BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Anton Nazarov (Saint Petersburg State University)
DTSTART:20230113T090000Z
DTEND:20230113T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/1
DESCRIPTION:Title: Skew Howe duality\, limit shapes of Young diagrams and universal
fluctuations\nby Anton Nazarov (Saint Petersburg State University) as
part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nSchur-Weyl\, Howe
and skew Howe dualities in representation theory of groups lead to multipl
icity-free decompositions of certain spaces into irreducible representatio
ns and can be used to introduce probability measures on Young diagrams tha
t parameterize irreducible representations. It is interesting to study the
behavior of such measures in the limit\, when groups become infinite or i
nfinite-dimensional. Schur-Weyl duality and GL(n)-GL(k) Howe duality are r
elated 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) Howe duality was considered by Gravner\, Tracy and Widom\, who were in
terested in the local fluctuations of the diagrams\, the limit shapes were
studied Sniady and Panova. They demonstrated that results by Romik and Pi
ttel on limit shapes of rectangular Young tableaux are applicable in this
case.\nWe consider skew Howe dualities for the actions of classical Lie gr
oup pairs: GL(n)-GL(k)\, Sp(2n)-Sp(2k)\, SO(2n)-O(2k) on the exterior alge
bras. We describe explicitly the limit shapes for probability measures def
ined by the ratios of dimensions and demonstrate that they are essentially
the same for all classical Lie groups. Using orthogonal polynomials we pr
ove central limit theorem for global fluctuations around these limit shape
s. Using free-fermionic representation we study local fluctuations for mor
e general measures given by ratios of representation characters for skew G
L(n)-GL(k) Howe duality. These fluctuations are described by Tracy-Widom d
istribution in the generic case and in the corner by a certain discrete di
stribution\, first obtained in papers by Gravner\, Tracy and Widom. Study
of local fluctuations for other classical series remains an open problem\,
but we present numerical evidence that these distributions are universal.
\n\nBased on joint works with Dan Betea\, Pavel Nikitin\, Olga Postnova\,\
nDaniil Sarafannikov and Travis Scrimshaw. See arXiv:2010.16383\,\n2111.12
426\, 2208.10331\, 2211.13728.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Talalaev (MSU\, YarSU\, ITEP)
DTSTART:20230120T090000Z
DTEND:20230120T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/2
DESCRIPTION:Title: The full Toda system\, QR decomposition and geometry of the flag
varieties\nby Dmitry Talalaev (MSU\, YarSU\, ITEP) as part of BIMSA In
tegrable Systems Seminar\n\n\nAbstract\nThe full Toda system is a generali
zation of an open Toda chain\, which is one of the archetypal examples of
integrable systems. The open Toda chain illustrates the connection of the
theory of integrable systems with the theory of Lie algebras and Lie group
s\, is a representative of the Adler-Kostant-Symes scheme for constructing
and solving such systems. Until recently\, only some of the results from
this list were known for the full Toda system. I will talk about the const
ruction\, the commutative family\, quantization and solution of the full T
oda system by the QR decomposition method\, as well as about the applicati
on of this system to the geometry of flag vaireties. The material of my ta
lk is based on several joint works with A. Sorin\, Yu. Chernyakov and G. S
harygin.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Yakubovich (Saint Petersburg State University)
DTSTART:20230127T090000Z
DTEND:20230127T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/3
DESCRIPTION:Title: Random growth of Young diagrams with uniform marginals\nby Yu
ri Yakubovich (Saint Petersburg State University) as part of BIMSA Integra
ble Systems Seminar\n\n\nAbstract\nMany (random) growth procedures for int
eger partitions/Young diagrams has been introduced\nin the literature and
intensively studied. The examples include Pitman's `Chinese restaurant'\nc
onstruction\, Kerov's Plancherel growth and many others. These procedures
amount to\ninsertion of a new box to a Young diagram on each step\, follo
