BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Chris Bowman (University of Kent)
DTSTART:20200915T073000Z
DTEND:20200915T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/1
DESCRIPTION:Title:
Tautological p-Kazhdan–Lusztig Theory for cyclotomic Hecke algebras\
nby Chris Bowman (University of Kent) as part of OIST representation theor
y seminar\n\n\nAbstract\nWe discuss a new explicit isomorphism between (tr
uncations of) quiver Hecke algebras and Elias–Williamson’s diagrammati
c endomorphism algebras of Bott–Samelson bimodules. This allows us to de
duce that the decomposition numbers of these algebras (including as exampl
es the symmetric groups and generalised blob algebras) are tautologically
equal to the associated p-Kazhdan–Lusztig polynomials\, provided that th
e characteristic is greater than the Coxeter number. This allows us to giv
e an elementary and explicit proof of the main theorem of Riche–Williams
on’s recent monograph and extend their categorical equivalence to cyclot
omic Hecke algebras\, thus solving Libedinsky–Plaza’s categorical blob
conjecture.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahir Can (Tulane University)
DTSTART:20200929T000000Z
DTEND:20200929T010000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/2
DESCRIPTION:Title:
Spherical Varieties and Combinatorics\nby Mahir Can (Tulane University
) as part of OIST representation theory seminar\n\n\nAbstract\nLet G be a
reductive complex algebraic group with a Borel subgroup B. A spherical G-v
ariety is an irreducible normal G-variety X where B has an open orbit. If
X is affine\, or if it is projective but endowed with a G-linearized ample
line bundle\, then the group action criteria for the sphericality is in f
act equivalent to the representation theoretic statement that a certain sp
ace of functions (related to X) is multiplicity-free as a G-module. In thi
s talk\, we will discuss the following question about a class of spherical
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://researchseminars.org/talk/OISTRTS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eoghan McDowell (Royal Holloway\, University of London)
DTSTART:20201013T073000Z
DTEND:20201013T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/3
DESCRIPTION:Title:
The image of the Specht module under the inverse Schur functor\nby Eog
han McDowell (Royal Holloway\, University of London) as part of OIST repre
sentation theory seminar\n\n\nAbstract\nThe Schur functor and its inverses
give an important connection between the representation theories of the s
ymmetric group and the general linear group. Kleshchev and Nakano proved i
n 2001 that when the characteristic of the field is at least 5\, the 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 characteris
tics 2 and 3: in characteristic 3\, the isomorphism holds\, and I will giv
e an elementary proof of this fact which covers also all characteristics o
ther than 2\; in characteristic 2\, the isomorphism does not hold for all
Specht modules\, and I will classify those for which it does. Our approach
is with Young tableaux\, tabloids and Garnir relations.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Washington and Jefferson College)
DTSTART:20201027T000000Z
DTEND:20201027T010000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/4
DESCRIPTION:Title:
Specht modules and cuspidal ribbon tableaux\nby Rob Muth (Washington a
nd Jefferson College) as part of OIST representation theory seminar\n\n\nA
bstract\nRepresentation theory of Khovanov-Lauda-Rouquier (KLR) algebras i
n affine type A can be studied through the lens of Specht modules\, associ
ated with the cellular structure of cyclotomic KLR algebras\, or through t
he lens of cuspidal modules\, associated with categorified PBW bases for t
he quantum group of affine type A. Cuspidal ribbons provide a sort of comb
inatorial bridge between these approaches. I will describe some recent res
ults on cuspidal ribbon tableaux\, and some implications in the world of K
LR representation theory\, such as bounds on labels of simple factors of S
pecht modules\, and the presentation of cuspidal modules. Portions of this
talk are joint work with Dina Abbasian\, Lena Difulvio\, Gabrielle Paster
nak\, Isabella Sholtes\, and Frances Sinclair.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jieru Zhu (Hausdorff Institute of Mathematics)
DTSTART:20201110T073000Z
DTEND:20201110T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/5
DESCRIPTION:Title:
Double centralizer properties for the Drinfeld double of the Taft algebras
\nby Jieru Zhu (Hausdorff Institute of Mathematics) as part of OIST re
presentation theory seminar\n\n\nAbstract\nThe Drinfeld double of the taft
algebra\, $D_n$\, whose ground field contains $n$-th roots of unity\, has
a known list of 2-dimensional irreducible modules. For each of such modul
e $V$\, we show that there is a well-defined action of the Temperley-Lieb
algebra $TL_k$ on the $k$-fold tensor product of $V$\, and this action com
mutes 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 algebra 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 functio
n introduced by Russell-Tymoczko. This is joint work with Georgia Benkart\
, Rekha Biswal\, Ellen Kirkman and Van Nguyen.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Wang (Osaka University)
DTSTART:20201117T073000Z
DTEND:20201117T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/6
DESCRIPTION:Title:
On $\\tau$-tilting finiteness of Schur algebras\nby Qi Wang (Osaka Uni
versity) as part of OIST representation theory seminar\n\n\nAbstract\nSupp
ort $\\tau$-tilting modules are introduced by Adachi\, Iyama and Reiten in
2012 as a generalization of classical tilting modules. One of the importa
nce of these modules is that they are bijectively corresponding to many ot
her objects\, such as two-term silting complexes and left finite semibrick
s. Let $V$ be an $n$-dimensional vector space over an algebraically closed
field $\\mathbb{F}$ of characteristic $p$. Then\, the Schur algebra $S(n\
,r)$ 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 Schur alg
ebra $S(n\,r)$ has only finitely many pairwise non-isomorphic basic suppor
t $\\tau$-tilting modules.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Jacon (University of Reims Champagne-Ardenne)
DTSTART:20201208T073000Z
DTEND:20201208T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/7
DESCRIPTION:Title:
Cores of Ariki-Koike algebras\nby Nicolas Jacon (University of Reims C
hampagne-Ardenne) as part of OIST representation theory seminar\n\n\nAbstr
act\nWe study a natural generalization of the notion of cores for l-partit
ions: the (e\, s)-cores. We relate this notion with the notion of weight a
s defined by Fayers and use it to describe the blocks of Ariki-Koike algeb
ras.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Fayers (Queen Mary University of London)
DTSTART:20210112T073000Z
DTEND:20210112T083000Z
DTSTAMP:20260422T225754Z
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 character
istic p\, the simple modules for the symmetric group \\(S_n\\) are the Jam
es modules \\(D^\\lambda\\)\, labelled by p-regular partitions of n. If we
let \\(sgn\\) denote the 1-dimensional sign module\, then for any p-regul
ar \\(\\lambda\\)\, the module \\(D^\\lambda\\otimes sgn\\) is also a simp
le module. So there is an involutory bijection \\(m_p\\) on the set of p-r
egular partitions such that \\(D^\\lambda\\otimes sgn=D^{m_p(\\lambda)}\\)
. The map \\(m_p\\) is called the Mullineux map\, and an important problem
is to describe \\(m_p\\) combinatorially. There are now several known sol
utions to this problem. I will describe the history of this problem and ex
plain the known combinatorial solutions\, and then give a new solution bas
ed on crystals and regularisation.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Chung (Okinawa Institute of Science and Technology)
DTSTART:20210126T073000Z
DTEND:20210126T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/9
DESCRIPTION:Title:
\\(\\imath\\)Quantum Covering Groups: Serre presentation and canonical bas
is\nby Chris Chung (Okinawa Institute of Science and Technology) as pa
rt of OIST representation theory seminar\n\n\nAbstract\nIn 2016\, Bao and
Wang developed a general theory of canonical basis for quantum symmetric p
airs \\((\\mathbf{U}\, \\mathbf{U}^\\imath)\\)\, generalizing the canonica
l basis of Lusztig and Kashiwara for quantum groups and earning them the 2
020 Chevalley Prize in Lie Theory. The \\(\\imath\\)divided powers are pol
ynomials in a single generator that generalize Lusztig's divided powers\,
which are monomials. They can be similarly perceived as canonical basis in
rank one\, and have closed form expansion formulas\, established by Berma
n and Wang\, that were used by Chen\, Lu and Wang to give a Serre presenta
tion for coideal subalgebras \\(\\mathbf{U}^\\imath\\)\, featuring novel \
\(\\imath\\)Serre relations when \\(\\tau(i) = i\\).\n\nQuantum covering g
roups\, developed by Clark\, Hill and Wang\, are a generalization that `co
vers' both the Lusztig quantum group and quantum supergroups of anisotropi
c type. In this talk\, I will talk about how the results for \\(\\imath\\)
-divided powers and the Serre presentation can be extended to the quantum
covering algebra setting\, and subsequently applications to canonical basi
s for \\(\\mathbf{U}^\\imath_\\pi\\)\, the quantum covering analogue of \\
(\\mathbf{U}^\\imath\\)\, and quantum covering groups at roots of 1.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Davidson (Reed College)
DTSTART:20210216T003000Z
DTEND:20210216T013000Z
DTSTAMP:20260422T225754Z
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 combinatori
ally defined diagrams which encode homomorphisms between tensor products o
f certain representations of Lie (super)algebras. I will describe some re
cent work with Jon Kujawa and Rob Muth which defines webs for the type P L
ie superalgebra\, and then uses these webs to deduce an analog of Howe dua
lity for this Lie superalgebra.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Yi Rui Low (National University of Singapore)
DTSTART:20210302T073000Z
DTEND:20210302T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/11
DESCRIPTION:Title: Adjustment matrices\nby Aaron Yi Rui Low (National University of Sing
apore) as part of OIST representation theory seminar\n\n\nAbstract\nJames'
s Conjecture predicts that the adjustment matrix for weight $w$ blocks of
the Iwahori-Hecke algebras $\\mathcal{H}_{n}$ and the $q$-Schur algebras $
\\mathcal{S}_{n}$ is the identity matrix when $w<\\textnormal{char}(\\math
bb{F})$. Fayers has proved James's Conjecture for blocks of $\\mathcal{H}_
