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BEGIN:VEVENT
SUMMARY:Anton Nazarov (Saint Petersburg State University)
DTSTART;VALUE=DATE-TIME:20230113T090000Z
DTEND;VALUE=DATE-TIME:20230113T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
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:20241013T142816Z
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:20241013T142816Z
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:20241013T142816Z
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:20241013T142816Z
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\n\nAbstract\nIn thi
s talk\, I propose a class of eigenfunctions for the elliptic van Diejen o
perators \n(Ruijsenaars operators of type BC) which are represented by ell
iptic hypergeometric \nintegrals of Selberg type. They are constructed fro
m simple seed eigenfunctions \nby integral transformations\, thanks to gau
ge symmetries and kernel function identities \nof the van Diejen operators
. \nBased on a collaboration with Farrokh Atai (University of Leeds\, UK)
.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/5/
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:20241013T142816Z
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\n\nAbstract\nThe famous
Painlevé equations play a significant role in modern mathematical physics
. The interest in their non-commutative extensions was motivated by the ne
eds of modern quantum physics as well as by natural attempts of mathematic
ians to extend ‘’classical’’ structures to the non-commutative cas
e.\n\nIn this talk we will consider several approaches that are useful for
detecting non-commutative analogs of the Painlevé equations. Namely\, th
e matrix Painlevé-Kovalevskaya test\, integrable non-abelian auxiliary au
tonomous systems\, and infinite non-commutative Toda equations. All of the
se methods allow us to find a finite list of non-abelian candidates for su
ch analogs. To provide their integrability\, one can present an isomonodro
mic Lax pair.\n\nThis talk is based on a series of papers joint with Vladi
mir Sokolov and on arXiv:2205.05107 joint with Vladimir Retakh\, Vladimir
Rubtsov\, and Georgy Sharygin (publ. in J. Phys. A: Math. Theor.).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/6/
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:20241013T142816Z
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\n\nAbstract\nBethe subalgebras form a fa
mily of maximal commutative subalgebras of the Yangian of a simple Lie alg
ebra\, parametrized by regular elements of the corresponding adjoint Lie g
roup. We introduce an affine (Kirillov-Reshetikhin) crystal structure on t
he set of eigenlines for a Bethe subalgebra in a representation of the Yan
gian (under certain conditions on the representation\, satisfied by all te
nsor products of Kirillov-Reshetikhin modules in type A). This helps to de
scribe the monodromy of solutions of Bethe ansatz for the corresponding XX
X Heisenberg magnet chain. \n\nThis is a joint project with Inna Mashanova
-Golikova and Vasily Krylov.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huijun Fan (School of Mathematical Sciences\, Peking University)
DTSTART;VALUE=DATE-TIME:20230324T090000Z
DTEND;VALUE=DATE-TIME:20230324T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/8
DESCRIPTION:Title: On the Geometry of Landau-Ginzburg Model\nby Huijun Fan (School of M
athematical Sciences\, Peking University) as part of BIMSA Integrable Syst
ems Seminar\n\n\nAbstract\nAn LG model (M\, f) is given by a noncompact co
mplex manifold M and the\nholomorphic function f defined on it\, which is
an important model in string theory.\nBecause of the mirror symmetry conje
cture\, the research on the geometric structure and\nquantization theory o
f LG model has attracted more and more attention. Given a Calabi-\nYau (CY
) manifold\, we can define Gromov-Witten theory (A theory) on it\, and als
o study\nthe variation of Hodge structure on its mirror manifold (B theory
). Accordingly\, LG model\nincludes A theory - FJRW theory and Hodge struc
ture variational theory.\nThis report starts with some examples\, gives th
e geometric and topological\ninformation contained by a LG model\, and der
ives the relevant Witten equation\n(nonlinear) and Schrodinger equation (l
inear). The study of the solution space of these\ntwo sets of equations wi
ll lead to different quantization theories. Secondly\, we give our\nrecent
correspondence theorem of Hodge structures between LG model and CY\nmanif
old. Finally\, we will discuss some relevant issues.\n\nBio: Huijun Fan is
the director of the Key Laboratory of Mathematics and Applied\nMathematic
s of the Ministry of Education of Peking University and the deputy directo
r of\nthe Sino-Russian Math Center. He has won national outstanding youth
grant\, Changjiang\nDistinguished Professor of the Ministry of Education\,
and the second prize of the National\nNatural Science Award. He is the pl
enary speaker of the 2021 annual meeting of the\nChinese Mathematical Soci
ety.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Nikitin (BIMSA)
DTSTART;VALUE=DATE-TIME:20230210T090000Z
DTEND;VALUE=DATE-TIME:20230210T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/9
DESCRIPTION:Title: Semifinite harmonic functions on Bratteli diagrams\nby Pavel Nikitin
(BIMSA) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nLocall
y semisimple algebras (LS-algebras) are inductive limits of semisimple alg
ebras\, and can be fully characterized by their Bratteli diagrams ($\\math
bb{N}$-graded graphs). (Finite) harmonic functions on Bratteli diagrams ar
e a standard tool in the representation theory of LS-algebras and semifini
te harmonic functions are a natural generalization. We plan to give an ove
rview of the subject\, starting with the classical results for the infinit
e symmetric group\, followed by the recent results for the infinite symmet
ric inverse semigroup. Joint work with N.Safonkin\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay (BIMSA)
DTSTART;VALUE=DATE-TIME:20230303T090000Z
DTEND;VALUE=DATE-TIME:20230303T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/10
DESCRIPTION:Title: Geometry of Discrete Integrable Systems: QRT Maps and Discrete Painlev
é Equations\nby Anton Dzhamay (BIMSA) as part of BIMSA Integrable Sys
tems Seminar\n\n\nAbstract\nMany interesting examples of discrete integrab
le systems can be studied from the geometric point of\nview. In this talk
we will consider two classes of examples of such system: autonomous (QRT m
aps) and\nnon-autonomous (discrete Painlevé equations). We introduce some
geometric tools to study these systems\, such as the blowup procedure to
construct algebraic surfaces on which the mappings are regularized\, linea
rization of the mapping on the Picard lattice of the surface and\, for dis
crete Painlevé equations\, the decomposition of the Picard lattice into c
omplementary pairs of the surface and symmetry sub-lattices and constructi
on of a birational representation of affine Weyl symmetry groups that give
s a complete algebraic description of our non-linear dynamic. \n\nThis tal
k is based on joint work with Stefan Carstea (Bucharest) and Tomoyuki\nTak
enawa (Tokyo).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigori Olshanski (IITP\, Skoltech\, and HSE Univ.)
DTSTART;VALUE=DATE-TIME:20230317T090000Z
DTEND;VALUE=DATE-TIME:20230317T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/11
DESCRIPTION:Title: The centralizer construction and Yangian-type algebras\nby Grigori
Olshanski (IITP\, Skoltech\, and HSE Univ.) as part of BIMSA Integrable Sy
stems Seminar\n\n\nAbstract\nIn the 1980s\, Vladimir Drinfeld introduced a
nd studied the notion of Yangian Y(g) associated with an arbitrary simple
complex Lie algebra g. The Yangian Y(g) is a deformation of U(g[x])\, the
universal enveloping algebra for the Lie algebra of polynomial currents g[
x]. The general definition of Yangian is radically simplified for the cla
ssical series A\, and it is even more convenient to work with the reductiv
e algebra g=gl(n).\n\nIn the same 1980s\, it was discovered that the Yangi
an Y(gl(n)) can be constructed in an alternative way\, starting from some
centralizers in the universal enveloping algebra U(gl(n+N)) and then letti
ng N go to infinity. This "centralizer construction" was then extended to
the classical series B\, C\, D\, which lead to the so-called twisted Yang
ians. The theory that arose from this is presented in Alexander Molev's bo
ok "Yangians and classical Lie algebras"\, Amer. Math. Soc.\, 2007.\n\nI w
ill report on the recent work arXiv:2208.04809\, where another version of
the centralizer construction is proposed. It produces a new family of alge
bras and reveals new effects and connections.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youjin Zhang (Tsinghua University)
DTSTART;VALUE=DATE-TIME:20230421T090000Z
DTEND;VALUE=DATE-TIME:20230421T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/12
DESCRIPTION:Title: Linear reciprocal transformations of bihamiltonian integrable hierarchi
es\nby Youjin Zhang (Tsinghua University) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nFor an integrable hierarchy which possesses
a bihamiltonian structure with semisimple hydrodynamic limit\, we prove t
hat the linear reciprocal transformation with respect to any of its symmet
ry transforms it to another bihamiltonian integrable hierarchy. Moreover\,
we show that the central invariants of the bihamiltonian structure are pr
eserved under the reciprocal transformation. The main tools that we use to
obtain this result are the bihamiltonian and variational bihamiltonian co
homologies defined for a bihamiltonian structure of hydrodynamic type. We
also apply this result to study the problem of classification of bihamilto
nian integrable hierarchies.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhe Sheng (Jilin University\, Changchun)
DTSTART;VALUE=DATE-TIME:20230331T090000Z
DTEND;VALUE=DATE-TIME:20230331T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/13
DESCRIPTION:Title: Rota-Baxter groups\, post-groups and related structures\nby Yunhe S
heng (Jilin University\, Changchun) as part of BIMSA Integrable Systems Se
minar\n\n\nAbstract\nRota-Baxter operators on Lie algebras were first stud
ied by Belavin\, Drinfeld and Semenov-Tian-Shansky as operator forms of th
e classical Yang-Baxter equation.\n\nAs a fundamental tool in studying int
egrable systems\, the factorization theorem of Lie groups by Semenov-Tian-
Shansky was obtained by integrating a factorization of Lie algebras from s
olutions of the modified Yang-Baxter equation. Integrating the Rota-Baxter
operators on Lie algebras\, we introduce the notion of Rota-Baxter operat
ors on Lie groups and more generally on groups. Then the factorization the
orem can be achieved directly on groups. As the underlying structures of
Rota-Baxter operators on groups\, the notion of post-groups was introduce
d. The differentiation of post-Lie groups gives post-Lie algebras. Post-gr
oups are also related to Lie-Butcher groups\, and give rise to solutions o
f Yang-Baxter equations. \n\nThe talk is based on the joint work with Chen
gming Bai\, Li Guo\, Honglei Lang and Rong Tang.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ievgen Makedonskyi (BIMSA)
DTSTART;VALUE=DATE-TIME:20230407T090000Z
DTEND;VALUE=DATE-TIME:20230407T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/14
DESCRIPTION:Title: Duality theorems for current algebras\nby Ievgen Makedonskyi (BIMSA
) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe study some
natural representations of current Lie algebras $g\\otimes \\Bbbk[t]$\, c
alled Weyl modules. They are natural analogues of irreducible representati
ons of simple Lie algebras. There are several current analogues of classic
al theorems about Lie algebras where these modules «play role» of irredu
cible modules. In my talk I will explain analogues of duality theorems\, n
amely Peter-Weyl theorem\, Schur-Weyl duality etc.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d’Angers\, ITTP Moscow and IGAP Tr
ieste)
DTSTART;VALUE=DATE-TIME:20230414T090000Z
DTEND;VALUE=DATE-TIME:20230414T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/15
DESCRIPTION:Title: Symplectic and Contact Geometry of Monge– Ampère equation: Introduct
ion and application\nby Vladimir Rubtsov (Université d’Angers\, ITT
P Moscow and IGAP Trieste) as part of BIMSA Integrable Systems Seminar\n\n
\nAbstract\nI am going to present an introduction into the geometric appro
ach to Monge– Ampère operators and equations based on contact and sympl
ectic structures of cotangent and the 1st jet bundles of a smooth manifold
. This approach was developed by V. Lychagin and goes back to the ideas of
E.Cartan and his successor T. Lepage. I shall try to make my talk self-co
ntained. I also plan to discuss various applications and links with import
ant geometric structures.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piergiulio Tempesta (Universidad Complutense de Madrid and Institu
to de Ciencias Matemáticas (ICMAT) – Madrid\, Spain)
DTSTART;VALUE=DATE-TIME:20230519T090000Z
DTEND;VALUE=DATE-TIME:20230519T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/16
DESCRIPTION:Title: Generalized Nijenhuis geometry and applications to Hamiltonian integrab
le systems\nby Piergiulio Tempesta (Universidad Complutense de Madrid
and Instituto de Ciencias Matemáticas (ICMAT) – Madrid\, Spain) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe propose a new\, inf
inite family of tensor fields\, whose first representatives are the classi
cal Nijenhuis and Haantjes tensors. We prove that the vanishing of a suita
ble higher-level Haantjes torsion is a sufficient condition for the integr
ability of the eigen-distributions of an operator field on a differentiabl
e manifold. This new condition\, which does not require the explicit knowl
edge of the spectral properties of the considered operator\, generalizes t
he celebrated Haantjes theorem\, because it provides us with an effective
integrability criterion applicable to the generic case of non-Nijenhuis an
d non-Haantjes tensors. \nWe also propose a tensorial approach to the theo
ry of classical Hamiltonian integrable systems\, based on the geometry of
Haantjes tensors. We introduce the family of symplectic-Haantjes manifolds
as a natural setting where the notion of integrability can be formulated.
