r operators $(A_1\, ...\, A_n)$. Spectral theory is expected to provide a
mechanism for studying their properties\, just like the case for an indivi
dual operator. However\, defining a spectrum for non-commuting operator sy
stems has been a difficult task. The challenge stems from an inherent prob
lem in finite dimension: is there an analogue of eigenvalues in several va
riables? Or equivalently\, is there a suitable notion of joint characteris
tic polynomial for multiple matrices $A_1\, ...\, A_n$? A positive answer
to this question seems to have emerged in recent years.\n\nDefinition. Given square matrices $A_1\, ...\, A_n$ of equal size\, their characte
ristic polynomial is defined as \n\\[Q_A(z):=\\det(z_0I+z_1A_1+\\cdots+z_n
A_n)\, z=(z_0\, ...\, z_n)\\in \\mathbb{C}^{n+1}.\\] Hence\, a multivariab
le analogue of the set of eigenvalues is the eigensurface (or ei
genvariety) \n $Z(Q_A):=\\{z\\in \\mathbb{C}^{n+1}\\mid Q_A(z)=0\\}$.
This talk will review some applications of this idea to problems involving
projection matrices and finite dimensional complex algebras. The talk is
self-contained and friendly to graduate students.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daisuke Sagaki (University of Tsukuba)
DTSTART:20241112T060000Z
DTEND:20241112T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/63
DESCRIPTION:Title: Toward a Pieri rule for double quantum Grothendieck polynomials\nby Daisuke Sagaki (University of Tsukuba) as part of OIST representatio
n theory seminar\n\n\nAbstract\nIn a joint work with Satoshi Naito (arXiv:
2211.01578)\, we proved a Pieri rule (conjectured by Lenart and Maeno) for
quantum Grothendieck polynomials\, which describes the product of the qua
ntum Grothendieck polynomial associated to a cyclic permutation and an arb
itrary quantum Grothendieck polynomial as a \\(\\mathbb{Z}[Q_1\,Q_2\,\\dot
s]\\)-linear combination of quantum Grothendieck polynomials. Recently\, i
n a joint work with Satoshi Naito and Duc-Khanh Nguyen\, we are trying to
extend this result to the case of double quantum Grothendieck polynomials.
In this talk\, I'd like to report on the progress of the joint work.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Ocal (OIST)
DTSTART:20241203T060000Z
DTEND:20241203T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/64
DESCRIPTION:Title: Deformations of Frobenius algebras and noncommutative 2d topologic
al quantum field theories\nby Pablo Ocal (OIST) as part of OIST repres
entation theory seminar\n\n\nAbstract\nIn this talk I will present an atte
mpt to define noncommutative 2d topological quantum field theories using d
eformations of Frobenius algebras. First\, we will overview the importance
and uses of 2d topological quantum field theories\, as well as their equi
valence to commutative Frobenius algebras. Then\, we will consider the def
ormations given by cotwisted tensor products\, characterize when these are
Frobenius algebras\, and explain their deficiencies for our goal. Afterwa
rds\, I will introduce the notion of warped tensor products of Frobenius a
lgebras and characterize when these are Frobenius algebras. This notion en
ables us to construct a family of bifunctors that could potentially yield
nonsymmetric monoidal structures on the category of Frobenius algebras\, w
hich would then deserve to be called noncommutative 2d topological quantum
field theories. This is work in progress with Rohan Das and Julia Plavnik
.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires and Guangdong Technion-
Israel Institute of Technology)
DTSTART:20250218T060000Z
DTEND:20250218T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/65
DESCRIPTION:Title: On the tau-tilting Hochschild (co)homology of an algebra\nby A
ndrea Solotar (University of Buenos Aires and Guangdong Technion-Israel In
stitute of Technology) as part of OIST representation theory seminar\n\n\n
Abstract\nIn this talk I will introduce the tau-tilting Hochschild cohomol
ogy and homology of a finite dimensional k-algebra A\, where k is a field\
, with coefficients in an A-bimodule X. I will compute the dimension of th
e n-th tau-tilting Hochschild cohomology for all n. The result is expresse
d as an alternating sum of the dimensions of classical Hochschild cohomolo
gy in lower degrees\, plus an alternating sum of the dimensions of vector
spaces taking into account the Ext-algebra of A as well as the Peirce deco
mposition of the bimodule X. I will also formulate a tau-tilting analogue
of a question by Happel and of Han’s conjecture. This is a joint work wi
th Claude Cibils\, Marcelo Lanzilotta and Eduardo Marcos.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (Southern University of Science and Technology)
DTSTART:20250403T050000Z
DTEND:20250403T060000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/66
DESCRIPTION:Title: Smooth representations of Affine Lie algebras\nby Vyacheslav F
utorny (Southern University of Science and Technology) as part of OIST rep
resentation theory seminar\n\n\nAbstract\nWe will discuss twisting localiz
ation functor on the category of smooth representations of Affine Lie alge