{n}$ of weights 3 and 4. We shall discuss some results on adjustment matri
ces that have been used to prove James's Conjecture for blocks of $\\mathc
al{S}_{n}$ of weights 3 and 4 in an upcoming paper. If time permits\, we w
ill look at a proof of the weight 3 case.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Kleshchev (University of Oregon)
DTSTART:20210330T003000Z
DTEND:20210330T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/12
DESCRIPTION:Title: Irreducible restrictions from symmetric groups to subgroups\nby Alexa
nder Kleshchev (University of Oregon) as part of OIST representation theor
y seminar\n\n\nAbstract\nWe motivate\, discuss history of\, and present a
solution to the following problem: describe pairs (G\,V) where V is an irr
educible representation of the symmetric group S_n of dimension >1 and G i
s a subgroup of S_n such that the restriction of V to G is irreducible. 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 Morotti.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alistair Savage (University of Ottawa)
DTSTART:20210202T003000Z
DTEND:20210202T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/13
DESCRIPTION:Title: Affinization of monoidal categories\nby Alistair Savage (University o
f Ottawa) as part of OIST representation theory seminar\n\n\nAbstract\nWe
define the affinization of an arbitrary monoidal category\, corresponding
to the category of string diagrams on the cylinder. We also give an alter
native characterization in terms of adjoining dot generators to the catego
ry. The affinization formalizes and unifies many constructions appearing
in the literature. We describe a large number of examples coming from Hec
ke-type algebras\, braids\, tangles\, and knot invariants.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catharina Stroppel (University of Bonn)
DTSTART:20210316T073000Z
DTEND:20210316T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/14
DESCRIPTION:Title: Verlinde rings and DAHA actions\nby Catharina Stroppel (University of
Bonn) as part of OIST representation theory seminar\n\n\nAbstract\nIn thi
s talk we will briefly recall how quantum groups at roots give rise Verlin
de algebras which can be realised as Grothendieck rings of certain monoida
l categories. The ring structure is quite interesting and was very much st
udied in type A. I will try to explain how one gets a natural action of ce
rtain 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://researchseminars.org/talk/OISTRTS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Wildon (Royal Holloway\, University of London)
DTSTART:20210427T073000Z
DTEND:20210427T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/15
DESCRIPTION:Title: Plethysms\, polynomial representations of linear groups and Hermite recip
rocity over an arbitrary field\nby Mark Wildon (Royal Holloway\, Unive
rsity of London) as part of OIST representation theory seminar\n\n\nAbstra
ct\nLet \\(E\\) be a \\(2\\)-dimensional vector space. Over the complex nu
mbers the irreducible polynomial representations of the special linear gro
up \\(SL(E)\\) are the symmetric powers \\(Sym^r E\\). Composing polynomia
l representations\, for example to form \\(Sym^4 Sym^2 E\\)\, corresponds
to the plethysm product on symmetric functions. Expressing such a plethysm
as a linear combination of Schur functions has been identified by Richard
Stanley as one of the fundamental open problems in algebraic combinatoric
s. In my talk I will use symmetric functions to prove some classical isomo
rphisms\, 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\, provided
suitable dualities are introduced\, Hermite reciprocity holds over arbitr
ary fields\; certain other isomorphisms (we can prove) have no modular gen
eralization. The final part is joint work with my Ph.D student Eoghan McDo
well.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stacey Law (University of Cambridge)
DTSTART:20210413T073000Z
DTEND:20210413T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/16
DESCRIPTION:Title: Sylow branching coefficients and a conjecture of Malle and Navarro\nb
y Stacey Law (University of Cambridge) as part of OIST representation theo
ry seminar\n\n\nAbstract\nThe relationship between the representation theo
ry of a finite group and that of its Sylow subgroups is a key area of inte
rest. For example\, recent results of Malle–Navarro and Navarro–Tiep
–Vallejo have shown that important structural properties of a finite gro
up \\(G\\) are controlled by the permutation character \\(\\mathbb{1}_P\\b
ig\\uparrow^G\\)\, where \\(P\\) is a Sylow subgroup of \\(G\\) and \\(\\m
athbb{1}_P\\) denotes the trivial character of \\(P\\). We introduce so-ca
lled Sylow branching coefficients for symmetric groups to describe multipl
icities associated with these induced characters\, and as an application c
onfirm a prediction of Malle and Navarro from 2012\, in joint work with E.
Giannelli\, J. Long and C. Vallejo.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Gurevich (Technion)
DTSTART:20210528T073000Z
DTEND:20210528T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/17
DESCRIPTION:Title: New constructions for irreducible representations in monoidal categories
of type A\nby Max Gurevich (Technion) as part of OIST representation t
heory seminar\n\n\nAbstract\nOne ever-recurring goal of Lie theory is the
quest for effective and elegant descriptions of collections of simple obje
cts in categories of interest. A cornerstone feat achieved by Zelevinsky i
n that regard\, was the combinatorial explication of the Langlands classif
ication for smooth irreducible representations of p-adic GL_n. It was a fo
rerunner for an exploration of similar classifications for various categor
ies of similar nature\, such as modules over affine Hecke algebras or quan
tum affine algebras\, to name a few. \nA next step - reaching an effective
understanding of all reducible finite-length representations remains larg
ely a difficult task throughout these settings.\n\nRecently\, joint with E
rez Lapid\, we have revisited the original Zelevinsky setting by suggestin
g a refined construction of all irreducible representations\, with the hop
e of shedding light on standing decomposition problems. This construction
applies the Robinson-Schensted-Knuth transform\, while categorifying the d
eterminantal Doubilet-Rota-Stein basis for matrix polynomial rings appeari
ng in invariant theory.\nIn this talk\, I would like to introduce the new
construction into the setting of modules over quiver Hecke (KLR) algebras.
In type A\, this category may be viewed as a quantization/gradation of th
e category of representations of p-adic groups. I will explain how adoptin
g that point of view and exploiting recent developments in the subject (su
ch as the normal sequence notion of Kashiwara-Kim) brings some conjectural
properties of the RSK construction (back in the p-adic setting) into reso
lution.\nTime permits\, I will discuss the relevance of the RSK constructi
on to the representation theory of cyclotomic Hecke algebras.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sira Gratz (University of Glasgow)
DTSTART:20210615T073000Z
DTEND:20210615T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/18
DESCRIPTION:Title: Grassmannians\, Cluster Algebras and Hypersurface Singularities\nby S
ira Gratz (University of Glasgow) as part of OIST representation theory se
minar\n\n\nAbstract\nGrassmannians are objects of great combinatorial 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 combinatorics is
intimately related to algebraic and geometric concepts such as to represe
ntations of algebras and hypersurface singularities. At the core lies the
idea of generating an object from a so-called “cluster” via the concep
t of “mutation”. \n\nIn this talk\, we offer an overview of Grassmanni
an combinatorics in a cluster theoretic framework\, and ultimately take th
em to the limit to explore the a priori simple question: What happens if w
e allow infinite clusters? We introduce the notion of a cluster algebra of
infinite rank (based on joint work with Grabowski)\, and of a Grassmannia
n category of infinite rank (based on joint work with August\, Cheung\, Fa
ber and Schroll).\n
LOCATION:https://researchseminars.org/talk/OISTRTS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Millan Berdasco (Queen Mary University of London)
DTSTART:20210706T073000Z
DTEND:20210706T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/19
DESCRIPTION:Title: On the computation of decomposition numbers of the symmetric group\nb
y Diego Millan Berdasco (Queen Mary University of London) as part of OIST
representation theory seminar\n\n\nAbstract\nThe most important open probl
em in the modular representation theory of the symmetric group is finding
the multiplicity of the simple modules as composition factors of the Spech
t modules. In characteristic 0 the Specht modules are just the simple modu
les of the symmetric group algebra\, but in positive characteristic they m
ay no longer be simple. We will survey the rich interplay between represen
tation theory and combinatorics of integer partitions\, review a number of
results in the literature which allow us to compute composition series fo
r certain infinite families of Specht modules from a finite subset of them
\, and discuss the extension of these techniques to other Specht modules.\
n
LOCATION:https://researchseminars.org/talk/OISTRTS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hankyung Ko (Uppsala University)
DTSTART:20210928T073000Z
DTEND:20210928T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/20
DESCRIPTION:Title: Bruhat orders and Verma modules\nby Hankyung Ko (Uppsala University)
as part of OIST representation theory seminar\n\n\nAbstract\nThe Bruhat or
der on a Weyl group has a representation theoretic interpretation in terms
of Verma modules. The talk concerns resulting interactions between combin
atorics and homological algebra. I will present several questions around t
he 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://researchseminars.org/talk/OISTRTS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich (University of Hamburg)
DTSTART:20211012T060000Z
DTEND:20211012T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/21
DESCRIPTION:Title: Knots and quivers\, HOMFLYPT and DT\nby Paul Wedrich (University of H
amburg) as part of OIST representation theory seminar\n\n\nAbstract\nI wil
l describe a surprising connection between the colored HOMFLY-PT polynomia
ls of knots and the motivic Donaldson-Thomas invariants of certain symmetr
ic quivers\, which was conjectured by Kucharski-Reineke-Stosic-Sulkowski.