In particular\, the theory of separation of variables for classical Hamil
tonian systems can also be formulated in the context of our new geometric
structures.\n\nReferences:\nP. Tempesta\, G. Tondo\, Contemporary Mathemat
ics\, AMS (2023) (to appear)\nD. Reyes\, P. Tempesta\, G. Tondo\, J. Nonli
near Science 33\, 35 (2023)\nP. Tempesta\, G. Tondo\, Communications in Ma
thematical Physics 389\, 1647-1671 (2022)\nP. Tempesta\, G. Tondo\, Annali
Mat. Pura Appl. 201\, 57-90 (2022)\nP. Tempesta\, G. Tondo\, J. Geometry
and Physics 160\, 103968 (2021)\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto D'Onofrio (Università Bicocca and University of Surrey)
DTSTART;VALUE=DATE-TIME:20230428T090000Z
DTEND;VALUE=DATE-TIME:20230428T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/17
DESCRIPTION:Title: Singularities in geophysical fluid dynamics through Monge-Ampère geome
try\nby Roberto D'Onofrio (Università Bicocca and University of Surre
y) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe semigeos
trophic equations are a mathematical model representing atmospheric motion
on a subcontinental scale. Their remarkable mathematical features enable
the equations to model singular behaviours like weather fronts. This talk
presents a new approach to classifying these singular structures using the
geometry of Monge-Ampère equations.\n\nIn the geometrical view\, solutio
ns are understood as Lagrangian submanifolds of a suitably defined phase s
pace equipped with a pseudo-Riemannian metric. We show the interplay betwe
en solution singularities\, elliptic-hyperbolic transitions of the Monge-A
mpère operator\, and the degeneracies of the metric on a few examples\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunfeng Jiang (Southeast University\, Nanjing)
DTSTART;VALUE=DATE-TIME:20230526T090000Z
DTEND;VALUE=DATE-TIME:20230526T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/18
DESCRIPTION:Title: Spin-s rational Q-system\nby Yunfeng Jiang (Southeast University\,
Nanjing) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nRation
al Q-system is an efficient method for solving Bethe ansatz equations (BAE
). One important feature of this method is that\, unlike solving BAE direc
tly\, it gives only physical solutions of BAE. Therefore\, it is intimatel
y related to the completeness problem of Bethe ansatz. In this talk\, I wi
ll first introduce the rational Q-system and discuss the completeness prob
lem of the spin-$1/2$ Heisenberg spin chain. Then I will move to the discu
ssion of the spin-$s$ Heisenberg spin chain where the situation is more co
mplicated. The key new feature here is that repeated roots are allowed. I
will present the rational Q-system for the higher spin models and discuss
the completeness problem for the spin-$s$ Heisenberg spin chain. The solut
ion of the proposed Q-system gives precisely the all the physical solution
s required by completeness of Bethe ansatz.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuyuki Kawahigashi (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20230616T090000Z
DTEND;VALUE=DATE-TIME:20230616T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/19
DESCRIPTION:Title: $\\alpha$-induction\, tensor categories and operator algebras\nby Y
asuyuki Kawahigashi (University of Tokyo) as part of BIMSA Integrable Syst
ems Seminar\n\n\nAbstract\nTensor categories play an important role in the
ory of subfactors in\noperator algebras in connection to conformal field t
heory and condensed\nmatter physics. A certain induction procedure called
$\\alpha$-induction has\nbeen studied as a quantum version of the classic
al induction in group\nrepresentation theory. I will present this without
assuming knowledge on\noperator algebras.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Matushko (Steklov MI RAS\, Moscow)
DTSTART;VALUE=DATE-TIME:20230505T090000Z
DTEND;VALUE=DATE-TIME:20230505T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/20
DESCRIPTION:Title: Anisotropic spin generalization of elliptic Ruijsenaars-Macdonald opera
tors and related integrable long-range spin chains\nby Maria Matushko
(Steklov MI RAS\, Moscow) as part of BIMSA Integrable Systems Seminar\n\n\
nAbstract\nWe propose commuting set of matrix-valued difference operators
in terms of the elliptic Baxter-Belavin R-matrix in the fundamental repres
entation of GL(M). In the scalar case M = 1 these operators are the ellipt
ic Ruijsenaars-Macdonald operators\, while in the general case they can be
viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonia
ns. We show that commutativity of the operators for any M is equivalent to
a set of R-matrix identities and prove them for the elliptic Baxter-Belav
in R-matrix. We show that the Polychronakos freezing trick can be applied
to this model. It provides the commuting set of Hamiltonians for long-rang
e spin chain. We also discuss the trigonometric degenerations based on the
XXZ R-matrix. \nThe talk is based on joint work with Andrei Zotov arXiv:2
201.05944 arXiv:2202.01177\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Roulstone (University of Surrey Guildford)
DTSTART;VALUE=DATE-TIME:20230602T090000Z
DTEND;VALUE=DATE-TIME:20230602T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/21
DESCRIPTION:Title: Applications of symplectic geometry in fluid dynamics\nby Ian Rouls
tone (University of Surrey Guildford) as part of BIMSA Integrable Systems
Seminar\n\n\nAbstract\nWe present a brief history of the application of me
thods from symplectic geometry to fluid dynamics\, and to geophysical syst
ems in particular. The material will cover both analytical and numerical a
pplications\, and emphasize the importance of geometric concepts in operat
ional weather prediction models. This seminar relates to others given rece
ntly in this series by Rubtsov and by D'Onofrio\, and there will be a focu
s on the role of partial differential equations of Monge—Ampere type.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Sergeev (Australian National University and University of C
anberra\, Canberra)
DTSTART;VALUE=DATE-TIME:20230609T090000Z
DTEND;VALUE=DATE-TIME:20230609T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/22
DESCRIPTION:Title: Spectral equations for a class of entire $Q$-operators\nby Sergey S
ergeev (Australian National University and University of Canberra\, Canber
ra) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThere is a
class of $\\mathcal{U}_q(\\widehat{sl}_2)$ models models where the infinit
e dimensional evaluation representations lead to Baxter's $TQ=Q+Q$ equatio
n where $Q$ is an entire function rather than a polynomial. I will give a
general introduction to the method of solving the Baxter equation in this
case.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Lamers (Institut de Physique Théorique (IPhT))
DTSTART;VALUE=DATE-TIME:20230512T090000Z
DTEND;VALUE=DATE-TIME:20230512T103000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/23
DESCRIPTION:Title: Bethe ansatz inside Calogero--Sutherland models\nby Jules Lamers (I
nstitut de Physique Théorique (IPhT)) as part of BIMSA Integrable Systems
Seminar\n\n\nAbstract\nThe Haldane--Shastry spin chain has long-range int
eractions and remarkable properties including Yangian symmetry at finite l
ength and explicit highest-weight wave functions featuring Jack polynomial
s. This stems from the trigonometric spin-Calogero--Sutherland model\, whi
ch is intimately related to affine Hecke algebras\, already enjoys these p
roperties from affine Schur–Weyl duality and reduces to the Haldane--Sha
stry chain in the ‘freezing’ limit. I will present some new results fo
r these models\, including Heisenberg-like symmetries whose spectrum can b
e characterised by Bethe ansatz.\n\nBased on recent work with D. Serban an
d ongoing work with G. Ferrando\, F. Levkovich-Maslyuk and D. Serban.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriy G. Bardakov (Sobolev Institute of Mathematics\, Novosibirs
k\, Russia)
DTSTART;VALUE=DATE-TIME:20230919T080000Z
DTEND;VALUE=DATE-TIME:20230919T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/24
DESCRIPTION:Title: Yang-Baxter equation\, relative Rota-Baxter operators and skew braces\nby Valeriy G. Bardakov (Sobolev Institute of Mathematics\, Novosibirsk
\, Russia) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe
Yang-Baxter equation is a fundamental equation in mathematical\nphysics a
nd statistical mechanics\, it has connections with knot\ntheory\, braid t
heory and some algebraic systems. \n\nIn my talk I recall the definition o
f the Yang-Baxter equation\, Braid equation\, skew brace and relative R
ota-Baxter operators on group. Further we discuss connections between the
se objects\, suggest some way for construction of relative Rota-Baxter ope
rators\, using known Rota-Baxter operators\, describe some of these operat
ors on 2-step nilpotent groups and construct some solutions to the Yang-Ba
xter equation on 2-step nilpotent groups. \n\n\nThis is joint work with T.