bras and Gelfand-Tsetlin realizations.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emerson Escolar (Kobe University)
DTSTART:20250422T060000Z
DTEND:20250422T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/67
DESCRIPTION:Title: Representation Theory and (Barcoding) Invariants for Persistence\nby Emerson Escolar (Kobe University) as part of OIST representation th
eory seminar\n\n\nAbstract\nPersistent homology is one of the main tools o
f topological data analysis\, which has seen rapid growth recently. In the
first part of this talk\, I discuss some of the ways representation theor
y is being used for persistent homology\, focusing on "invariants". In par
ticular\, the persistence barcode\, which can be obtained from an indecomp
osable decomposition of a persistence module into intervals\, plays a cent
ral role. For multi-parameter persistent homology\, where persistence modu
les are no longer always interval-decomposable\, many alternative invarian
ts have been proposed. Naturally\, identifying the relationships among inv
ariants\, or ordering them by their discriminating power\, is a fundamenta
l question. The second part of this talk\, based on arXiv:2412.04995\, add
resses this. I discuss our formalization of the notion of "barcoding invar
iants"\, which generalizes the persistence barcode\, and results concernin
g the comparison of their discriminating powers.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Brundan (University of Oregon)
DTSTART:20250311T060000Z
DTEND:20250311T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/68
DESCRIPTION:Title: Quasi-split 2-iquantum groups\nby Jonathan Brundan (University
of Oregon) as part of OIST representation theory seminar\n\n\nAbstract\nI
n 2008\, Khovanov\, Lauda and Rouquier introduced a family of graded 2-cat
egories which could be called "2-quantum groups" because they categorify q
uantum groups. I will explain the definition of a new family of graded 2-c
ategories which play the same role for quasi-split iquantum groups. This i
s joint work with Weiqiang Wang and Ben Webster.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iryna Kashuba (Southern University of Science and Technology)
DTSTART:20250403T063000Z
DTEND:20250403T073000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/69
DESCRIPTION:Title: One-sided representations of Jordan algebras\nby Iryna Kashuba
(Southern University of Science and Technology) as part of OIST represent
ation theory seminar\n\n\nAbstract\nBy Drozd's celebrated Tame-Wild Theore
m\, any finite-dimensional associative algebra over an algebraically close
d field is either of tame or of wild representation type. We define a repr
esentation type of Jordan algebra J with respect to its one-sided represen
tations as a representation type of its universal associative envelope S(J
). We give a criterion for finiteness and tameness of one-sided representa
tion of Jordan algebras with zero radical square. This is a joint result w
ith Viktor Bekkert and Vera Serganova.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University\, Prague)
DTSTART:20250513T060000Z
DTEND:20250513T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/70
DESCRIPTION:Title: Autoequivalences of triangulated categories via Hochschild cohomol
ogy\nby Sebastian Opper (Charles University\, Prague) as part of OIST
representation theory seminar\n\n\nAbstract\nI will talk about a general t
ool which allows one to study symmetries of (enhanced) triangulated catego
ries in the form of their derived Picard groups. In general\, these groups
are rather elusive to computations which require a rather good understand
ing of the whole category at hand. A result of Keller shows that the Lie a
lgebra of the derived Picard group of an algebra can be identified with it
s Hochschild cohomology equipped with the Gerstenhaber Lie bracket. Mimick
ing the classical relationship between Lie groups and Lie algebras\, I wil
l explain how to "integrate'' elements in the Hochschild cohomology of a d
g category over fields of characteristic zero to elements in the derived P
icard group via a generalized exponential map. Afterwards we discuss prope
rties of this exponential and a few applications. This includes necessary
conditions for the uniqueness of enhancement of triangulated functors and
uniqueness of Fourier-Mukai kernels. Other applications concern derived Pi
card groups of categories arising in algebra and geometry such as derived
categories of graded gentle algebras and their corresponding partially wra
pped Fukaya categories.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berta Hudak (National Center for Theoretical Sciences\, Taipei)
DTSTART:20250603T060000Z
DTEND:20250603T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/71
DESCRIPTION:Title: Representation theory of the Hu algebras\nby Berta Hudak (Nati
onal Center for Theoretical Sciences\, Taipei) as part of OIST representat
ion theory seminar\n\n\nAbstract\nHu algebras were first defined by Hu whe
n he stated a Morita equivalence between Hecke algebras of type D and of t
ype A. Motivated by his work\, Lai-Nakano-Xiang introduced the notion of q
uantum wreath products and gave a definition of Hu algebras in this sense.