I will outline a proof of this correspondence for arborescent links via qu
ivers associated with 4-ended tangles. Finally\, I will speculate about ho
w much of the HOMFLY-PT skein theory might carry over to the realm of DT q
uiver 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://researchseminars.org/talk/OISTRTS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tianyuan Xu (University of Colorado at Boulder)
DTSTART:20211130T003000Z
DTEND:20211130T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/22
DESCRIPTION:Title: On Kazhdan–Lusztig cells of a-value 2\nby Tianyuan Xu (University o
f Colorado at Boulder) as part of OIST representation theory seminar\n\n\n
Abstract\nThe Kazhdan–Lusztig (KL) cells of a Coxeter group are subsets
of the group defined using the KL basis of the associated Iwahori–Hecke
algebra. The cells of symmetric groups can be computed via the Robinson–
Schensted correspondence\, but for general Coxeter groups combinatorial de
scriptions of KL cells are largely unknown except for cells of a-value 0 o
r 1\, where a refers to an N-valued function defined by Lusztig that is co
nstant on each cell. In this talk\, we will report some recent progress on
KL cells of a-value 2. In particular\, we classify Coxeter groups with fi
nitely many elements of a-value 2\, and for such groups we characterize an
d count all cells of a-value 2 via certain posets called heaps. We will al
so mention some applications of these results for cell modules. This is jo
int work with Richard Green.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Seelinger (University of Michigan)
DTSTART:20211026T003000Z
DTEND:20211026T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/23
DESCRIPTION:Title: Diagonal harmonics and shuffle theorems\nby George Seelinger (Univers
ity of Michigan) as part of OIST representation theory seminar\n\n\nAbstra
ct\nThe Shuffle Theorem\, conjectured by Haglund\, Haiman\, Loehr\, Remmel
and Ulyanov\, and proved by Carlsson and Mellit\, describes the character
istic of the $S_n$-module of diagonal harmonics as a weight generating fun
ction over labeled Dyck paths under a line with slope −1. The Shuffle Th
eorem has been generalized in many different directions\, producing a numb
er of theorems and conjectures. We provide a generalized shuffle theorem f
or paths under any line with negative slope using different methods from p
revious proofs of the Shuffle Theorem. In particular\, our proof relies on
showing a "stable" shuffle theorem in the ring of virtual GL_l-characters
. Furthermore\, we use our techniques to prove the Extended Delta Conjectu
re\, yet another generalization of the original Shuffle Conjecture.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arik Wilbert (University of South Alabama)
DTSTART:20211109T003000Z
DTEND:20211109T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/24
DESCRIPTION:Title: Real Springer fibers and odd arc algebras\nby Arik Wilbert (Universit
y of South Alabama) as part of OIST representation theory seminar\n\n\nAbs
tract\nArc algebras were introduced by Khovanov in a successful attempt to
lift the quantum sl2 Reshetikhin-Turaev invariant for tangles to a homolo
gical invariant. When restricted to knots and links\, Khovanov’s homolog
y theory categorifies the Jones polynomial. Ozsváth-Rasmussen-Szabó disc
overed a different categorification of the Jones polynomial called odd Kho
vanov homology. Recently\, Naisse-Putyra were able to extend odd Khovanov
homology to tangles using so-called odd arc algebras which were originally
constructed by Naisse-Vaz. The goal of this talk is to discuss a geometri
c approach to understanding odd arc algebras and odd Khovanov homology usi
ng Springer fibers over the real numbers. This is joint work with J. N. Eb
erhardt and G. Naisse.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Creedon (City\, University of London)
DTSTART:20211116T073000Z
DTEND:20211116T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/25
DESCRIPTION:Title: Defining an Affine Partition Algebra\nby Samuel Creedon (City\, Unive
rsity of London) as part of OIST representation theory seminar\n\n\nAbstra
ct\nIn this talk we motivate the construction of a new algebra called the
affine partition algebra. We summarise some of its basic properties and de
scribe an action which extends the Schur-Weyl duality between the symmetri
c group and partition algebra. We establish connections to the affine part
ition category defined recently by Brundan and Vargas and show that such a
category is a full subcategory of the Heisenberg category.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joanna Meinel (Federal Office for Information Security\, Bonn)
DTSTART:20211214T073000Z
DTEND:20211214T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/26
DESCRIPTION:Title: Decompositions of tensor products: Highest weight vectors from branching<
/a>\nby Joanna Meinel (Federal Office for Information Security\, Bonn) as
part of OIST representation theory seminar\n\n\nAbstract\nWe consider tens
or powers of the natural sl_n-representation\, and we look for description
s of highest weight vectors therein: We discuss explicit formulas for n=2\
, a recursion for n=3\, and for bigger n we demonstrate how Jucys-Murphy e
lements 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://researchseminars.org/talk/OISTRTS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Tubbenhauer (University of Sydney)
DTSTART:20220201T073000Z
DTEND:20220201T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/27
DESCRIPTION:Title: On weighted KLRW algebras\nby Daniel Tubbenhauer (University of Sydne
y) as part of OIST representation theory seminar\n\n\nAbstract\nWeighted K
LRW algebras are diagram algebras that depend on continuous \nparameters.