Kozlovskaya\, P. Sokolov\, K. Zimireva\, and M. Zonov\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Pochinka (HSE University)
DTSTART;VALUE=DATE-TIME:20231017T080000Z
DTEND;VALUE=DATE-TIME:20231017T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/25
DESCRIPTION:Title: Andronov School of Nonlinear Oscillations\nby Olga Pochinka (HSE Un
iversity) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nAndro
nov's school began to take shape in 1931\, when Alexander Alexandrovich hi
mself\, together with his wife E.A. Leontovich\, moved from Moscow to Nizh
ny Novgorod. \nBy the time of the move\, A.A. Andronov was an established
scientist. Even then\, he introduced a number of new concepts into science
\, including self-oscillations\, concepts of the roughness of the system\,
the bifurcation value of the parameter\, the phase portrait\, and so on.
This is a long-lived school in which a unified scientific program has been
actively developed by several generations of scientists.\nIn my report\,
I will touch upon the scientific direction of the school\, which is associ
ated with rough (structurally stable) dynamic systems. The simplest of th
em - "Morse-Smale systems" got their name after the publication of S. Smal
e's work "On gradient dynamical system // Ann. Math. 74\, 1961\, P.199-206
". He introduced a class of flows on manifolds of arbitrary dimension that
copy the properties of coarse flows on the plane described in 1937 by A.
Andronov and L. Pontryagin. For the introduced streams Smale proved the va
lidity of inequalities similar to Morse inequalities for non-degenerate fu
nctions\, after which such flows were called Morse-Smale flows. S. Smale c
onsidered it extremely important to study such flows\, since he assumed th
at\, by analogy with coarse flows on the plane\, Morse-Smale flows exhaust
the class of structurally stable flows on manifolds and are dense in the
set all threads. Fortunately\, it turned out that the multidimensional str
ucturally stable world is much wider\, and the Morse-Smale systems represe
nt only its regular part - structurally stable systems with a non-wanderin
g set consisting of a finite number of orbits. Due to the close connection
of Morse-Smale systems with the carrier manifold\, various topological ob
jects\, including wild ones\, are realized as invariant subsets of such sy
stems. This leads to a wide variety of Morse-Smale systems (especially on
multidimensional manifolds) and\, accordingly\, complicates their topologi
cal classification.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Appel (Dipartimento SMFI Università di Parma)
DTSTART;VALUE=DATE-TIME:20231024T080000Z
DTEND;VALUE=DATE-TIME:20231024T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/26
DESCRIPTION:Title: The R-matrix of the affine Yangian\nby Andrea Appel (Dipartimento S
MFI Università di Parma) as part of BIMSA Integrable Systems Seminar\n\n\
nAbstract\nLet $\\mathfrak{g}$ be an affine Lie algebra with associated Ya
ngian $Y_h(\\mathfrak{g})$.\nWe prove the existence of two meromorphic $R$
--matrices associated to any pair of representations of $Y_h(\\mathfrak{g}
)$ in the category $\\mathcal{O}$. \nThey are related by a unitary constra
int and constructed as products of the form $\\mathcal R^{\\uparrow/\\down
arrow}(s)=\\mathcal R^+(s)\\cdot\\mathcal R^{0\,\\uparrow/\\downarrow}(s)\
\cdot\\mathcal R^-(s)$\, where $\\mathcal R^+(s) = \\mathcal R^-_{21}(-s)^
{-1}$. \nThe factors $\\mathcal R^{0\,\\uparrow/\\downarrow}(s)$ are merom
orphic\, abelian $R$--matrices\,\nwith a WKB--type singularity in $\\hbar$
\, and $\\mathcal R^-(s)$ is a rational twist. \nOur proof relies on two
novel ingredients.\nThe first is an irregular\, abelian\, additive differe
nce equation\nwhose difference operator is given in terms of the $q$--Cart
an matrix of $\\mathfrak g$.\nThe regularisation of this difference equati
on gives rise to \n$\\mathcal R^{0\,\\uparrow/\\downarrow}(s)$ as the\nex
ponentials of the two canonical fundamental solutions.\nThe second key ing
redient is\na higher order analogue of the adjoint action of \nthe affine
Cartan subalgebra $\\mathfrak h\\subset\\mathfrak g$ on $Y_h(\\mathfrak g)
$. This action has no classical counterpart\, and produces\na system of li
near equations from which $\\mathcal R^-(s)$\nis recovered as the unique s
olution. \nMoreover\, we show that both $\\mathcal R^{\\uparrow/\\downarro
w}(s)$\ngive rise to the same rational $R$--matrix \non the tensor product
of any two highest--weight representations.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Safonkin (University of Reims Champagne-Ardenne\, Reims & S
kolkovo Institute of Science and Technology\, Moscow)
DTSTART;VALUE=DATE-TIME:20230926T080000Z
DTEND;VALUE=DATE-TIME:20230926T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/27
DESCRIPTION:Title: Yangian-type algebras and double Poisson brackets.\nby Nikita Safon
kin (University of Reims Champagne-Ardenne\, Reims & Skolkovo Institute of
Science and Technology\, Moscow) as part of BIMSA Integrable Systems Semi
nar\n\n\nAbstract\nLet A be an arbitrary associative algebra. With the hel
p of Olshanski’s centralizer construction one can define a sequence Y_1(
A)\, Y_2(A)\,... of "Yangian-type algebras" (they possess a number of pr
operties of the Yangians of series A). I will discuss a link between these
Yangian-type algebras and a class of double Poisson brackets on free asso
ciative algebras. The talk is based on the joint paper with Grigori Olshan
ski arXiv:2308.13325.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis Napper (University of Surrey)
DTSTART;VALUE=DATE-TIME:20231121T080000Z
DTEND;VALUE=DATE-TIME:20231121T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/28
DESCRIPTION:Title: (Higher) Monge—Ampere Geometry of the Navier—Stokes Equations\n
by Lewis Napper (University of Surrey) as part of BIMSA Integrable Systems
Seminar\n\n\nAbstract\nThe Poisson equation for the pressure of a homogen
eous\, incompressible Navier--Stokes flow is a key diagnostic relation for
understanding the formation of vortices in turbulence. Building on the ob
servation that\, in two dimensions\, the aforementioned equation is a Mong
e--Amp{\\`e}re equation for the stream function\, this talk introduces a f
ramework for studying this relation from the perspective of (multi-)symple
ctic geometry.\n\nWhile reviewing the geometry of Monge--Amp{\\`e}re equat
ions presented by Rubtsov\, D'Onofrio\, and Roulstone in earlier seminars
of this series\, we demonstrate how an associated metric on the phase spac
e of a two-dimensional fluid flow encodes the dominance of vorticity and s
train. We then discuss how multi-symplectic geometry may be used to genera
lise to fluid flows on Riemannian manifolds in higher dimensions\, culmina
ting in a Weiss--Okubo-type criterion in these cases. Throughout\, we make
comments on how the signatures and curvatures of our structures may be in
terpreted in terms of the geometric and topological properties of vortices
.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Kazakov (HSE University)
DTSTART;VALUE=DATE-TIME:20231010T080000Z
DTEND;VALUE=DATE-TIME:20231010T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/29
DESCRIPTION:Title: On robust chaos\nby Alexey Kazakov (HSE University) as part of BIMS
A Integrable Systems Seminar\n\n\nAbstract\nOne of the most fundamental pr
oblems in multidimensional chaos theory is the study of strange attractors
which are robustly chaotic (i.e.\, they remain chaotic after small pertur
bations of the system). It was hypothesized in [1] that the robustness of
chaoticity is equivalent to the pseudohyperbolicity of the attractor. Pseu
dohyperbolicity is a generalization of hyperbolicity. The main characteris
tic property of a pseudohyperbolic attractor is that each of its orbits ha
s a positive maximal Lyapunov exponent. In addition\, this property must b
e preserved under small perturbations. The foundations of the theory of ps
eudohyperbolic attractors were laid by Turaev and Shilnikov [2\,3]\, who s
howed that the class of pseudohyperbolic attractors\, besides the classica
l Lorenz and hyperbolic attractors\, also includes wild attractors which c
ontain orbits with a homoclinic tangency.\n\nIn this talk we give a
review on the theory of pseudohyperbolic attractors arising in both system
s with continuous and discrete time. At first\, we explain what is meant u
nder pseudohyperbolic attractors. Then\, we describe our methods for the p
seudohyperbolicity verification. We demonstrate the applicability of these
methods for several well-known systems (with both pseudohyperbolic and no
n-pseudohyperbolic attractors). Finally\, we present new examples of pseud
ohyperbolic attractors.\n\n[1] Gonchenko\, S.\, Kazakov\, A.\, & Turaev
\, D. (2021). Wild pseudohyperbolic attractor in a four-dimensional Lorenz
system. Nonlinearity\, 34(4)\, 2018.\n[2] Turaev\, D. V.\, & Shilnikov\,
L. P. (1998). An example of a wild strange attractor. Sbornik: Mathematics
\, 189(2)\, 291.\n[3] Turaev\, D. V.\, & Shilnikov\, L. P. (2008\, Februar
y). Pseudohyperbolicity and the problem on periodic perturbations of Loren
z-type attractors. In Doklady Mathematics (Vol. 77\, pp. 17-21).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Basalaev (HSE University)
DTSTART;VALUE=DATE-TIME:20231107T080000Z
DTEND;VALUE=DATE-TIME:20231107T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/30
DESCRIPTION:Title: Integrable systems of A\,D and B-type Dubrovin-Frobenius manifolds\
nby Alexey Basalaev (HSE University) as part of BIMSA Integrable Systems S
eminar\n\n\nAbstract\nGiven a series of WDVV or open-WDVV equation solutio
ns satisfying the certain stabilization conditions\, one can construct an
infinite system of commuting partial differential equations.\nWe illustrat
e these fact on the examples of A and D type Dubrovin--Frobenius manifolds
and their "open extensions". These give KP\, a reduction of a 2-componen
t BKP and 2D Toda hierarchies respectively. Following D.Zuo to a B_n type
Coxeter group one can associate n different WDVV solutions that are not n
ecessarily polynomial. We will prove that these Dubrovin--Frobenius struc
tures stabilize too and present the integrable systems associated to them.
