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SUMMARY:Anton Nazarov (Saint Petersburg State University)
DTSTART;VALUE=DATE-TIME:20230113T090000Z
DTEND;VALUE=DATE-TIME:20230113T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/1
DESCRIPTION:Title: Skew Howe duality\, limit shapes of Young diagrams and universal fluctua
tions\nby Anton Nazarov (Saint Petersburg State University) as part of
BIMSA Integrable Systems Seminar\n\n\nAbstract\nSchur-Weyl\, Howe and ske
w Howe dualities in representation theory of groups lead to multiplicity-f
ree decompositions of certain spaces into irreducible representations and
can be used to introduce probability measures on Young diagrams that param
eterize irreducible representations. It is interesting to study the behavi
or of such measures in the limit\, when groups become infinite or infinite
-dimensional. Schur-Weyl duality and GL(n)-GL(k) Howe duality are related
to classical works of Anatoly Vershik and Sergey Kerov\, as well as Logand
-Schepp\, Cohn-Larsen-Propp and Baik-Deift-Johannson. Skew GL(n)-GL(k) How
e duality was considered by Gravner\, Tracy and Widom\, who were intereste
d in the local fluctuations of the diagrams\, the limit shapes were studie
d Sniady and Panova. They demonstrated that results by Romik and Pittel on
limit shapes of rectangular Young tableaux are applicable in this case.\n
We consider skew Howe dualities for the actions of classical Lie group pai
rs: GL(n)-GL(k)\, Sp(2n)-Sp(2k)\, SO(2n)-O(2k) on the exterior algebras. W
e describe explicitly the limit shapes for probability measures defined by
the ratios of dimensions and demonstrate that they are essentially the sa
me for all classical Lie groups. Using orthogonal polynomials we prove cen
tral limit theorem for global fluctuations around these limit shapes. Usin
g free-fermionic representation we study local fluctuations for more gener
al measures given by ratios of representation characters for skew GL(n)-GL
(k) Howe duality. These fluctuations are described by Tracy-Widom distribu
tion in the generic case and in the corner by a certain discrete distribut
ion\, first obtained in papers by Gravner\, Tracy and Widom. Study of loca
l fluctuations for other classical series remains an open problem\, but we
present numerical evidence that these distributions are universal.\n\nBas
ed on joint works with Dan Betea\, Pavel Nikitin\, Olga Postnova\,\nDaniil
Sarafannikov and Travis Scrimshaw. See arXiv:2010.16383\,\n2111.12426\, 2
208.10331\, 2211.13728.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Talalaev (MSU\, YarSU\, ITEP)
DTSTART;VALUE=DATE-TIME:20230120T090000Z
DTEND;VALUE=DATE-TIME:20230120T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/2
DESCRIPTION:Title: The full Toda system\, QR decomposition and geometry of the flag varieti
es\nby Dmitry Talalaev (MSU\, YarSU\, ITEP) as part of BIMSA Integrabl
e Systems Seminar\n\n\nAbstract\nThe full Toda system is a generalization
of an open Toda chain\, which is one of the archetypal examples of integra
ble systems. The open Toda chain illustrates the connection of the theory
of integrable systems with the theory of Lie algebras and Lie groups\, is
a representative of the Adler-Kostant-Symes scheme for constructing and so
lving such systems. Until recently\, only some of the results from this li
st were known for the full Toda system. I will talk about the construction
\, the commutative family\, quantization and solution of the full Toda sys
tem by the QR decomposition method\, as well as about the application of t
his system to the geometry of flag vaireties. The material of my talk is b
ased on several joint works with A. Sorin\, Yu. Chernyakov and G. Sharygin
.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Yakubovich (Saint Petersburg State University)
DTSTART;VALUE=DATE-TIME:20230127T090000Z
DTEND;VALUE=DATE-TIME:20230127T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/3
DESCRIPTION:Title: Random growth of Young diagrams with uniform marginals\nby Yuri Yaku
bovich (Saint Petersburg State University) as part of BIMSA Integrable Sys
tems Seminar\n\n\nAbstract\nMany (random) growth procedures for integer pa
rtitions/Young diagrams has been introduced\nin the literature and intensi
vely studied. The examples include Pitman's `Chinese restaurant'\nconstruc
tion\, Kerov's Plancherel growth and many others. These procedures amount
to\ninsertion of a new box to a Young diagram on each step\, following ce
rtain Markovian procedure.\nHowever\, no such procedure leading to the uni
form measure on partitions of $n$ after $n$\nsteps is known. I will descr
ibe a Markiovian procedure of adding a rectangular block\nto a Young diagr
am with the property that given the growing chain visits some level $n$\,
it\npasses through each partition of $n$ with equal probabilities\, thus l
eading to the uniform\nmeasure on levels. I will explain connections to s
ome classical probabilistic objects.\nAlso I plan to discuss some aspects
of asymptotic behavior of this Markov chain and explain\nwhy the limit sha
pe is formed.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuancheng Xie (Peking University)
DTSTART;VALUE=DATE-TIME:20230203T090000Z
DTEND;VALUE=DATE-TIME:20230203T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/4
DESCRIPTION:Title: On the full Kostant-Toda lattice and the flag varieties\nby Yuanchen
g Xie (Peking University) as part of BIMSA Integrable Systems Seminar\n\n\
nAbstract\nIn 1967\, Japanese physicist Morikazu Toda proposed an integrab
le lattice model to\ndescribe motions of a chain of particles with exponen
tial interactions between nearest\nneighbors. Since then\, Toda lattice an
d its generalizations have become the test models\nfor various techniques
and philosophies in integrable systems and wide connections are\nbuilt wit
h many other branches of mathematics. In this talk\, I will characterize s
ingular\nstructure of solutions of the so-called full Kostant-Toda (f-KT)
lattices defined on simple\nLie algebras in two different ways: through th
e τ-functions and through the Kowalevski-\nPainlevé analysis. Fixing the