Varying these parameters gives a way to interpolate between \nvarious alge
bras that appear in (categorical) representation theory \nsuch as semisimp
le algebras\, KLR algebras\, quiver Schur algebras and diagrammatic Chered
nik algebras.\n\nThis talk is a friendly (and diagrammatic!) introduction
explaining these algebras\, with no prior knowledge about any of these ass
umed.\n\nBased on joint work A. Mathas.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Spencer (University of Cambridge)
DTSTART:20220301T073000Z
DTEND:20220301T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/28
DESCRIPTION:Title: (Some) Gram Determinants for \\(A_n\\) nets\nby Robert Spencer (Unive
rsity of Cambridge) as part of OIST representation theory seminar\n\n\nAbs
tract\nThe nets giving a diagrammatic description of the category of (tens
or products of) fundamental representations of \\(sl_n\\) form a cellular
category. We can then ask about the natural inner form on certain cell mod
ules. In this talk\, we will calculate the determinant of some of these fo
rms in terms of certain traces of clasps or magic weave elements (for whic
h there is a conjectured formula due to Elias). The method appears moderat
ely general and gives a result which is hopefully illuminating and applica
ble to other monoidal\, cellular categories.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Murray (Maynooth University)
DTSTART:20220322T073000Z
DTEND:20220322T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/29
DESCRIPTION:Title: A Schur-positivity conjecture inspired by the Alperin-Mckay conjecture\nby John Murray (Maynooth University) as part of OIST representation the
ory seminar\n\n\nAbstract\nThe McKay conjecture asserts that a finite grou
p has the same number of odd degree irreducible characters as the normaliz
er of a Sylow 2-subgroup. The Alperin-McKay (A-M) conjecture generalizes t
his to the height-zero characters in 2-blocks.\n\nIn his original paper\,
McKay already showed that his conjecture holds for the finite symmetric gr
oups S_n. In 2016\, Giannelli\, Tent and the speaker established a canonic
al bijection realising A-M for S_n\; the height-zero irreducible character
s in a 2-block are naturally parametrized by tuples of hooks whose lengths
are certain powers of 2\, and this parametrization is compatible with res
triction to an appropriate 2-local subgroup.\n\nNow corresponding to a 2-b
lock of the symmetric group S_n\, there is a 2-block of a maximal Young su
bgroup of S_n of the same weight. An obvious question is whether our canon
ical bijection is compatible with restriction of height-zero characters be
tween these blocks.\n\nAttempting to prove this compatibility lead me to f
ormulate a conjecture asserting the Schur-positivity of certain difference
s of skew-Schur functions. The corresponding skew-shapes have triangular i
nner-shape\, but otherwise do not refer to the 2-modular theory. I will de
scribe my conjecture and give positive evidence in its favour.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Doty (Loyola University Chicago)
DTSTART:20220215T003000Z
DTEND:20220215T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/30
DESCRIPTION:Title: Schur-Weyl duality for braid and twin groups via the Burau representation
\nby Stephen Doty (Loyola University Chicago) as part of OIST represen
tation theory seminar\n\n\nAbstract\nThe natural permutation representatio
n of the symmetric group admits a q-analogue known as the Burau representa
tion. The symmetric group admits two natural covering groups: the braid gr
oup of Artin and the twin group of Khovanov\, obtained respectively by for
getting the cubic and quadratic relations in the Coxeter presentation of t
he symmetric group. By computing centralizers of tensor powers of the Bura
u representation\, we obtain new instances of Schur-Weyl duality for braid
groups and twin groups\, in terms of the partial permutation and partial
Brauer algebras. The method produces many representations of each group th
at can be understood combinatorially. (This is joint work with Tony Giaqui
nto.)\n
LOCATION:https://researchseminars.org/talk/OISTRTS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kay Jin Lim (Nanyang Technological University)
DTSTART:20220420T073000Z
DTEND:20220420T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/31
DESCRIPTION:Title: Descent Algebra of Type A\nby Kay Jin Lim (Nanyang Technological Univ
ersity) as part of OIST representation theory seminar\n\n\nAbstract\nFor a
finite Coxeter group W\, L. Solomon defined certain subalgebra of the gro
up algebra kW which is now commonly known as the Solomon’s descent algeb
ra. As usual\, the type A and B cases have special interest for both the a
lgebraists and combinatorists. In this talk\, I will be particularly focus
ing on the type A and modular case. It is closely related to the represent
ation theory of the symmetric group and the (higher) Lie representations.\
n
LOCATION:https://researchseminars.org/talk/OISTRTS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dean Yates (Queen Mary University of London)
DTSTART:20220405T073000Z
DTEND:20220405T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/32
DESCRIPTION:Title: Spin representations of the symmetric group\nby Dean Yates (Queen Mar
y University of London) as part of OIST representation theory seminar\n\n\
nAbstract\nSpin representations of the symmetric group S_n can be thought
of equivalently as either projective representations of S_n\, or as linear
representations of a double cover S_n+ of S_n. Whilst the line
ar representation theory of S_n is dictated by removing ‘rim-hooks’ fr
om (the Young diagrams of) partitions of n\, the projective representation
theory of S_n is controlled by removing ‘bars’ from bar partitions of
n (i.e. partitions of n into distinct parts). We will look at some combin
atorial results on bar partitions from a recent paper of the author before
discussing methods for determining the modular decomposition of spin repr
esentations over fields of positive characteristic.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinsuke Tsuchioka (Tokyo Institute of Technology)
DTSTART:20220614T073000Z
DTEND:20220614T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/33
DESCRIPTION:Title: An example of A2 Rogers-Ramanujan bipartition identities of level 3\n
by Shinsuke Tsuchioka (Tokyo Institute of Technology) as part of OIST repr
esentation theory seminar\n\n\nAbstract\nIn the 1970s\, Lepowsky-Milne dis
covered a similarity between the infinite products of the Rogers-Ramanujan
identities (RR identities\, for short) and the principal characters of th
e level 3 standard modules of the affine Lie algebra of type \\(A^{(1)}_{1
}\\). Subsequently\, Lepowsky-Wilson gave a Lie-theoretic interpretation a
nd 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 typ
e \\(A^{(1)}_{2}\\).\n
LOCATION:https://researchseminars.org/talk/OISTRTS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Duquesne University)
DTSTART:20220705T073000Z
DTEND:20220705T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/34
DESCRIPTION:Title: Superalgebra deformations of web categories\nby Rob Muth (Duquesne Un
iversity) as part of OIST representation theory seminar\n\n\nAbstract\nFor
a superalgebra A\, and even subalgebra a\, one may define an associated d
iagrammatic monoidal supercategory Web(A\,a)\, which generalizes a number
of symmetric web category constructions. In this talk\, I will define and
discuss Web(A\,a)\, focusing on two interesting applications: Firstly\, We
b(A\,a) is equipped with an asymptotically faithful functor to the categor
y of gl_n(A)-modules generated by symmetric powers of the natural module\,
and may be used to establish Howe dualities between gl_n(A) and gl_m(A) i
n some cases. Secondly\, Web(A\,a) yields a diagrammatic presentation for
the ‘Schurification' T^A_a(n\,d). For various choices of A/a\, these Sch
urifications have proven connections to RoCK blocks of Hecke algebras\, an
d conjectural connections to RoCK blocks of Schur algebras and Sergeev sup
eralgebras. This is joint work with Nicholas Davidson\, Jonathan Kujawa\,
and Jieru Zhu.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Mathas (University of Sydney)
DTSTART:20220810T060000Z
DTEND:20220810T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/35
DESCRIPTION:Title: Content systems and KLR algebras\nby Andrew Mathas (University of Syd
ney) as part of OIST representation theory seminar\n\n\nAbstract\nIn 1901
Young gave an explicit construction of the ordinary irreducible representa
tions of the symmetric groups. In doing this\, he introduced content funct
ions for partitions\, which are now a key statistic in the semisimple repr
esentation theory of the symmetric groups. In this talk I will describe a
generalisation of Young's ideas to the cyclotomic KLR algebras of affine t
ypes A and C. This is quite surprising because Young's seminormal forms ar
e creatures from the semisimple world whereas the cyclotomic KLR algebras
are rarely semisimple. As an application\, we show that these algebras are
cellular and construct their irreducible representations. A special case
of these results gives new information about the symmetric groups in chara
cteristic p>0. If time permits\, I will describe how these results lead to
an explicit categorification of the corresponding integrable highest weig
ht modules.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alice Dell'Arciprete (University of East Anglia)
DTSTART:20220719T073000Z
DTEND:20220719T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/36
DESCRIPTION:Title: Scopes equivalence for blocks of Ariki-Koike algebras\nby Alice Dell'
Arciprete (University of East Anglia) as part of OIST representation theor
y seminar\n\n\nAbstract\nWe consider representations of the Ariki-Koike al
gebra\, a $q$-deformation of the group algebra of the complex reflection g
roup $C_r \\wr S_n$. The representations of this algebra are naturally ind
exed by multipartitions of $n$. We examine blocks of the Ariki-Koike algeb
ra\, in an attempt to generalise the combinatorial representation theory o
f the Iwahori-Hecke algebra. In particular\, we prove a sufficient conditi
on such that restriction of modules leads to a natural correspondence betw
een the multipartitions of $n$ whose Specht modules belong to a block $B$
and those of $n-\\delta_i(B)$ whose Specht modules belong to the block $B'
$\, obtained from $B$ applying a Scopes' equivalence.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinéad Lyle (University of East Anglia)
DTSTART:20220721T073000Z
DTEND:20220721T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/37
DESCRIPTION:Title: Rouquier blocks for Ariki-Koike algebras\nby Sinéad Lyle (University
of East Anglia) as part of OIST representation theory seminar\n\n\nAbstra
ct\nThe Rouquier blocks\, also known as the RoCK blocks\, are important bl