\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bart Vlaar (BIMSA)
DTSTART;VALUE=DATE-TIME:20231113T053000Z
DTEND;VALUE=DATE-TIME:20231113T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/31
DESCRIPTION:Title: Baxter Q-operators for open spin chains\nby Bart Vlaar (BIMSA) as p
art of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe discuss some rec
ent progress on Baxter Q-operators for the XXZ spin chain with diagonal bo
undary conditions. A key tool is the universal K-matrix for affine quantum
groups. Joint work with Alec Cooper and Robert Weston.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (University of Angers)
DTSTART;VALUE=DATE-TIME:20231128T080000Z
DTEND;VALUE=DATE-TIME:20231128T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/32
DESCRIPTION:Title: Kontsevich and Buchstaber polynomials\, multiplication kernels and Cala
bi–Yau Differential operators\nby Vladimir Rubtsov (University of An
gers) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe discus
s several result on ongoing work in collaboration (with I. Gaiur & D. Van
Straten and with V. Buchstaber & I. Gaiur) on interesting properties of m
ultiplicative generalized Bessel kernels\, which include the famous Clause
n and Sonine –Gegenbauer formulas\, examples of polynomials for Kontsev
ich discriminant locus given as addition laws for special 2-valued formal
groups (Buchstaber–Novikov–Veselov) as well as connections with «peri
od functions» solving some Picard–Fuchs type equations and associated w
ith analogues of Landau–Ginzburg superpotentials.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgy Sharygin (Sino-Russian Mathematics Center\, Moscow State Un
iversity)
DTSTART;VALUE=DATE-TIME:20231031T080000Z
DTEND;VALUE=DATE-TIME:20231031T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/33
DESCRIPTION:Title: Argument shift method for the universal enveloping algebras\nby Geo
rgy Sharygin (Sino-Russian Mathematics Center\, Moscow State University) a
s part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nArgument shift m
ethod is a construction that produces a commutative subalgebra of a Poisso
n algebra by differentiating its central elements along a suitable vector
field. An important particular case of this situation is when the Poisson
algebra is equal to the space of (polynomial) functions on a dual space of
a Lie algebra $g$. In my talk I will discuss an attempt to raise this pro
cedure to the universal enveloping algebra of $g$. Based on a joint work w
ith Y.Ikeda and A.Molev\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Kostov (BIMSA & Institut de physique théorique\, Université
Paris-Saclay\, CNRS and CEA)
DTSTART;VALUE=DATE-TIME:20231016T053000Z
DTEND;VALUE=DATE-TIME:20231016T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/34
DESCRIPTION:Title: Loop-gas formulation of two-dimensional integrable models\nby Ivan
Kostov (BIMSA & Institut de physique théorique\, Université Paris-Saclay
\, CNRS and CEA) as part of BIMSA Integrable Systems Seminar\n\nLecture he
ld in Room A6-1 in BIMSA.\n\nAbstract\nI will formulate the finite-volume
thermodynamics of a massive integrable QFT in terms of a has of relativist
ic loops. The loops interact through scattering factors associated with th
eir intersections. For the doubly periodic spacetime\, after decoupling th
e pairwise interactions by a Hubbard-Stratonovich transformation\, the sum
over loops can be performed explicitly. The resulting effective theory be
comes mean field type in the limit when one of the periods becomes asympto
tically large. The mean field obeys the Thermodynamical Bethe Ansatz equat
ions.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hrachya Babujian (BIMSA & Yerevan Physics Institute\, Armenia)
DTSTART;VALUE=DATE-TIME:20231023T053000Z
DTEND;VALUE=DATE-TIME:20231023T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/35
DESCRIPTION:Title: The form factor program: asymptotic factorization of n-particle SU(N) f
orm factors\nby Hrachya Babujian (BIMSA & Yerevan Physics Institute\,
Armenia) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe inv
estigate the high energy behavior of the SU(N) chiral Gross-Neveu model in
1 + 1 dimensions. The model is integrable and matrix elements of several
local operators (form factors) are known exactly. The form factors show ra
pidity space clustering\, which means factorization\, if a group of rapidi
ties is shifted to infinity. We analyze this phenomenon for the SU(N) mode
l. For several operators the factorization formulas are presented explicit
ly.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaomeng Xu (Beijing International Center for Mathematical Researc
h (BICMR))
DTSTART;VALUE=DATE-TIME:20231026T030000Z
DTEND;VALUE=DATE-TIME:20231026T040000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/36
DESCRIPTION:Title: Integrability in Stokes phenomenon.\nby Xiaomeng Xu (Beijing Intern
ational Center for Mathematical Research (BICMR)) as part of BIMSA Integra
ble Systems Seminar\n\n\nAbstract\nIt is well known that for a meromorphic
linear system with only regular singularities\, any formal solution is ne
cessarily convergent. It is less well known that for meromorphic linear sy
stems with irregular singularities\, a prescribed asymptotics at an irregu
lar singular point determine different fundamental solutions in different
sectorial regions surrounding the singular point. The transition matrices
between the preferred solutions in the different sectoral regions are know
n as the Stokes matrices. This talk shows a relation between Stokes matric
es and various structures appearing in integrability. It then explains tha
t how the theory of quantum groups\, Yangians\, crystal basis and so on ca
n be used to study the Stokes phenomenon.\n\nWorkshop on Lie theory and in
tegrable systems at BIMSA\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Zhedanov (Renmin University of China\, Beijing. School of
Mathematics)
DTSTART;VALUE=DATE-TIME:20231026T020000Z
DTEND;VALUE=DATE-TIME:20231026T030000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/37
DESCRIPTION:Title: Heun operators from different points of view: quantum and classical
\nby Oleksiy Zhedanov (Renmin University of China\, Beijing. School of Mat
hematics) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe di
scuss recent construction of Heun operators as bilinear combinations of tw
o generators of the Askey-Wilson algebra (as well as of its degenerate cas
es). This construction is related to an important "band and time limiting"
problem in Fourier analysis. Classical mechanical analogs of the Heun ope
rators give rise to several families of dynamical systems having explicit
solutions in terms of elliptic functions.\n\nWorkshop on Lie theory and in
tegrable systems at BIMSA\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Osipov (Visitor of Sino-Russian mathematical center of PKU\,
Steklov Mathematical Institute of RAS\, HSE University)
DTSTART;VALUE=DATE-TIME:20231026T053000Z
DTEND;VALUE=DATE-TIME:20231026T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/38
DESCRIPTION:Title: Local analog of the Deligne-Riemann-Roch isomorphism for line bundles o
n a family of curves.\nby Denis Osipov (Visitor of Sino-Russian mathem
atical center of PKU\, Steklov Mathematical Institute of RAS\, HSE Univers
ity) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nI will spe
ak about a local analog of the Deligne-Riemann-Roch theorem for line bund
les on a family of smooth projective curves. First\, I recall the Deligne-
Riemann-Roch theorem. Then I will speak about its local analog. The two pa
rts for this local analog of the Deligne-Riemann-Roch theorem consist of t
he central extensions of the group that is the semidirect product of the
group of invertible functions on the formal punctured disc and the group
of automorphisms on this disc. These central extensions are by the multip
licative group. The theorem is that these central extensions are equivalen
t over the ground field of rational numbers. \nThe talk is based on my re
сent preprint arXiv:2308.0649.\n\nWorkshop on Lie theory and integrable
systems at BIMSA\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov (Moscow State University\, now a visitor of SRMC
in PKU)
DTSTART;VALUE=DATE-TIME:20231026T063000Z
DTEND;VALUE=DATE-TIME:20231026T073000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/39
DESCRIPTION:Title: Commuting scalar partial differential (and not only) operators and modu
li spaces of torsion-free sheaves.\nby Alexander Zheglov (Moscow State
University\, now a visitor of SRMC in PKU) as part of BIMSA Integrable Sy
stems Seminar\n\n\nAbstract\nIn my talk I’ll give an overview of the res
ults obtained by me\, as well as jointly with co-authors\, related to the
problem of classifying commuting (scalar) differential\, or more generally
\, differential-difference or integral-differential operators in several v
ariables. The problem\, under some reasonable restrictions\, essentially r
educes to the description of projective algebraic varieties that have a no
n-empty moduli space of torsion-free sheaves with a fixed Hilbert polynomi
al. \n\nMore precisely\, it turns out to be possible to classify the so-ca
lled quasi-elliptic rings\, which describe a wide class of operator rings
appeared in the theory of (quantum) integrable systems. They are contained
in a certain non-commutative “universal” ring - a purely algebraic an
alogue of the ring of pseudodifferential operators on a manifold and admit
(under some weak restrictions) a convenient algebraic-geometric descripti
on. This description is a natural generalization of the classification of
rings of commuting ordinary differential or difference operators\, describ
ed in the works of Krichever\, Novikov\, Drinfeld\, Mumford\, Mulase. More
over\, already in the case of dimension two there are significant restrict
ions on the geometry of spectral manifolds.\n\nWorkshop on Lie theory and
integrable systems at BIMSA\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Belousov (Steklov Mathematical Institute\, St. Petersburg\,
Russia)
DTSTART;VALUE=DATE-TIME:20231114T080000Z
DTEND;VALUE=DATE-TIME:20231114T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/40
DESCRIPTION:Title: Baxter Q-operators in Ruijsenaars hyperbolic system\nby Nikita Belo
usov (Steklov Mathematical Institute\, St. Petersburg\, Russia) as part of
BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe eigenfunctions of the
Ruijsenaars hyperbolic system were constructed by M. Hallnäs and S. Ruij
senaars in 2012. \n\nRecently in the joint work with S. Derkachov\, S. Kha
rchev and S. Khoroshkin we proved some properties of these eigenfunctions
using the so-called Baxter Q-operators. In the talk I will explain the mot
ivation behind these operators\, their key properties and how they are use
d to prove the bispectral symmetry\, orthogonality and completeness of the
eigenfunctions.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takashi Takebe (BIMSA)
DTSTART;VALUE=DATE-TIME:20231106T053000Z
DTEND;VALUE=DATE-TIME:20231106T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/41
DESCRIPTION:Title: Dispersionless integrable hierarchies and Loewner type equations\nb
y Takashi Takebe (BIMSA) as part of BIMSA Integrable Systems Seminar\n\n\n
Abstract\nDispersionless integrable hierarchies are obtained as certain li
mits of classical integrable hierarchies such as the KP hierarchy and the
Toda lattice hierarchy. They were introduced in 1990's and studied first\,
for example\, in relation to string theory. In this century it was found
that dispersionless hierarchies are closely related to the theory of confo
rmal mappings. I shall talk about the relation of dispersionless hierarchi