In this talk\, we will first introduce Hu algebras as quantum wreath prod
ucts\, then show that these algebras are cellular by constructing a cellul
ar basis. Finally\, we present the necessary conditions for two modules to
belong to the same block.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Ono (University of Virginia)
DTSTART:20250729T060000Z
DTEND:20250729T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/72
DESCRIPTION:Title: Partitions Detect Primes\nby Ken Ono (University of Virginia)
as part of OIST representation theory seminar\n\n\nAbstract\nThis talk pre
sents “partition theoretic” analogs of the classical work of Matiyasev
ich that resolved Hilbert’s Tenth Problem in the negative. The Diophanti
ne equations we consider involve equations of MacMahon’s partition funct
ions and their natural generalizations. Here we explicitly construct infin
itely many Diophantine equations in partition functions whose solutions ar
e precisely the prime numbers. To this end\, we produce explicit additive
bases of all graded weights of quasimodular forms\, which is of independen
t interest with many further applications. This is joint work with Will Cr
aig and Jan-Willem van Ittersum.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mee Seong Im (Johns Hopkins University)
DTSTART:20250804T070000Z
DTEND:20250804T080000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/73
DESCRIPTION:Title: Entropy\, cocycles\, algebraic K-theory and diagrammatics\nby
Mee Seong Im (Johns Hopkins University) as part of OIST representation the
ory seminar\n\n\nAbstract\nI will discuss how cocycles appear in a graphic
al network. Furthermore\, the\nShannon entropy of a finite probability dis
tribution has a natural interpretation in terms of\ndiagrammatics. I will
explain the diagrammatics and their connections to infinitesimal\ndilogari
thms and entropy. If I have time\, I will talk about how algebraic K-theor
y appears in\ndiagrammatics.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Khovanov (Johns Hopkins University)
DTSTART:20250805T040000Z
DTEND:20250805T050000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/74
DESCRIPTION:Title: The Delannoy category and its diagrammatics\nby Mikhail Khovan
ov (Johns Hopkins University) as part of OIST representation theory semina
r\n\n\nAbstract\nN.Harman and A.Snowden discovered a semisimple monoidal p
ivotal category\, called the Delannoy category\, where composition of morp
hisms is given by computing the compact Euler characteristic of subspaces
of the Euclidean space described by inequalities on the coordinates. In th
e talk we will explain a diagrammatic description of their category\, foll
owing a joint work with N.Snyder. The number of simple objects in the Dela
nnoy category grows exponentially\, but a suitable monoidal subcategory ha
s the Grothendieck ring isomorphic to the ring of integer-valued one-varia
ble polynomials. This subcategory can be viewed as a categorification of t
he latter ring.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lobb (Durham University)
DTSTART:20250804T053000Z
DTEND:20250804T063000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/75
DESCRIPTION:Title: Peg problems and peg progress\nby Andrew Lobb (Durham Universi
ty) as part of OIST representation theory seminar\n\n\nAbstract\nDraw any
closed curve you like on a piece of paper. Formulated in 1911\, the Toepli
tz Square Peg Problem (which remains unsolved) conjectures that there exis
t four points on this curve at the vertices of a square. Over the past fiv
e years there has been much progress made on relatives of the TSPP\, and t
his progress began partly at OIST during the early months of the pandemic.
I shall give a snapshot of where things stand\, and an indication of some
of the new ideas that have revitalized interest in this area. The talk sh
all be very accessible\, with no specialized knowledge assumed.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (OIST)
DTSTART:20251209T060000Z
DTEND:20251209T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/76
DESCRIPTION:Title: Branching rule on winding subalgebras of affine Kac-Moody algebras
\nby Duc-Khanh Nguyen (OIST) as part of OIST representation theory sem
inar\n\n\nAbstract\nIn this work\, by using the Lakshmibai-Seshadri paths\
, we give the branching rule for representations of affine Kac-Moody algeb
ras to their winding subalgebras. As a corollary\, we can describe branchi
ng multiplicities in the language of paths. An analog of Steinberg’s for
mula for branching multiplicities is also given.\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Turek (OIST)
DTSTART:20260120T060000Z
DTEND:20260120T070000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/77
DESCRIPTION:Title: Balanced columns of decomposition matrices\nby Pavel Turek (OI
ST) as part of OIST representation theory seminar\n\n\nAbstract\nThe decom
position matrices describe how the irreducible modules of symmetric groups
in characteristic zero decompose in prime characteristic. Understanding t
hese matrices\, and in particular\, finding a combinatorial description of
their entries\, is a central open problem in the representation theory of
symmetric groups. The main result of the talk is a description of columns
of these matrices indexed by ‘d-balanced’ partitions for d=2. It is a
consequence of a more general result which describes these columns for an
y d>1 under some additional assumptions. As a further result\, we show tha
t there are many 2-balanced partitions. The key players in the proof of th
e presented results are Foulkes modules\, which are used to construct cert
ain projective modules\, and the Jantzen-Schaper formula\, which allows us
to transfer the algebraic problem into a combinatorial system of equaliti
es\, which can then be solved using a new algorithm defined on Young diagr
ams. This is joint work with Bim Gustavsson\, David Hemmer and Stacey Law.
\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bim Gustavsson (University of Birmingham)
DTSTART:20260609T063000Z
DTEND:20260609T073000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/78
DESCRIPTION:by Bim Gustavsson (University of Birmingham) as part of OIST r
epresentation theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Duquesne University)
DTSTART:20260728T063000Z
DTEND:20260728T073000Z
DTSTAMP:20260404T111105Z
UID:OISTRTS/79
DESCRIPTION:by Rob Muth (Duquesne University) as part of OIST representati
on theory seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OISTRTS/79/
END:VEVENT
END:VCALENDAR