ocks of the symmetric groups algebras and the Hecke algebras of type $A$\,
with the partitions labelling the Specht modules that belong to these blo
cks having a particular abacus configuration. We generalise the definition
of Rouquier blocks to the Ariki-Koike algebras\, where the Specht modules
are indexed by multipartitions\, and explore the properties of these bloc
ks.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Meng Tan (National University of Singapore)
DTSTART:20220920T073000Z
DTEND:20220920T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/38
DESCRIPTION:Title: Young’s seminormal basis vectors and their denominators\nby Kai Men
g Tan (National University of Singapore) as part of OIST representation th
eory seminar\n\n\nAbstract\nThe dual Specht module of the symmetric group
algebra over $\\mathbb{Q}$ has two distinguished bases\, namely the standa
rd basis and Young’s seminormal basis. We study how the Young’s semino
rmal basis vectors are expressed in terms of the standard basis\, as well
as the denominators of the coefficients in these expressions. We obtain cl
osed formula for some Young’s seminormal basis vectors\, as well as part
ial results for the denominators in general. This is a joint work with Min
g Fang (Chinese Academy of Sciences) and Kay Jin Lim (Nanyang Technologica
l University).\n
LOCATION:https://researchseminars.org/talk/OISTRTS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giada Volpato (University of Florence)
DTSTART:20221115T073000Z
DTEND:20221115T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/39
DESCRIPTION:Title: On the restriction of a character of \\(\\mathfrak{S}_n\\) to a Sylow \\(
p\\)-subgroup\nby Giada Volpato (University of Florence) as part of OI
ST representation theory seminar\n\n\nAbstract\nThe relevance of the McKay
Conjecture in the representation theory of finite groups has led to inves
tigate how irreducible characters decompose when restricted to Sylow \\(p\
\)-subgroups. In this talk we will focus on the symmetric groups. Since th
e linear constituents of the restriction to a Sylow \\(p\\)-subgroup has b
een studied a lot by E. Giannelli and S. Law\, we will concentrate on cons
tituents of higher degree. In particular\, we will describe the set of the
irreducible characters which allow a constituent of a fixed degree\, sepa
rating the cases of \\(p\\) being odd and \\(p=2\\). This is a joint work
with Eugenio Giannelli.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haralampos Geranios (University of York)
DTSTART:20221011T073000Z
DTEND:20221011T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/40
DESCRIPTION:Title: On self-extensions of irreducible modules for symmetric groups\nby Ha
ralampos Geranios (University of York) as part of OIST representation theo
ry seminar\n\n\nAbstract\nWe work in the context of the modular representa
tion theory of the symmetric groups. A long-standing conjecture\, from the
late 80s\, suggests that there are no (non-trivial) self-extensions of ir
reducible modules over fields of odd characteristic. In this talk we will
highlight several new positive results on this conjecture. This is a joint
work with S. Kleshchev and L. Morotti.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chun-Ju Lai (Academia Sinica)
DTSTART:20221025T003000Z
DTEND:20221025T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/41
DESCRIPTION:Title: Quasi-hereditary covers\, Hecke subalgebras and quantum wreath product\nby Chun-Ju Lai (Academia Sinica) as part of OIST representation theory
seminar\n\n\nAbstract\nThe Hecke algebra is in general not quasi-hereditar
y\, meaning that its module category is not a highest weight category\; wh
ile it admits a quasi-hereditary cover via category O for certain rational
Cherednik algebras due to Ginzburg-Guay-Opdam-Rouquier. It was proved in
type A that this category O can be realized using q-Schur algebra\, but th
is realization problem remains open beyond types A/B/C. An essential 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 about a new
theory allowing us to take the ``quantum wreath product'' of an algebra b
y a Hecke algebra. Our wreath product produces the Ariki-Koike algebra as
a special case\, as well as new ``Hecke algebras'' of wreath products betw
een symmetric groups. We expect them to play a role in answering the reali
zation problem for complex reflection groups. This is a joint work with Da
n Nakano and Ziqing Xiang.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loïc Poulain d'Andecy (University of Reims Champagne-Ardenne)
DTSTART:20221101T073000Z
DTEND:20221101T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/42
DESCRIPTION:Title: KLR-type presentation of affine Hecke algebras of type B\nby Loïc Po
ulain d'Andecy (University of Reims Champagne-Ardenne) as part of OIST rep
resentation theory seminar\n\n\nAbstract\nKLR algebras of type A have been
a revolution in the representation theory of Hecke algebras of a type A f
lavour\, thanks to the the Brundan-Kleshchev-Rouquier isomorphism relating
them explicitly to the affine Hecke algebra of type A. KLR algebras of ot
her types exist but are not related to affine Hecke algebras of other type
s. In this talk I will present a generalisation of the KLR presentation fo
r the affine Hecke algebra of type B and I will discuss some applications.
This talk is based on joint works with Salim Rostam and Ruari Walker.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolle González (UC Berkeley)
DTSTART:20221129T003000Z
DTEND:20221129T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/44
DESCRIPTION:Title: Higher Rank Rational (q\,t)-Catalan Polynomials and a Finite Shuffle Theo
rem\nby Nicolle González (UC Berkeley) as part of OIST representation
theory seminar\n\n\nAbstract\nThe classical shuffle theorem states that t
he Frobenius character of the space of diagonal harmonics is given by a ce
rtain combinatorial sum indexed by parking functions on square lattice pat
hs. The rational shuffle theorem\, conjectured by Gorsky-Negut and proven
by Mellit\, states that the geometric action on symmetric functions (descr
ibed by Schiffmmann-Vasserot) of certain elliptic Hall algebra elements $P
_{(m\,n)}$ yield the bigraded Frobenius character of a certain Sn represen
tation. This character is known as the Hikita polynomial. In this talk I w
ill introduce the higher rank rational (q\,t)-Catalan polynomials and show
these are equal to finite truncations of the Hikita polynomial. By genera
lizing results of Gorsky-Mazin-Vazirani and constructing an explicit bijec
tion between rational semistandard parking functions and affine compositio
ns\, I will derive a finite analog of the rational shuffle theorem in the
context of spherical double affine Hecke algebras.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Turek (Royal Holloway\, University of London)
DTSTART:20230124T073000Z
DTEND:20230124T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/45
DESCRIPTION:Title: On stable modular plethysms of the natural module of $\\textrm{SL}_2(\\ma
thbb{F}_p)$ in characteristic $p$\nby Pavel Turek (Royal Holloway\, Un
iversity of London) as part of OIST representation theory seminar\n\n\nAbs
tract\nTo study polynomial representations of general and special linear g
roups in characteristic zero one can use formal characters to work with sy
mmetric functions instead. The situation gets more complicated when workin
g over a field $k$ of non-zero characteristic. However\, by describing the
representation ring of $k\\textrm{SL}_2(\\mathbb{F}_p)$ modulo projective
modules appropriately we are able to use symmetric functions with a suita
ble specialisation to study a family of polynomial representations of $k\\
textrm{SL}_2(\\mathbb{F}_p)$ in the stable category. In this talk we descr
ibe how this introduction of symmetric functions works and how to compute
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 thes
e modular plethysms are projective and which are `close' to being projecti
ve. If time permits\, we describe how to generalise these classifications
using a rule for exchanging Schur functors and tensoring with an endotrivi
al module.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rowena Paget (University of Kent)
DTSTART:20230110T073000Z
DTEND:20230110T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/46
DESCRIPTION:Title: Plethysm and the Partition Algebra\nby Rowena Paget (University of Ke
nt) as part of OIST representation theory seminar\n\n\nAbstract\nThe symme
tric group $S_{mn}$ acts naturally on the collection of set partitions of
a set of size mn into n sets each of size m. The irreducible constituents
of the associated ordinary character are largely unknown\; in particular\
, they are the subject of the longstanding Foulkes Conjecture. There are e
quivalent reformulations using polynomial representations of infinite gene
ral linear groups or using plethysms of symmetric functions. I will revi
ew plethysm from these three perspectives before presenting a new approach
to studying plethysm: using the Schur-Weyl duality between the symmetric
group and the partition algebra. This method allows us to study stability
properties of certain plethysm coefficients. This is joint work with Chris
Bowman. If time permits\, I will also discuss some new results with Chris
Bowman and Mark Wildon.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soichi Okada (Nagoya University)
DTSTART:20230314T013000Z
DTEND:20230314T023000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/47
DESCRIPTION:Title: Intermediate symplectic characters and enumeration of shifted plane parti
tions\nby Soichi Okada (Nagoya University) as part of OIST representat
ion theory seminar\n\n\nAbstract\nThe intermediate symplectic characters\,
introduced by R. Proctor\, interpolate between Schur functions and symple
ctic characters. They arise as the characters of indecomposable representa
tions of the intermediate symplectic group\, which is defined as the group
of linear transformations fixing a (not necessarily non-degenerate) skew-
symmetric bilinear form. In this talk\, we present Jacobi-Trudi-type deter
minant formulas and bialternant formulas for intermediate symplectic chara
cters. By using the bialternant formula\, we can derive factorization form
ulas for sums of intermediate symplectic characters\, which allow us to gi
ve a proof and variations of Hopkins' conjecture on the number of shifted
plane partitions of double-staircase shape with bounded entries.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Williams (Lancaster University)
DTSTART:20230829T073000Z
DTEND:20230829T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/48
DESCRIPTION:Title: Higher-dimensional cluster combinatorics and representation theory\nb
y Nicholas Williams (Lancaster University) as part of OIST representation
theory seminar\n\n\nAbstract\nPerhaps the most prominent example of a clus
ter algebra is the type A cluster algebra\, where clusters are in bijectio