es and the Loewner equations for conformal mappings.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandr Buryak (National Research University Higher School of Eco
nomics\, Skolkovo Institute of Science and Technology)
DTSTART;VALUE=DATE-TIME:20231205T080000Z
DTEND;VALUE=DATE-TIME:20231205T093000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/42
DESCRIPTION:Title: Quantum intersection numbers and the Gromov-Witten invariants of the Ri
emann sphere.\nby Alexandr Buryak (National Research University Higher
School of Economics\, Skolkovo Institute of Science and Technology) as pa
rt of BIMSA Integrable Systems Seminar\n\n\nAbstract\nQuantum intersection
numbers were introduced through a natural quantization of the KdV hierarc
hy in a work of Buryak\, Dubrovin\, Guere\, and Rossi. Because of the Kont
sevich-Witten theorem\, a part of the quantum intersection numbers coincid
es with the classical intersection numbers of psi-classes on the moduli sp
aces of stable algebraic curves. I will talk about our joint work in progr
ess with Xavier Blot\, where we relate the quantum intersection numbers to
the stationary relative Gromov-Witten invariants of the Riemann sphere\,
with an insertion of a Hodge class. Using the Okounkov-Pandharipande appro
ach to such invariants (with the trivial Hodge class) through the infinite
wedge formalism\, we then give a short proof of an explicit formula for t
he ``purely quantum'' part of the quantum intersection numbers\, found bef
ore by Xavier\, which in particular relates these numbers to the one-part
double Hurwitz numbers.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Reshetikhin (YSMC\, Tsinghua University & BIMSA)
DTSTART;VALUE=DATE-TIME:20231126T013000Z
DTEND;VALUE=DATE-TIME:20231126T023000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/43
DESCRIPTION:Title: Hybrid integrable systems\nby Nicolai Reshetikhin (YSMC\, Tsinghua
University & BIMSA) as part of BIMSA Integrable Systems Seminar\n\n\nAbstr
act\nWorkshop Kirillov–75. Combinatorics and Bethe ansatz. November 26
–27\n\nThis talk is focused on quantum integrable systems on a classical
background. In physics such systems are known as Born-Oppenheimer approxi
mations\, when heavy atoms are classical and electrons are quantum. In mat
hematics\, perhaps\, most known structures of this type are Azumaya algebr
as (an algebra that is finite dimensional over the center) and quantum gro
ups at roots of unity. After the description of general mathematical frame
work several natural examples will be given\, such as spin chains\, spin C
alogero-Moser systems and isomonodromic deformations. The talk is based on
joint work with A. Liashyk and I. Sechin.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Smirnov (Independent University of Moscow and GTIIT)
DTSTART;VALUE=DATE-TIME:20231126T023000Z
DTEND;VALUE=DATE-TIME:20231126T033000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/44
DESCRIPTION:Title: Lascoux polynomials and Gelfand-Zetlin polytopes\nby Evgeny Smirnov
(Independent University of Moscow and GTIIT) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nWorkshop Kirillov–75. Combinatorics and B
ethe ansatz. November 26–27\n\nI will speak about a new combinatorial de
scription for stable Grothendieck polynomials and Lascoux polynomials in t
erms of cellular decompositions of Gelfand-Zetlin polytopes. This generali
zes an earlier result on key polynomials (aka characters of Demazure modul
es) by Kiritchenko\, Timorin and myself. The talk is based on a joint work
with Ekaterina Presnova.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Zhedanov (Renmin University of China)
DTSTART;VALUE=DATE-TIME:20231126T050000Z
DTEND;VALUE=DATE-TIME:20231126T060000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/45
DESCRIPTION:Title: CMV-bispectrality\nby Oleksiy Zhedanov (Renmin University of China)
as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWorkshop Kiril
lov–75. Combinatorics and Bethe ansatz. November 26–27\n\nFor Szego po
lynomials on the unit circle we present explicit examples of bispectrality
which makes these polynomials similar to "classical" orthogonal polynomia
ls. These examples admit extension to much wider class of special Baxter p
olynomials. Affine and double affine Hecke algebras of rank 1 arise natura
lly in this approach from first principles.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhuoke Yang (BIMSA)
DTSTART;VALUE=DATE-TIME:20231126T060000Z
DTEND;VALUE=DATE-TIME:20231126T070000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/46
DESCRIPTION:Title: New approaches to Lie algebra weight systems\nby Zhuoke Yang (BIMSA
) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWorkshop Kiri
llov–75. Combinatorics and Bethe ansatz. November 26–27\n\nIn this tal
k we introduce a universal weight system (a function on chord diagrams sat
isfying the 4-term relation) taking values in the ring of polynomials in i
nfinitely many variables\, whose particular specialisations are weight sys
tems associated with the Lie algebras gl(N) and Lie superalgebras gl(M|N).
We extend this weight system to permutations and provide an efficient rec
ursion for its computation.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Feigin (Hebrew university in Jerusalem)
DTSTART;VALUE=DATE-TIME:20231126T070000Z
DTEND;VALUE=DATE-TIME:20231126T080000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/47
DESCRIPTION:Title: Tolya and fermionic formulas\nby Boris Feigin (Hebrew university in
Jerusalem) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWor
kshop Kirillov–75. Combinatorics and Bethe ansatz. November 26–27\n\nI
explain what are the fermionic formulas and why they are interesting and
important and present some relatively new results — fermionic formulas r
elated with triplet-like vertex algebras.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Shapiro (Stockholm University & BIMSA)
DTSTART;VALUE=DATE-TIME:20231127T053000Z
DTEND;VALUE=DATE-TIME:20231127T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/48
DESCRIPTION:Title: Zonotopal algebras of graphs and their generalizations\nby Boris Sh
apiro (Stockholm University & BIMSA) as part of BIMSA Integrable Systems S
eminar\n\n\nAbstract\nWorkshop Kirillov–75. Combinatorics and Bethe ansa
tz. November 26–27\n\nIn the late 1990s motivated by a question of V.Arn
old the speaker and M.Shapiro have studied the algebra generated by the cu
rvature forms of the standard linear bundles over the space of complete fl
ags in C^n. This was the first example of the so-called external zonotopal
algebra associated to the complete graph K_n. Since then a number of modi
fications and generalizations of this algebra defined for all undirected g
raphs has been introduced. I will briefly survey the field many advances i
n which were inspired by suggestions and ideas of Anatol Kirillov.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruijie XU (BIMSA)
DTSTART;VALUE=DATE-TIME:20231127T063000Z
DTEND;VALUE=DATE-TIME:20231127T073000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/49
DESCRIPTION:Title: Lattice walk as an exactly solvable model\nby Ruijie XU (BIMSA) as
part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWorkshop Kirillov
–75. Combinatorics and Bethe ansatz. November 26–27\n\nIn this talk\,
I will introduce the research of lattice walk in analytic combinatorics. S
tarting from simple one dimensional discrete random walks\, I will show ho
w algebraic structures affect the the solution. The result in two dimensio
nal walks is most attracting. We will meet many concepts such as algebraic
curves\, conformal mapping and Riemann surface in solving two dimensional
walks. In the last part of this talk\, I will talk about the relation bet
ween lattice walk and integrable phase model.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (University of Angers)
DTSTART;VALUE=DATE-TIME:20231212T080000Z
DTEND;VALUE=DATE-TIME:20231212T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/50
DESCRIPTION:Title: Kontsevich and Buchstaber polynomials\, multiplication kernels and Cala
bi–Yau Differential operators II\nby Vladimir Rubtsov (University of
Angers) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIt is
continuation of the previous talk at November 28.\n\nWe discuss several re
sult on ongoing work in collaboration (with I. Gaiur & D. Van Straten and
with V. Buchstaber & I. Gaiur) on interesting properties of multiplicativ
e generalized Bessel kernels\, which include the famous Clausen and Sonine
–Gegenbauer formulas\, examples of polynomials for Kontsevich discrimi
nant locus given as addition laws for special 2-valued formal groups (Buch
staber–Novikov–Veselov) as well as connections with «period functions
» solving some Picard–Fuchs type equations and associated with analogue
s of Landau–Ginzburg superpotentials.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenwei Ruan (University of Wisconsin - Madison)
DTSTART;VALUE=DATE-TIME:20231222T053000Z
DTEND;VALUE=DATE-TIME:20231222T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/51
DESCRIPTION:Title: A uniform approach to the Damiani\, Beck\, and alternating PBW bases fo
r the positive part of $U_q(\\hat{\\mathfrak{sl}}_2)$\nby Chenwei Ruan
(University of Wisconsin - Madison) as part of BIMSA Integrable Systems S
eminar\n\n\nAbstract\nThe $q$-deformed enveloping algebra $U_q(\\hat{\\mat
hfrak{sl}}_2)$ and its positive part $U^+_q$\nare studied in both mathemat
ics and mathematical physics. The literature contains at least three\nPBW
bases for $U^+_q$\, called the Damiani\, the Beck\, and the alternating PB
W bases.\nThese PBW bases are related via exponential formulas. In this ta
lk\, we will introduce\nan exponential generating function whose argument
is a power series involving the\nBeck PBW basis and an integer parameter $
m$. The cases $m = 2$ and $m = −1$ yield the\nknown exponential formulas
for the Damiani and alternating PBW bases\, respectively.\nWe will give p
resent two results on the generating function for an arbitrary integer m.\
nThe first result gives a factorization of the generating function. In the
second result\,\nwe express the coefficients of the generating function i
n closed form.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov
DTSTART;VALUE=DATE-TIME:20231219T053000Z
DTEND;VALUE=DATE-TIME:20231219T063000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/52
DESCRIPTION:Title: Kontsevich and Buchstaber polynomials\, multiplication kernels and Cala
bi–Yau Differential operators III\nby Vladimir Rubtsov as part of BI
MSA Integrable Systems Seminar\n\n\nAbstract\nIt is continuation of the pr
evious talk at November 28 and December 12.\n\nWe discuss several result o
n ongoing work in collaboration (with I. Gaiur & D. Van Straten and with
V. Buchstaber & I. Gaiur) on interesting properties of multiplicative gene
ralized Bessel kernels\, which include the famous Clausen and Sonine –Ge
genbauer formulas\, examples of polynomials for Kontsevich discriminant l
ocus given as addition laws for special 2-valued formal groups (Buchstaber
–Novikov–Veselov) as well as connections with «period functions» sol
ving some Picard–Fuchs type equations and associated with analogues of L
andau–Ginzburg superpotentials.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tao Gui (Peking University)
DTSTART;VALUE=DATE-TIME:20240227T080000Z
DTEND;VALUE=DATE-TIME:20240227T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/53
DESCRIPTION:Title: Asymptotic Log-concavity of Dominant Lower Bruhat Intervals via the Bru
nn--Minkowski Inequality\nby Tao Gui (Peking University) as part of BI
MSA Integrable Systems Seminar\n\n\nAbstract\nBj\\"orner and Ekedahl [Ann.