spectral parameters which are invariant under the f-KT flows\,\nwe build
a one to one correspondence between solutions of the f-KT lattices and poi
nts in\nthe corresponding flag varieties.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masatoshi Noumi (Rikkyo University\, Tokyo\, Japan)
DTSTART;VALUE=DATE-TIME:20230217T090000Z
DTEND;VALUE=DATE-TIME:20230217T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/5
DESCRIPTION:Title: Elliptic van Diejen difference operators and elliptic hypergeometric int
egrals of Selberg type\nby Masatoshi Noumi (Rikkyo University\, Tokyo\
, Japan) as part of BIMSA Integrable Systems Seminar\n\nInteractive livest
ream: https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE
9SUT09\nPassword hint: BIMSA\n\nAbstract\nIn this talk\, I propose a class
of eigenfunctions for the elliptic van Diejen operators \n(Ruijsenaars op
erators of type BC) which are represented by elliptic hypergeometric \nint
egrals of Selberg type. They are constructed from simple seed eigenfunctio
ns \nby integral transformations\, thanks to gauge symmetries and kernel f
unction identities \nof the van Diejen operators. \nBased on a collaborat
ion with Farrokh Atai (University of Leeds\, UK).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/5/
URL:https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9S
UT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Bobrova (National Research University Higher School of Econo
mics)
DTSTART;VALUE=DATE-TIME:20230224T090000Z
DTEND;VALUE=DATE-TIME:20230224T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/6
DESCRIPTION:Title: Different approaches for constructing non-abelian Painlevé equations\nby Irina Bobrova (National Research University Higher School of Economi
cs) as part of BIMSA Integrable Systems Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9SUT0
9\nPassword hint: BIMSA\n\nAbstract\nThe famous Painlevé equations play a
significant role in modern mathematical physics. The interest in their no
n-commutative extensions was motivated by the needs of modern quantum phys
ics as well as by natural attempts of mathematicians to extend ‘’class
ical’’ structures to the non-commutative case.\n\nIn this talk we will
consider several approaches that are useful for detecting non-commutative
analogs of the Painlevé equations. Namely\, the matrix Painlevé-Kovalev
skaya test\, integrable non-abelian auxiliary autonomous systems\, and inf
inite non-commutative Toda equations. All of these methods allow us to fin
d a finite list of non-abelian candidates for such analogs. To provide the
ir integrability\, one can present an isomonodromic Lax pair.\n\nThis talk
is based on a series of papers joint with Vladimir Sokolov and on arXiv:2
205.05107 joint with Vladimir Retakh\, Vladimir Rubtsov\, and Georgy Shary
gin (publ. in J. Phys. A: Math. Theor.).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/6/
URL:https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9S
UT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Rybnikov (National Research University Higher School of Eco
nomics)
DTSTART;VALUE=DATE-TIME:20230310T090000Z
DTEND;VALUE=DATE-TIME:20230310T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/7
DESCRIPTION:Title: Bethe subalgebras and Kirillov-Reshetikhin crystals\nby Leonid Rybni
kov (National Research University Higher School of Economics) as part of B
IMSA Integrable Systems Seminar\n\nInteractive livestream: https://us02web
.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9SUT09\nPassword hint
: BIMSA\n\nAbstract\nBethe subalgebras form a family of maximal commutativ
e subalgebras of the Yangian of a simple Lie algebra\, parametrized by reg
ular elements of the corresponding adjoint Lie group. We introduce an affi
ne (Kirillov-Reshetikhin) crystal structure on the set of eigenlines for a
Bethe subalgebra in a representation of the Yangian (under certain condit
ions on the representation\, satisfied by all tensor products of Kirillov-
Reshetikhin modules in type A). This helps to describe the monodromy of so
lutions of Bethe ansatz for the corresponding XXX Heisenberg magnet chain.
\n\nThis is a joint project with Inna Mashanova-Golikova and Vasily Krylo
v.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/7/
URL:https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9S
UT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huijun Fan (Peking University)
DTSTART;VALUE=DATE-TIME:20230324T090000Z
DTEND;VALUE=DATE-TIME:20230324T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/8
DESCRIPTION:by Huijun Fan (Peking University) as part of BIMSA Integrable
Systems Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/81546
904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9SUT09\nPassword hint: BIMSA\nAbstrac
t: TBA\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/8/
URL:https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9S
UT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Nikitin (BIMSA)
DTSTART;VALUE=DATE-TIME:20230210T090000Z
DTEND;VALUE=DATE-TIME:20230210T103000Z
DTSTAMP;VALUE=DATE-TIME:20230208T075257Z
UID:BIMSA-ISS/9
DESCRIPTION:Title: Semifinite harmonic functions on Bratteli diagrams\nby Pavel Nikitin
(BIMSA) as part of BIMSA Integrable Systems Seminar\n\nInteractive livest
ream: https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE
9SUT09\nPassword hint: BIMSA\n\nAbstract\nLocally semisimple algebras (LS-
algebras) are inductive limits of semisimple algebras\, and can be fully c
haracterized by their Bratteli diagrams ($\\mathbb{N}$-graded graphs). (Fi
nite) harmonic functions on Bratteli diagrams are a standard tool in the r
epresentation theory of LS-algebras and semifinite harmonic functions are
a natural generalization. We plan to give an overview of the subject\, sta
rting with the classical results for the infinite symmetric group\, follow
ed by the recent results for the infinite symmetric inverse semigroup. Joi
nt work with N.Safonkin\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/9/
URL:https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9S
UT09
END:VEVENT
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