n with triangulations of a convex polygon\, as observed by Fomin and Zelev
insky. A categorical version of this relationship is that triangulations o
f a convex polygon are in bijection with cluster-tilting objects in the cl
uster category of the path algebra of the type A quiver. In each case\, mu
tating the cluster or cluster-tilting object corresponds to flipping a dia
gonal inside a quadrilateral. It is natural to wonder whether any similar
relationship exists for triangulations of higher-dimensional polytopes. In
deed\, in a beautiful paper Oppermann and Thomas show that triangulations
of even-dimensional cyclic polytopes are in bijection with cluster-tilting
objects in the cluster categories of the higher Auslander algebras of typ
e A\, which were introduced by Iyama. Mutating the cluster-tilting objects
corresponds to bistellar flips of triangulations\, which are the higher-d
imensional analogues of flipping a diagonal inside a quadrilateral. In thi
s talk\, we will outline the work of Oppermann and Thomas\, and explain th
e odd-dimensional half of the picture too. Indeed\, the speaker has shown
that triangulations of odd-dimensional cyclic polytopes are in bijection w
ith equivalence classes of maximal green sequences for the higher Auslande
r algebras of type A\, where maximal green sequences are maximal chains of
cluster-tilting objects.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Sambale (Leibniz Universität Hannover)
DTSTART:20231010T073000Z
DTEND:20231010T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/49
DESCRIPTION:Title: Groups of p-central type\nby Benjamin Sambale (Leibniz Universität H
annover) as part of OIST representation theory seminar\n\n\nAbstract\nA fi
nite group \\(G\\) with center \\(Z\\) is of central type if there exists an irreducible
character \\(\\chi\\) such that \\(\\chi(1)^2=|G:Z|\\). Howlett–Isaacs have shown tha
t such groups are solvable. A corresponding theorem for \\(p\\)-Brauer characters was proved by Navarro–Späth–Tie
p 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://researchseminars.org/talk/OISTRTS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Norton (University of Kent)
DTSTART:20231024T073000Z
DTEND:20231024T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/50
DESCRIPTION:Title: Decomposition numbers for unipotent blocks with small $sl_2$-weight in fi
nite classical groups\nby Emily Norton (University of Kent) as part of
OIST representation theory seminar\n\n\nAbstract\nThere are many familiar
module categories admitting a categorical action of a Lie algebra. The co
mbinatorial shadow of such an action often yields answers to module-theore
tic questions\, for instance via crystals. In proving a conjecture of Gerb
er\, Hiss\, and Jacon\, it was shown by Dudas\, Varagnolo\, and Vasserot t
hat the category of unipotent representations of a finite classical group
has such a categorical action. In this talk I will explain how we can use
the categorical action to deduce closed formulas for certain families of d
ecomposition numbers of these groups. This is joint work in progress with
Olivier Dudas.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ulrich Thiel (University of Kaiserslautern-Landau)
DTSTART:20231107T073000Z
DTEND:20231107T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/51
DESCRIPTION:Title: The rank one property for free Frobenius extensions\nby Ulrich Thiel
(University of Kaiserslautern-Landau) as part of OIST representation theor
y seminar\n\n\nAbstract\nThe Cartan matrix of a finite-dimensional algebra
is the matrix of multiplicities of simple modules in indecomposable proje
ctive modules. This is crucial information about the representation theory
of the algebra. In my talk I will present a general setting including sev
eral important examples from Lie theory\, such as restricted quantized env
eloping algebras at roots of unity\, in which we could prove that the Cart
an matrix has the remarkable property of being blockwise of rank one. This
is joint work with Gwyn Bellamy.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Yong (University of Illinois at Urbana-Champaign)
DTSTART:20231128T003000Z
DTEND:20231128T013000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/52
DESCRIPTION:Title: Newell-Littlewood numbers\nby Alexander Yong (University of Illinois
at Urbana-Champaign) as part of OIST representation theory seminar\n\n\nAb
stract\nThe Newell-Littlewood numbers are defined in terms of the Littlewo
od-Richardson coefficients from algebraic combinatorics. Both appear in re
presentation theory as tensor product multiplicities for a classical Lie g
roup. This talk concerns the question: Which multiplicities are nonzero? I
n 1998\, Klyachko established common linear inequalities defining both the
eigencone for sums of Hermitian matrices and the saturated Littlewood-Ric
hardson cone. We prove some analogues of Klyachko's nonvanishing results f
or the Newell-Littlewood numbers. This is joint work with Shiliang Gao\, G
idon Orelowitz\, and Nicolas Ressayre. The presentation is based on arXiv:
2005.09012\, arXiv:2009.09904\, and arXiv:2107.03152.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaveh Mousavand (OIST)
DTSTART:20231212T073000Z
DTEND:20231212T083000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/53
DESCRIPTION:Title: Some applications of bricks in classical and modern problems in represent
ation theory\nby Kaveh Mousavand (OIST) as part of OIST representation
theory seminar\n\n\nAbstract\nBricks (also known as Schur representations
) form a special subfamily of indecomposable modules\, and they are used i
n the algebraic and geometric study of representation theory of algebras.
We start by looking at some classical results on bricks\, including a char
acterization of locally representation-directed algebras (due to Dräxler)
. Then\, we consider some new directions of research in which bricks have
played crucial roles. More specifically\, we briefly recall an elegant cor
respondence between bricks and indecomposable $\\tau$-rigid-modules (due t
o Demonet-Iyama-Jasso)\, which has many applications in $\\tau$-tilting th
eory. We use the notion of $\\tau$-rigidity to give a new characterization
of locally representation-directed algebras\, and to further generalize t
his family. If time permits\, we also report on some new results on an ope
n conjecture (so-called the 2nd brick-Brauer-Thrall conjecture) which I po
sed in 2019. Part of this talk is based on my recent joint work with Charl
es Paquette.\n
LOCATION:https://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:20260422T225754Z
UID:OISTRTS/54
DESCRIPTION:Title: From Klyachko models to perfect models\nby Eric Marberg (The Hong Kon
g University of Science and Technology (HKUST)) as part of OIST representa
tion theory seminar\n\n\nAbstract\nIn this talk a "model" of a finite grou
p or semisimple algebra means a representation containing a unique irreduc
ible subrepresentation from each isomorphism class. In the 1980s Klyachko
identified an elegant model for the general linear group over a finite fie
ld with $q$ elements. There is an informal sense in which taking the $q \\
to 1$ limit of Klyachko's construction gives a model for the symmetric gro
up\, which can be extended to its Iwahori-Hecke algebra. The resulting Hec
ke algebra representation is a special case of a "perfect model"\, which i
s a more flexible construction that can be considered for any finite Coxet
er group. In this talk\, I will classify exactly which Coxeter groups have
perfect models\, and discuss some notable features of this classification
. For example\, each perfect model gives rise to a pair of related W-graph
s\, which are dual in types B and D but not in type A. Various interesting
questions about these W-graphs remain open. This is joint work with Yifen
g Zhang.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Travis Scrimshaw (Hokkaido University)
DTSTART:20240119T050000Z
DTEND:20240119T060000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/55
DESCRIPTION:Title: An Overview of Kirillov-Reshtikhin Modules and Crystals\nby Travis Sc
rimshaw (Hokkaido University) as part of OIST representation theory semina
r\n\n\nAbstract\nKirillov-Reshetikhin (KR) modules are an important class
of finite dimensional representations associated to an affine Lie algebra
and the associated Yangian and quantum group. KR modules are known to appe
ar in many integrable systems and govern the dynamics. In this talk\, we w
ill give an overview of the role KR modules play in the category of finite
dimensional representations\, R-matrices and the fusion construction\, th
eir (conjectural) crystal bases\, and how they relate to Demazure modules.
In particular\, we will focus on how to construct their crystal bases com
binatorially and the different types of character theories. As time permit
s\, we will discuss some of the relations with (quantum) integrable system
s.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peigen Cao (Nagoya University)
DTSTART:20240131T043000Z
DTEND:20240131T053000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/56
DESCRIPTION:Title: Bongartz co-completions in cluster algebras and its applications\nby
Peigen Cao (Nagoya University) as part of OIST representation theory semin
ar\n\n\nAbstract\nA cluster algebra is a Z-subalgebra of a rational functi
on field generated by a special set of generators called cluster variables
\, which are grouped into overlapping subsets of fixed size\, called clust
ers. One can travel from one cluster to the others by a recursive process
called mutation. In this talk I will introduce Bongartz co-completions in
cluster algebras and give its applications to Fomin-Zelevinsky’s conject
ures on denominator vectors and exchange graphs of cluster algebras.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuta Kimura (Osaka Metropolitan University)
DTSTART:20240228T043000Z
DTEND:20240228T053000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/57
DESCRIPTION:Title: Classifying torsion classes of Noetherian algebras\nby Yuta Kimura (O
saka Metropolitan University) as part of OIST representation theory semina
r\n\n\nAbstract\nLet R be a commutative Noetherian ring and A a Noetherian
R-algebra. In this talk\, we study classification of torsion classes\, to
rsion free classes and Serre subcategories of modA. In the case where A=R\
, such subcategories were classified by Gabriel\, Takahashi and Stanley-Wa
ng by using prime ideals of R. If R is a field\, then A is a finite dimens
ional algebra\, and there are many studies of such subcategories relating
with tilting theory. For a Noetherian algebra case\, localization of A at
a prime ideal of R plays an important role. We see that classification can
be reduced to finite dimensional algebras. If A is commutative\, our resu
lts cover cases of commutative rings. This is joint work with Osamu Iyama.