of Math. (2)\, 170(2): 799-817\, 2009] pioneered the study of length-enum
erating sequences associated with parabolic lower Bruhat intervals in crys
tallographic Coxeter groups. In this talk\, we study the asymptotic behavi
or of these sequences in affine Weyl groups. We prove that the length-enum
erating sequences associated with the dominant intervals corresponding to
a dominant coroot lattice element are ``asymptotically'' log-concave. More
precisely\, we prove that a certain sequence of discrete measures natural
ly constructed from the length-enumerating sequences converges weakly to a
continuous measure constructed from a certain polytope. Moreover\, a cert
ain sequence of step functions naturally constructed from the length-enume
rating sequences uniformly converges to the density function of that conti
nuous measure\, which implies the weak convergence and that the sequences
of numbers of elements in each layer of the dilated dominant interval conv
erges to a sequence of volumes of hyperplane sections of the polytope. By
the Brunn--Minkovski inequality\, the density function is log-concave. Our
approach relies on the ``dominant lattice formula''\, which yields a new
bridge between the discrete nature of Betti numbers of parabolic affine Sc
hubert varieties and the continuous nature of the geometry of convex polyt
opes. Our technique can be seen as a refinement in our context of the clas
sical Ehrhart's theory relating the volume of a polytope and the number of
lattice points the polytope contains\, by replacing the volume by volumes
of transversal sections and the number the total lattice points by the nu
mber of lattice points of a given length. Joint with Gaston Burrull and Ho
ngsheng Hu.\n\nShort bio: I got my Ph. D. in 2023 from the Academy of Math
ematics and Systems Science\, Chinese Academy of Sciences. Currently I am
a postdoc of the Beijing International Center for Mathematical Research\,
Peking University. My research interests are Lie theory\, geometric/combin
atorial representation theory\, and combinatorial Hodge theory. And I have
broad interests in topological\, geometric\, and combinatorial problems r
elated to representation theory.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando (HSE University\, Skolkovo Institute of Science and
Technology)
DTSTART;VALUE=DATE-TIME:20240305T080000Z
DTEND;VALUE=DATE-TIME:20240305T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/54
DESCRIPTION:Title: Inducing graph invariants from the universal gl-weight system\nby S
ergei Lando (HSE University\, Skolkovo Institute of Science and Technolog
y) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWeight syste
ms\, which are functions on chord diagrams satisfying certain 4-\nterm rel
ations\, appear naturally in Vassiliev's theory of \nnite type knot invari
ants.\nIn particular\, a weight system can be constructed from any \nnite
dimensional\nLie algebra endowed with a nondegenerate invariant bilinear f
orm. Recently\,\nM. Kazarian suggested to extend the gl(N)-weight system f
rom chord diagrams\n(treated as involutions without \nxed point) to arbitr
ary permutations\, which\nled to a recurrence formula allowing for an eec
tive computation of its values\,\nelaborated by Zhuoke Yang. In turn\, the
recurrence helped to unify the gl(N)\nweight systems\, for N = 1\, 2\, 3\
, . . . \, into a universal gl-weight system. The\nlatter takes values in
the ring of polynomials C[N][C1\, C2\, . . . ] in in\nnitely many\nvariabl
es C1\, C2\, . . . (Casimir elements)\, whose coe\ncients are polynomials
in N.\nThe universal gl-weight system carries a lot of information about c
hord\ndiagrams and intersection graphs. The talk will address the question
which graph\ninvariants can be extracted from it. We will discuss the int
erlace polynomial\,\nthe enhanced skew-characteristic polynomial\, and the
chromatic polynomial. In\nparticular\, we show that the interlace polynom
ial of the intersection graphs can\nbe obtained by a speci\nc substitution
for the variables N\, C1\, C2\, . . . . This allows\none to extend it fro
m chord diagrams to arbitrary permutations.\nQuestions concerning other gr
aph and delta-matroid invariants and their\npresumable extensions will be
formulated.\nThe talk is based on a work of the speaker and a PhD student
Nadezhda\nKodaneva.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Oblezin (BIMSA)
DTSTART;VALUE=DATE-TIME:20240312T080000Z
DTEND;VALUE=DATE-TIME:20240312T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/55
DESCRIPTION:Title: On matrix element representation of the GKZ hypergeometric functions\nby Sergey Oblezin (BIMSA) as part of BIMSA Integrable Systems Seminar\n
\n\nAbstract\nIn the talk\, I shall present our joint paper with A.Gerasim
ov and D.Lebedev. In this paper\, we develop a representation theory appro
ach to the study of generalized hypergeometric functions of Gelfand\, Kapr
anov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions m
ay be identified with matrix elements of non-reductive Lie algebras L(N)
of oscillator type. The Whittaker functions associated with principal seri
es representations of gl(n\,R) being special cases of GKZ hypergeometric
functions\, thus admit along with a standard matrix element representatio
ns associated with reductive Lie algebra gl(n\,R)\, another matrix elemen
t representation in terms of L(n(n-1)).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuai Guo (Peking University)
DTSTART;VALUE=DATE-TIME:20240319T080000Z
DTEND;VALUE=DATE-TIME:20240319T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/56
DESCRIPTION:Title: Birkhoff Factorization\, Givental’s Quantization\, and BCOV’s Feynm
an Rule\nby Shuai Guo (Peking University) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nBCOV’s Feynman rule is a conjectural algo
rithm used to compute the higher genus Gromov-Witten invariants of Calabi-
Yau threefolds. The Feynman graph that appears in BCOV’s rule can be int
erpreted as a form of geometric quantization. In this presentation\, I wil
l attempt to extract it from the A-model perspective and realize it as Giv
ental’s R-matrix quantization action. Finally\, I will explain how mixed
field theory applies to this quantization formalism of the Feynman rule.
\nThis talk is based on a series of joint works with H.-L. Chang\, J. Li\,
W.-P. Li\, and Y. Zhou\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenglang Yang (Chinese Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20240326T080000Z
DTEND;VALUE=DATE-TIME:20240326T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/57
DESCRIPTION:Title: A connection between the topological vertex and multi-component KP hier
archy\nby Chenglang Yang (Chinese Academy of Sciences) as part of BIMS
A Integrable Systems Seminar\n\n\nAbstract\nThe topological vertex\, devel
oped by Aganagic\, Klemm\, Marino and Vafa\, provides an explicit algorith
m to compute the open Gromov-Witten invariants of smooth toric Calabi-Yau
threefolds in mathematics\, as well as the A-model topological string ampl
itudes in physics. In this talk\, I will introduce our recent work on the
connection between the topological vertex and multi-component KP hierarchy
. \n\nThis talk is based on a joint work with Zhiyuan Wang and Jian Zhou.\
n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limeng Xia (Jiangsu University)
DTSTART;VALUE=DATE-TIME:20240412T133000Z
DTEND;VALUE=DATE-TIME:20240412T143000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/58
DESCRIPTION:Title: GIM algebras and their modules\nby Limeng Xia (Jiangsu University)
as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIn this talk\,
we mainly introduce some background of the structure\, the representation
and the quantization of the generalized intersection matrix algebras. Then
we introduce a result on finite dimensional modules over indefinite type
Kac-Moody Lie algebras. It is given in a joint work with Hongmei Hu and Y
ilan Tan.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Mishnyakov (Nordita)
DTSTART;VALUE=DATE-TIME:20240409T080000Z
DTEND;VALUE=DATE-TIME:20240409T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/59
DESCRIPTION:Title: Superintegrability of matrix models and BPS algebras\nby Victor Mis
hnyakov (Nordita) as part of BIMSA Integrable Systems Seminar\n\n\nAbstrac
t\nThe prominent role of matrix models in physics and mathematics is well
known. It is especially interesting that some of those models are exactly
solvable\, meaning the one can find explicit formulas for correlation func
tions. This phenomenon has also been called superintegrability of matrix m
odels. I will present some recent attempt to study it systematically and s
earch for its algebraic origins. It leads to an interesting connection wit
h the rapidly developing field of BPS algebras and their representations.\
n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glutsyuk Alexey (CNRS\, ENS de Lyon\; HSE University and IITP (Mos
cow))
DTSTART;VALUE=DATE-TIME:20240416T080000Z
DTEND;VALUE=DATE-TIME:20240416T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/60
DESCRIPTION:Title: Model of Josephson junction\, dynamical systems on $\\mathbb T^2$\, iso
monodromic deformations and Painleve 3 equations\nby Glutsyuk Alexey (
CNRS\, ENS de Lyon\; HSE University and IITP (Moscow)) as part of BIMSA In
tegrable Systems Seminar\n\n\nAbstract\nThe tunneling effect predicted by
B.Josephson (Nobel \nPrize\, 1973) concerns the Josephson junction: two
superconductors \nseparated by a narrow dielectric. It states existence o
f a supercurrent through it and equations governing it. The overdamped Jo
sephson junction \nis modeled by a family of differential equations on 2-
torus depending on 3\n parameters: $B$ (abscissa)\, $A$ (ordinate)\, \n$\
\omega$ (frequency). We study its \nrotation number $\\rho(B\,A\;\\omega)$
\nas a function of $(B\,A)$ with fixed $\\omega$. \nThe phase-lock areas
are those level sets $L_r:=\\{\\rho=r\\}$ that have non-empty \ninterior
s. They exist only for integer rotation number values $r$: this is the ro
tation number quantization effect discovered by Buchstaber\, Karpov and Te
rtychnyi. They are \nanalogues of the famous Arnold tongues. \nEach $L_r$
is an infinite chain of domains going vertically to infinity \n and sep
arated by points called constrictions (expect for those with $A=0$). \n
See the phase-lock area portraits for $\\omega=2$\, 1\, 0.3 at the presen
tation.\n\nWe show that: 1) all constrictions in $L_r$ lie in the vertic
al line $\\{ B=\\omega r\\}$\; \n2) each constriction is positive\, that
is\, some its punctured neighborhood in \nthe vertical line lies in $\\op
eratorname{Int}(L_r)$. These results\, obtained in collaboration with Yuli
a Bibilo\, confirm experiences of physicists (pictures from physical books
of 1970-th) \nand two mathematical conjectures.\n\nThe proof uses an equ
ivalent description of model by linear systems of differential equations
on $\\oc$ (found by Buchstaber\, Karpov and Tertychnyi)\, their isomono
dromic deformations described by \nPainleve 3 equations and methods o
f the theory of slow-fast systems.\n\nIf the time allows we will discuss
new results and open questions.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuantong Qu (Nottingham University)
DTSTART;VALUE=DATE-TIME:20240423T080000Z
DTEND;VALUE=DATE-TIME:20240423T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/61
DESCRIPTION:Title: Special functions over finite Chevalley groups\nby Xuantong Qu (Not
tingham University) as part of BIMSA Integrable Systems Seminar\n\n\nAbstr
act\nMany special functions appearing in the study of integrable systems h
ave their finite field counterparts with extensive connections with number
theory and algebraic geometry. For instance\, it is well known that Gauss
sums are finite field analogues of Gamma-functions and Kloosterman sums a
re finite field analogues of Bessel functions. In this talk I will present
a new approach of studying certain special functions over finite fields u
sing representation theory of finite Chevalley groups. Namely\, I will fir
st define finite field analogues of Gamma-functions and Whittaker function
s and then identify them as matrix elements of representations of (subgrou
ps of) general linear groups over a finite field and compare them with the
ir counterparts defined over real groups.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luyao Wang (School of Mathematical Sciences\, Capital Normal Unive
rsity)
DTSTART;VALUE=DATE-TIME:20240402T080000Z
DTEND;VALUE=DATE-TIME:20240402T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/62
DESCRIPTION:Title: W-representation for multi-character partition function\nby Luyao W
ang (School of Mathematical Sciences\, Capital Normal University) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe discuss several resu
lts on work in collaboration (with V.Mishnyakov\, A.Popolitov\, F.Liu\, R.
Wang and with B. Kang\, K.Wu\, W.Z. Zhao).\nWe construct W-representations
for multi-character expansions\, which involve a generic number of sets o
f time variables. We propose integral representations for such kind of par
tition functions which are given by tensor models and multi-matrix models
with multi-trace couplings. In addition\, we present the W-representation
for a two-tensor model with order-3. We derive the compact expressions of
correlators from the W-representation\, and analyze the free energy in the
large N limit. By establishing the correspondence between the two-color D
yck order in Fredkin spin chain and the tree operator on the ring\, we pro
ve that the entanglement scaling of Fredkin spin chain beyond the logarith
mic scaling in ordinary critical systems.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen-Li Yang (Physics School\, Northwest University\, Xian)
DTSTART;VALUE=DATE-TIME:20240507T080000Z
DTEND;VALUE=DATE-TIME:20240507T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/63
DESCRIPTION:Title: Off-diagonal Bethe ansatz approach to quantum integrable models\nby
Wen-Li Yang (Physics School\, Northwest University\, Xian) as part of BIM
SA Integrable Systems Seminar\n\n\nAbstract\nApplying the recent developed
method-the off-diagonal Bethe ansatz method\, we construct the exact solu
tions of the Heisenberg spin chain with various boundary conditions. The r
esults allow us to calculate the boundary energy of the system in the ther
modynamic limit. The method used here can be generalized to study the ther
modynamic properties and boundary energy of other high rank models with no
n-diagonal boundary fields.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masashi Hamanaka (Nagoya University)
DTSTART;VALUE=DATE-TIME:20240521T080000Z
DTEND;VALUE=DATE-TIME:20240521T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/65
DESCRIPTION:Title: Anti-Self-Dual Yang-Mills Equations and a Unification of Integrable Sys
tems\nby Masashi Hamanaka (Nagoya University) as part of BIMSA Integra
ble Systems Seminar\n\n\nAbstract\nAnti-self-dual Yang-Mills (ASDYM) equat
ions have played important roles in quantum field theory (QFT)\, geometry
and integrable systems for more than 50 years. In particular\, instantons\
, global solutions of them\, have revealed nonperturbative aspects of QFT
['t Hooft\,...] and have given a new insight into the study of the four-di
mensional geometry [Donaldson]. Furthermore\, it is well known as the Ward
conjecture that the ASDYM equations can be reduced to many integrable sys
tems\, such as the KdV eq. and Toda eq. Integrability aspects of them can
be understood from the viewpoint of the twistor theory [Mason-Woodhouse\,.
..]. The ASDYM equation is realized as the equation of motion of the four-
dimensional Wess-Zumino-Witten (4dWZW) model in Yang's form. The 4dWZW mo
del is analogous to the two dimensional WZW model and possesses aspects of
conformal field theory and twistor theory [Losev-Moore-Nekrasov-Shatashvi
li\,...]. \n\nOn the other hand\, 4d Chern-Simons (CS) theory has connecti
ons to many solvable models such as spin chains and principal chiral model
s [Costello-Witten-Yamazaki\, ...]. These two theories (4dCS and 4dWZW) ha
ve been derived from a 6dCS theory like a ``double fibration'' [Costello\,
Bittleston-Skinner].\n\nThis suggests a nontrivial duality correspondence
between the 4dWZW model and the 4dCS theory. \nWe note that the Ward conj
ecture holds mostly in the split signature (+\,+\,−\,−) and then the 4
dWZW model describes the open N=2 string theory in the four-dimensional sp
ace-time. Hence a unified theory of integrable systems (6dCS-->4dCS/4dWZW)
can be proposed in this context with the split signature. \n\nIn this tal
k\, I would like to discuss integrability aspects of the ASDYM equation an
d construct soliton/instanton solutions of it by the Darboux/ADHM procedur
es\, respectively. We calculate the 4dWZW action density of the solutions
and found that the soliton solutions behaves as the KP-type solitons\, tha
t is\, the one-soliton solution has localized action (energy) density on a
3d hyperplane in 4-dimensions (soliton wall) and the N-soliton solution d
escribes N intersecting soliton walls with phase shifts. Our soliton solut
ions would describe a new-type of physical objects (3-brane) in the N=2 st
ring theory. If time permits\, I would mention reduction to lower-dimensio
ns and extension to noncommutative spaces. \n\nThis talk is based on our w
orks: [arXiv:2212.11800\, 2106.01353\, 2004.09248\, 2004.01718] and forthc
oming papers.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Chalykh (University of Leeds)
DTSTART;VALUE=DATE-TIME:20240416T092000Z
DTEND;VALUE=DATE-TIME:20240416T102000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/66
DESCRIPTION:Title: Elliptic complex reflection groups and Seiberg–Witten integrable syst
ems\nby Oleg Chalykh (University of Leeds) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nFor any abelian variety $X$ with an action
of a finite complex reflection group $W$\, Etingof\, Felder\, Ma and Vese
lov constructed a family of integrable systems on $T^*X$. When $X$ is a pr
oduct of $n$ copies of an elliptic curve $E$ and $W=S_n$\, this reproduces
the usual elliptic Calogero-Moser system. Recently\, together with Ph
ilip Argyres (Cincinnati) and Yongchao Lü (KIAS)\, we proposed that many
of these integrable systems at the classical level can be interpreted as S
eiberg-Witten integrable systems of certain supersymmetric quantum f
ield theories. I will describe our progress in understanding this connecti
on for the case $X=E^n$ where $E$ is an elliptic curve with the symmetry g
roup $Z_m$ (of order $m=2\,3\,4\,6$)\, and $W$ is the wreath product of $Z
_m$ and $S_n$. I will mostly talk about $n=1$ case\, which is already rath
er interesting. Based on: arXiv 2309.12760.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Veselov (Loughborough\, UK)
DTSTART;VALUE=DATE-TIME:20240521T092000Z
DTEND;VALUE=DATE-TIME:20240521T102000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/67
DESCRIPTION:Title: Delay Painleve-I equation and Masur-Veech volumes\nby Alexander Ves
elov (Loughborough\, UK) as part of BIMSA Integrable Systems Seminar\n\n\n
Abstract\nThe subject of the talk is the delay version of the Painleve-I e
quation obtained as a delay periodic reduction of Shabat's dressing chain.
We study the formal entire solutions to this equation and introduce a new
family of interesting polynomials (called Bernoulli-Catalan polynomials).