\n
LOCATION:https://researchseminars.org/talk/OISTRTS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eoghan McDowell (OIST)
DTSTART:20240416T060000Z
DTEND:20240416T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/58
DESCRIPTION:Title: Spin representations of the symmetric group which reduce modulo 2 to Spec
ht modules\nby Eoghan McDowell (OIST) as part of OIST representation t
heory seminar\n\n\nAbstract\nWhen do two ordinary irreducible representati
ons of a group have the same p-modular reduction? In this talk I will addr
ess this question for the double cover of the symmetric group\, and more g
enerally give a necessary and sufficient condition for a spin representati
on of the symmetric group to reduce modulo 2 to a multiple of a Specht mod
ule (in the sense of Brauer characters or in the Grothendieck group). I wi
ll explain some of the techniques used in the proof\, including describing
a function which swaps adjacent runners in an abacus display for the labe
lling partition of a character. This is joint work with Matthew Fayers.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kay Jin Lim (Nanyang Technological University)
DTSTART:20241001T060000Z
DTEND:20241001T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/59
DESCRIPTION:Title: Integral Basic Algebras\nby Kay Jin Lim (Nanyang Technological Univer
sity) as part of OIST representation theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OISTRTS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kai Meng Tan (National University of Singapore)
DTSTART:20241015T060000Z
DTEND:20241015T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/60
DESCRIPTION:Title: Cores and core blocks of Ariki-Koike algebras\nby Kai Meng Tan (Natio
nal University of Singapore) as part of OIST representation theory seminar
\n\n\nAbstract\nThis talk will consist of two parts. In the first part\, w
e will see how certain results (such as the Nakayama 'Conjecture') for the
symmetric groups and Iwahori-Hecke algebras of type A can be generalised
to Ariki-Koike algebras using the map from the set of multipartitions to t
hat of (single) partitions first defined by Uglov. In the second part\, we
look at Fayers's core blocks\, and see how these blocks may be classified
using the notation of moving vectors first introduced by Yanbo Li and Xia
ngyu Qi. If time allows\, we will discuss Scopes equivalences between thes
e blocks arising as a consequence of this classification.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (OIST)
DTSTART:20240917T060000Z
DTEND:20240917T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/61
DESCRIPTION:Title: Application of (K-theoretic) Peterson isomorphism\nby Duc-Khanh Nguye
n (OIST) as part of OIST representation theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OISTRTS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rongwei Yang (University at Albany\, SUNY)
DTSTART:20241029T060000Z
DTEND:20241029T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/62
DESCRIPTION:Title: Linear algebra in several variables\nby Rongwei Yang (University at A
lbany\, SUNY) as part of OIST representation theory seminar\n\n\nAbstract\
nMany mathematical and scientific problems concern systems of linear opera
tors $(A_1\, ...\, A_n)$. Spectral theory is expected to provide a mechani
sm for studying their properties\, just like the case for an individual op
erator. However\, defining a spectrum for non-commuting operator systems h
as been a difficult task. The challenge stems from an inherent problem in
finite dimension: is there an analogue of eigenvalues in several variables
? Or equivalently\, is there a suitable notion of joint characteristic pol
ynomial for multiple matrices $A_1\, ...\, A_n$? A positive answer to this
question seems to have emerged in recent years.\n\nDefinition. Giv
en square matrices $A_1\, ...\, A_n$ of equal size\, their characteristic
polynomial is defined as \n\\[Q_A(z):=\\det(z_0I+z_1A_1+\\cdots+z_nA_n)\,
z=(z_0\, ...\, z_n)\\in \\mathbb{C}^{n+1}.\\] Hence\, a multivariable anal
ogue of the set of eigenvalues is the eigensurface (or eigenvari
ety) \n $Z(Q_A):=\\{z\\in \\mathbb{C}^{n+1}\\mid Q_A(z)=0\\}$. This ta
lk will review some applications of this idea to problems involving projec
tion matrices and finite dimensional complex algebras. The talk is self-co
ntained and friendly to graduate students.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daisuke Sagaki (University of Tsukuba)
DTSTART:20241112T060000Z
DTEND:20241112T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/63
DESCRIPTION:Title: Toward a Pieri rule for double quantum Grothendieck polynomials\nby D
aisuke Sagaki (University of Tsukuba) as part of OIST representation theor
y seminar\n\n\nAbstract\nIn a joint work with Satoshi Naito (arXiv:2211.01
578)\, we proved a Pieri rule (conjectured by Lenart and Maeno) for quantu
m Grothendieck polynomials\, which describes the product of the quantum Gr
othendieck polynomial associated to a cyclic permutation and an arbitrary
quantum Grothendieck polynomial as a \\(\\mathbb{Z}[Q_1\,Q_2\,\\dots]\\)-l
inear combination of quantum Grothendieck polynomials. Recently\, in a joi
nt work with Satoshi Naito and Duc-Khanh Nguyen\, we are trying to extend
this result to the case of double quantum Grothendieck polynomials. In thi
s talk\, I'd like to report on the progress of the joint work.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Ocal (OIST)
DTSTART:20241203T060000Z
DTEND:20241203T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/64
DESCRIPTION:Title: Deformations of Frobenius algebras and noncommutative 2d topological quan
tum field theories\nby Pablo Ocal (OIST) as part of OIST representatio
n theory seminar\n\n\nAbstract\nIn this talk I will present an attempt to
define noncommutative 2d topological quantum field theories using deformat
ions of Frobenius algebras. First\, we will overview the importance and us
es of 2d topological quantum field theories\, as well as their equivalence
to commutative Frobenius algebras. Then\, we will consider the deformatio
ns given by cotwisted tensor products\, characterize when these are Froben
ius algebras\, and explain their deficiencies for our goal. Afterwards\, I
will introduce the notion of warped tensor products of Frobenius algebras
and characterize when these are Frobenius algebras. This notion enables u
s to construct a family of bifunctors that could potentially yield nonsymm
etric monoidal structures on the category of Frobenius algebras\, which wo
uld 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://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:20260422T225754Z
UID:OISTRTS/65
DESCRIPTION:Title: On the tau-tilting Hochschild (co)homology of an algebra\nby Andrea S
olotar (University of Buenos Aires and Guangdong Technion-Israel Institute
of Technology) as part of OIST representation theory seminar\n\n\nAbstrac
t\nIn this talk I will introduce the tau-tilting Hochschild cohomology 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 the n-th
tau-tilting Hochschild cohomology for all n. The result is expressed as an
alternating sum of the dimensions of classical Hochschild cohomology in l
ower degrees\, plus an alternating sum of the dimensions of vector spaces
taking into account the Ext-algebra of A as well as the Peirce decompositi
on of the bimodule X. I will also formulate a tau-tilting analogue of a qu
estion by Happel and of Han’s conjecture. This is a joint work with Clau
de Cibils\, Marcelo Lanzilotta and Eduardo Marcos.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Futorny (Southern University of Science and Technology)
DTSTART:20250403T050000Z
DTEND:20250403T060000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/66
DESCRIPTION:Title: Smooth representations of Affine Lie algebras\nby Vyacheslav Futorny
(Southern University of Science and Technology) as part of OIST representa
tion theory seminar\n\n\nAbstract\nWe will discuss twisting localization f
unctor on the category of smooth representations of Affine Lie algebras an
d Gelfand-Tsetlin realizations.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emerson Escolar (Kobe University)
DTSTART:20250422T060000Z
DTEND:20250422T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/67
DESCRIPTION:Title: Representation Theory and (Barcoding) Invariants for Persistence\nby
Emerson Escolar (Kobe University) as part of OIST representation theory se
minar\n\n\nAbstract\nPersistent homology is one of the main tools of topol
ogical data analysis\, which has seen rapid growth recently. In the first
part of this talk\, I discuss some of the ways representation theory is be
ing used for persistent homology\, focusing on "invariants". In particular
\, the persistence barcode\, which can be obtained from an indecomposable
decomposition of a persistence module into intervals\, plays a central rol
e. For multi-parameter persistent homology\, where persistence modules are
no longer always interval-decomposable\, many alternative invariants have
been proposed. Naturally\, identifying the relationships among invariants
\, or ordering them by their discriminating power\, is a fundamental quest
ion. The second part of this talk\, based on arXiv:2412.04995\, addresses
this. I discuss our formalization of the notion of "barcoding invariants"\
, which generalizes the persistence barcode\, and results concerning the c
omparison of their discriminating powers.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Brundan (University of Oregon)
DTSTART:20250311T060000Z
DTEND:20250311T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/68
DESCRIPTION:Title: Quasi-split 2-iquantum groups\nby Jonathan Brundan (University of Ore
gon) as part of OIST representation theory seminar\n\n\nAbstract\nIn 2008\