Using the recent results by Di Yang\, Don Zagier and Youjin Zhang\, we ap
ply the theory of these polynomials to the problem of calculation of the M
asur-Veech volumes of the moduli spaces of meromorphic quadratic different
ials.\n \nThe talk is based on a joint work with John Gibbons and Alex St
okes.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Sechin (BIMSA\, China)
DTSTART;VALUE=DATE-TIME:20240604T080000Z
DTEND;VALUE=DATE-TIME:20240604T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/68
DESCRIPTION:Title: Ruijsenaars duality for B\, C\, D Toda chains\nby Ivan Sechin (BIMS
A\, China) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe u
se the Hamiltonian reduction method to construct the Ruijsenaars dual syst
ems to generalized Toda chains associated with the classical Lie algebras
of types $B$\,$C$\,$D$. The dual systems turn out to be the $B$\,$C$ and $
D$ analogues of the rational Goldfish model\, which is\, as in the type $A
$ case\, the strong coupling limit of rational Ruijsenaars systems. We exp
lain how both types of systems emerge in the reduction of the cotangent bu
ndle of a Lie group and provide the formulae for dual Hamiltonians. We com
pute explicitly the higher Hamiltonians of Goldfish models using the Cauch
y-Binet theorem. \n\nJoint work with Mikhail Vasilev\, arXiv:2405.08620.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Feher (University of Szeged and Wigner Research Centre for
Physics\, Hungary)
DTSTART;VALUE=DATE-TIME:20240611T080000Z
DTEND;VALUE=DATE-TIME:20240611T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/69
DESCRIPTION:Title: Bi-Hamiltonian structures of integrable many-body models from Poisson r
eduction\nby Laszlo Feher (University of Szeged and Wigner Research Ce
ntre for Physics\, Hungary) as part of BIMSA Integrable Systems Seminar\n\
n\nAbstract\nWe review our results on bi-Hamiltonian structures of trigono
metric spin Sutherland\nmodels built on collective spin variables. Our bas
ic observation was that the cotangent\nbundle $T^∗U(n)$ and its holomorp
hic analogue $T^∗GL(n\,\\mathbb C)$\, as well as $T^∗GL(n\,\\mathbb C)
_{\\mathbb R}$\, carry\na natural quadratic Poisson bracket\, which is com
patible with the canonical linear one.\nThe quadratic bracket arises by ch
ange of variables and analytic continuation from\nan associated Heisenberg
double. Then\, the reductions of $T^∗U(n)$ and $T^∗GL(n\,\\mathbb C)$
by\nthe conjugation actions of the corresponding groups lead to the real
and holomorphic\nspin Sutherland models\, respectively\, equipped with a b
i-Hamiltonian structure. The\nreduction of $T^∗GL(n\,\\mathbb C)_{\\math
bb R}$ by the group $U(n) \\times U(n)$ gives a generalized Sutherland\nmo
del coupled to two $u(n)^∗$-valued spins. We also show that a bi-Hamilto
nian structure\non the associative algebra $gl(n\,\\mathbb R)$ that appear
ed in the context of Toda models can be\ninterpreted as the quotient of co
mpatible Poisson brackets on $T^∗GL(n\,\\mathbb R)$. Before our\nwork\,
all these reductions were studied using the canonical Poisson structures o
f the\ncotangent bundles\, without realizing the bi-Hamiltonian aspect.\n\
nReferences\n\n[1] L. Feher\, Reduction of a bi-Hamiltonian hierarchy on $
T^∗U(n)$ to spin Ruijsenaars–\nSutherland models\, Lett. Math. Phys. 1
10\, 1057-1079 (2020).\n\n[2] L. Feher\, Bi-Hamiltonian structure of spin
Sutherland models: the holomorphic case\,\nAnn. Henri Poincar´e 22\, 4063
-4085 (2021).\n\n[3] L. Feher\, Bi-Hamiltonian structure of Sutherland mod
els coupled to two $u(n)^∗$-valued\nspins from Poisson reduction\, Nonli
nearity 35\, 2971-3003 (2022).\n\n[4] L. Feher and B. Juhasz\, A note on q
uadratic Poisson brackets on $gl(n\,\\mathbb R)$ related to\nToda lattices
\, Lett. Math. Phys. 112:45 (2022).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Khoroshkin (HSE University)
DTSTART;VALUE=DATE-TIME:20241008T080000Z
DTEND;VALUE=DATE-TIME:20241008T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/70
DESCRIPTION:Title: Ruijsenaars spectral transform\nby Sergey Khoroshkin (HSE Univers
ity) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nRecent suc
cess in the study of Baxter $Q$ operators in Ruijsenaars \nhyperbolic syst
em led to establishing\, besides of bispectral duality\, of \nthe duali
ty concerning reflection of the coupling constant. It \nalso gives a way
to prove orthogonality and completeness of the wave \nfunctions. The corr
esponding integral transform\, defined for complex valued parameters\,\nca
n be regarded as a generalization of Laplace transform. We prove an anal
og of classical inversion\nformula and apply it for establishing $L_2$ iso
morphisms of Ruijsenaars spectral transform in 4 regimes of unitarity of
the system.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filipp Uvarov (Skoltech\, HSE University)
DTSTART;VALUE=DATE-TIME:20241029T080000Z
DTEND;VALUE=DATE-TIME:20241029T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/71
DESCRIPTION:Title: Deligne's category\, monodromy-free pseudo-differential operators and G
audin model for the Lie superalgebra $gl(m|n)$.\nby Filipp Uvarov (Sko
ltech\, HSE University) as part of BIMSA Integrable Systems Seminar\n\nInt
eractive livestream: https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LWTN
vUmdqL0g1QUxJMFNVZz09\nPassword hint: BIMSA\nView-only livestream: https:/
/youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij\n\nAbstract\
nThe Deligne's category is a formal way to define an interpolation of the
category of finite-dimensional representations of the Lie group $GL(n)$ to
any complex number $n$. It is used in various constructions\, which all t
ogether can be named as representation theory in complex rank. In the talk
\, I will present one of such constructions\, namely\, the interpolation o
f the algebra of higher Gaudin Hamiltonians (the Bethe algebra) associated
with the Lie algebra $gl(n)$.\n \nOne can also interpolate monodromy-free
differential operators of order $n$ desribing eigenvectors of Gaudin Hami
ltonians\, obtaining "monodromy-free" pseudo-differential operators. In jo
int work with L. Rybnikov and B. Feigin arXiv:2304.04501\, we prove that t
he Bethe algebra in Deligne's category is isomorphic to the algebra of fun
ctions on certain pseudo-differential operators. Our work is motivated by
the Bethe ansatz conjecture for the case of Lie superalgebra $gl(m|n)$. Th
e conjecture says that eigenvectors in this case are described by ratios o
f differential operators of orders $m$ and $n$. We prove that such ratios
are "monodromy-free" pseudo-differential operators.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/71/
URL:https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LWTNvUmdqL0g1QUxJMFNV
Zz09
URL:https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Povolotsky (JINR Dubna)
DTSTART;VALUE=DATE-TIME:20241022T080000Z
DTEND;VALUE=DATE-TIME:20241022T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/72
DESCRIPTION:Title: Exact densities of clusters in critical percolation and of loops in O(1
) dense loop model on a cylinder of finite circumference.\nby Alexande
r Povolotsky (JINR Dubna) as part of BIMSA Integrable Systems Seminar\n\nI
nteractive livestream: https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LW
TNvUmdqL0g1QUxJMFNVZz09\nPassword hint: BIMSA\nView-only livestream: https
://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij\n\nAbstrac
t\nThe percolation problem provides one of the basic examples of phase tra
nsition and critical behavior manifested in the statistics of percolation
clusters. The critical bond percolation model on a square lattice is close
ly related to the $O(1)$ dense loop model\, which\, in turn\, can be mappe
d on the exactly solvable six-vertex model at special values of the Boltzm
ann weights\, known as the Razumov-Stroganov combinatorial point. This poi
nt is known for providing the possibility to obtain exact results in fini
te-size systems. I will review the latest results on calculating the exact
densities of percolation clusters in critical percolation\, as well as lo
ops in the $O(1$) dense loop model on an infinite cylinder of a finite ci
rcumference.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/72/
URL:https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LWTNvUmdqL0g1QUxJMFNV
Zz09
URL:https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Pribytok (BIMSA)
DTSTART;VALUE=DATE-TIME:20241015T080000Z
DTEND;VALUE=DATE-TIME:20241015T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/73
DESCRIPTION:Title: Superdeformed CP $\\sigma$-models\, RG-flow and Conformal limits\nb
y Anton Pribytok (BIMSA) as part of BIMSA Integrable Systems Seminar\n\nIn
teractive livestream: https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LWT
NvUmdqL0g1QUxJMFNVZz09\nPassword hint: BIMSA\nView-only livestream: https:
//youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij\n\nAbstract
\nWe prove that the supersymmetric deformed $\\mathbb{CP}^1$ sigma model (
the generalization of the Fateev-Onofri-Zamolodchikov model) admits an equ
ivalent description as a generalized Gross-Neveu model. This formalism is
useful for the study of renormalization properties and pa cheese freerticu
larly for calculation of the one- and two-loop $\\beta$-function. Remarkab
ly we find new Nahm-type conditions\, which guarantee renormalizability an
d supersymmetric invariance. We show that in the UV the superdeformed mode
l flows to the super-Thirring CFT\, for which we also develop a superspace
approach. It is then demonstrated that the super-Thirring model is equiva
lent to a sigma model with the cylinder $\\mathbb{R}\\times S^1$ target sp
ace by an explicit computation of the correlation functions on both sides.
Apart from that\, we observe that the original model has another interest
ing conformal limit\, given by the supercigar model\, for which we also fi
nd a chiral dual and explicitly demonstrate agreement of the four-point fu
nctions on both sides. In addition\, we investigate novel relations of our
construction through mirror symmetry and dimensional reduction\, which in
the framework of $\\sigma$-models on toric varieties maps to a class of $
\\mathcal{N}=2$ Liouville (Landau-Ginzburg class)\, as well as topological
theories in higher $D$.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/73/
URL:https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LWTNvUmdqL0g1QUxJMFNV
Zz09
URL:https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Gaiur (University of Geneva)
DTSTART;VALUE=DATE-TIME:20241112T080000Z
DTEND;VALUE=DATE-TIME:20241112T090000Z
DTSTAMP;VALUE=DATE-TIME:20241013T142816Z
UID:BIMSA-ISS/74
DESCRIPTION:by Ilia Gaiur (University of Geneva) as part of BIMSA Integrab
le Systems Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/87
392090711?pwd=MWNaSk1LWTNvUmdqL0g1QUxJMFNVZz09\nPassword hint: BIMSA\nView
-only livestream: https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklM
W2Ntkh9S3jij\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/74/
URL:https://us02web.zoom.us/j/87392090711?pwd=MWNaSk1LWTNvUmdqL0g1QUxJMFNV
Zz09
URL:https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij
END:VEVENT
END:VCALENDAR