, Khovanov\, Lauda and Rouquier introduced a family of graded 2-categories
which could be called "2-quantum groups" because they categorify quantum
groups. I will explain the definition of a new family of graded 2-categori
es which play the same role for quasi-split iquantum groups. This is joint
work with Weiqiang Wang and Ben Webster.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iryna Kashuba (Southern University of Science and Technology)
DTSTART:20250403T063000Z
DTEND:20250403T073000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/69
DESCRIPTION:Title: One-sided representations of Jordan algebras\nby Iryna Kashuba (South
ern University of Science and Technology) as part of OIST representation t
heory seminar\n\n\nAbstract\nBy Drozd's celebrated Tame-Wild Theorem\, any
finite-dimensional associative algebra over an algebraically closed field
is either of tame or of wild representation type. We define a representat
ion type of Jordan algebra J with respect to its one-sided representations
as a representation type of its universal associative envelope S(J). We g
ive a criterion for finiteness and tameness of one-sided representation of
Jordan algebras with zero radical square. This is a joint result with Vik
tor Bekkert and Vera Serganova.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Opper (Charles University\, Prague)
DTSTART:20250513T060000Z
DTEND:20250513T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/70
DESCRIPTION:Title: Autoequivalences of triangulated categories via Hochschild cohomology
\nby Sebastian Opper (Charles University\, Prague) as part of OIST represe
ntation theory seminar\n\n\nAbstract\nI will talk about a general tool whi
ch allows one to study symmetries of (enhanced) triangulated categories in
the form of their derived Picard groups. In general\, these groups are ra
ther elusive to computations which require a rather good understanding of
the whole category at hand. A result of Keller shows that the Lie algebra
of the derived Picard group of an algebra can be identified with its Hochs
child cohomology equipped with the Gerstenhaber Lie bracket. Mimicking the
classical relationship between Lie groups and Lie algebras\, I will expla
in how to "integrate'' elements in the Hochschild cohomology of a dg categ
ory over fields of characteristic zero to elements in the derived Picard g
roup via a generalized exponential map. Afterwards we discuss properties o
f this exponential and a few applications. This includes necessary conditi
ons for the uniqueness of enhancement of triangulated functors and uniquen
ess of Fourier-Mukai kernels. Other applications concern derived Picard gr
oups of categories arising in algebra and geometry such as derived categor
ies of graded gentle algebras and their corresponding partially wrapped Fu
kaya categories.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Berta Hudak (National Center for Theoretical Sciences\, Taipei)
DTSTART:20250603T060000Z
DTEND:20250603T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/71
DESCRIPTION:Title: Representation theory of the Hu algebras\nby Berta Hudak (National Ce
nter for Theoretical Sciences\, Taipei) as part of OIST representation the
ory seminar\n\n\nAbstract\nHu algebras were first defined by Hu when he st
ated a Morita equivalence between Hecke algebras of type D and of type A.
Motivated by his work\, Lai-Nakano-Xiang introduced the notion of quantum
wreath products and gave a definition of Hu algebras in this sense. In thi
s talk\, we will first introduce Hu algebras as quantum wreath products\,
then show that these algebras are cellular by constructing a cellular basi
s. Finally\, we present the necessary conditions for two modules to belong
to the same block.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Ono (University of Virginia)
DTSTART:20250729T060000Z
DTEND:20250729T070000Z
DTSTAMP:20260422T225754Z
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 presents
“partition theoretic” analogs of the classical work of Matiyasevich th
at resolved Hilbert’s Tenth Problem in the negative. The Diophantine equ
ations we consider involve equations of MacMahon’s partition functions a
nd their natural generalizations. Here we explicitly construct infinitely
many Diophantine equations in partition functions whose solutions are prec
isely the prime numbers. To this end\, we produce explicit additive bases
of all graded weights of quasimodular forms\, which is of independent inte
rest with many further applications. This is joint work with Will Craig an
d Jan-Willem van Ittersum.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mee Seong Im (Johns Hopkins University)
DTSTART:20250804T070000Z
DTEND:20250804T080000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/73
DESCRIPTION:Title: Entropy\, cocycles\, algebraic K-theory and diagrammatics\nby Mee Seo
ng Im (Johns Hopkins University) as part of OIST representation theory sem
inar\n\n\nAbstract\nI will discuss how cocycles appear in a graphical netw
ork. Furthermore\, the\nShannon entropy of a finite probability distributi
on has a natural interpretation in terms of\ndiagrammatics. I will explain
the diagrammatics and their connections to infinitesimal\ndilogarithms an
d entropy. If I have time\, I will talk about how algebraic K-theory appea
rs in\ndiagrammatics.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Khovanov (Johns Hopkins University)
DTSTART:20250805T040000Z
DTEND:20250805T050000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/74
DESCRIPTION:Title: The Delannoy category and its diagrammatics\nby Mikhail Khovanov (Joh
ns Hopkins University) as part of OIST representation theory seminar\n\n\n
Abstract\nN.Harman and A.Snowden discovered a semisimple monoidal pivotal
category\, called the Delannoy category\, where composition of morphisms i
s given by computing the compact Euler characteristic of subspaces of the
Euclidean space described by inequalities on the coordinates. In the talk
we will explain a diagrammatic description of their category\, following a
joint work with N.Snyder. The number of simple objects in the Delannoy ca
tegory grows exponentially\, but a suitable monoidal subcategory has the G
rothendieck ring isomorphic to the ring of integer-valued one-variable pol
ynomials. This subcategory can be viewed as a categorification of the latt
er ring.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Lobb (Durham University)
DTSTART:20250804T053000Z
DTEND:20250804T063000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/75
DESCRIPTION:Title: Peg problems and peg progress\nby Andrew Lobb (Durham University) 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 Toeplitz Squa
re Peg Problem (which remains unsolved) conjectures that there exist four
points on this curve at the vertices of a square. Over the past five years
there has been much progress made on relatives of the TSPP\, and this pro
gress began partly at OIST during the early months of the pandemic. I shal
l 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 shall be
very accessible\, with no specialized knowledge assumed.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (OIST)
DTSTART:20251209T060000Z
DTEND:20251209T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/76
DESCRIPTION:Title: Branching rule on winding subalgebras of affine Kac-Moody algebras\nb
y Duc-Khanh Nguyen (OIST) as part of OIST representation theory seminar\n\
n\nAbstract\nIn this work\, by using the Lakshmibai-Seshadri paths\, we gi
ve the branching rule for representations of affine Kac-Moody algebras to
their winding subalgebras. As a corollary\, we can describe branching mult
iplicities in the language of paths. An analog of Steinberg’s formula fo
r branching multiplicities is also given.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Turek (OIST)
DTSTART:20260120T060000Z
DTEND:20260120T070000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/77
DESCRIPTION:Title: Balanced columns of decomposition matrices\nby Pavel Turek (OIST) as
part of OIST representation theory seminar\n\n\nAbstract\nThe decompositio
n matrices describe how the irreducible modules of symmetric groups in cha
racteristic zero decompose in prime characteristic. Understanding these ma
trices\, and in particular\, finding a combinatorial description of their
entries\, is a central open problem in the representation theory of symmet
ric groups. The main result of the talk is a description of columns of the
se matrices indexed by ‘d-balanced’ partitions for d=2. It is a conseq
uence of a more general result which describes these columns for any d>1 u
nder some additional assumptions. As a further result\, we show that there
are many 2-balanced partitions. The key players in the proof of the prese
nted results are Foulkes modules\, which are used to construct certain pro
jective modules\, and the Jantzen-Schaper formula\, which allows us to tra
nsfer the algebraic problem into a combinatorial system of equalities\, wh
ich can then be solved using a new algorithm defined on Young diagrams. Th
is is joint work with Bim Gustavsson\, David Hemmer and Stacey Law.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bim Gustavsson (University of Birmingham)
DTSTART:20260609T063000Z
DTEND:20260609T073000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/78
DESCRIPTION:by Bim Gustavsson (University of Birmingham) as part of OIST r
epresentation theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OISTRTS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Muth (Duquesne University)
DTSTART:20260728T063000Z
DTEND:20260728T073000Z
DTSTAMP:20260422T225754Z
UID:OISTRTS/79
DESCRIPTION:by Rob Muth (Duquesne University) as part of OIST representati
on theory seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OISTRTS/79/
END:VEVENT
END:VCALENDAR