wing certain Markovian procedure.\nHowever\, no such procedure leading to
the uniform measure on partitions of $n$ after $n$\nsteps is known. I wil
l describe a Markiovian procedure of adding a rectangular block\nto a Youn
g diagram with the property that given the growing chain visits some level
$n$\, it\npasses through each partition of $n$ with equal probabilities\,
thus leading to the uniform\nmeasure on levels. I will explain connectio
ns to some classical probabilistic objects.\nAlso I plan to discuss some a
spects of asymptotic behavior of this Markov chain and explain\nwhy the li
mit shape is formed.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuancheng Xie (Peking University)
DTSTART:20230203T090000Z
DTEND:20230203T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/4
DESCRIPTION:Title: On the full Kostant-Toda lattice and the flag varieties\nby Y
uancheng Xie (Peking University) as part of BIMSA Integrable Systems Semin
ar\n\n\nAbstract\nIn 1967\, Japanese physicist Morikazu Toda proposed an i
ntegrable lattice model to\ndescribe motions of a chain of particles with
exponential interactions between nearest\nneighbors. Since then\, Toda lat
tice and its generalizations have become the test models\nfor various tech
niques and philosophies in integrable systems and wide connections are\nbu
ilt with many other branches of mathematics. In this talk\, I will charact
erize singular\nstructure of solutions of the so-called full Kostant-Toda
(f-KT) lattices defined on simple\nLie algebras in two different ways: thr
ough the τ-functions and through the Kowalevski-\nPainlevé analysis. Fix
ing 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 points in\nthe corresponding flag varieties.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masatoshi Noumi (Rikkyo University\, Tokyo\, Japan)
DTSTART:20230217T090000Z
DTEND:20230217T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/5
DESCRIPTION:Title: Elliptic van Diejen difference operators and elliptic hypergeomet
ric integrals of Selberg type\nby Masatoshi Noumi (Rikkyo University\,
Tokyo\, Japan) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\
nIn this talk\, I propose a class of eigenfunctions for the elliptic van D
iejen operators \n(Ruijsenaars operators of type BC) which are represented
by elliptic hypergeometric \nintegrals of Selberg type. They are construc
ted from simple seed eigenfunctions \nby integral transformations\, thanks
to gauge symmetries and kernel function identities \nof the van Diejen op
erators. \nBased on a collaboration with Farrokh Atai (University of Leed
s\, UK).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Bobrova (National Research University Higher School of Econo
mics)
DTSTART:20230224T090000Z
DTEND:20230224T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/6
DESCRIPTION:Title: Different approaches for constructing non-abelian Painlevé equat
ions\nby Irina Bobrova (National Research University Higher School of
Economics) 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 needs of modern quantum physics as well as by natural attempts of mat
hematicians to extend ‘’classical’’ structures to the non-commutat
ive case.\n\nIn this talk we will consider several approaches that are use
ful for detecting non-commutative analogs of the Painlevé equations. Name
ly\, the matrix Painlevé-Kovalevskaya test\, integrable non-abelian auxil
iary autonomous systems\, and infinite non-commutative Toda equations. All
of these methods allow us to find a finite list of non-abelian candidates
for such analogs. To provide their integrability\, one can present an iso
monodromic Lax pair.\n\nThis talk is based on a series of papers joint wit
h Vladimir Sokolov and on arXiv:2205.05107 joint with Vladimir Retakh\, Vl
adimir Rubtsov\, and Georgy Sharygin (publ. in J. Phys. A: Math. Theor.).\
n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Rybnikov (National Research University Higher School of Eco
nomics)
DTSTART:20230310T090000Z
DTEND:20230310T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/7
DESCRIPTION:Title: Bethe subalgebras and Kirillov-Reshetikhin crystals\nby Leoni
d Rybnikov (National Research University Higher School of Economics) as pa
rt of BIMSA Integrable Systems Seminar\n\n\nAbstract\nBethe subalgebras fo
rm a family of maximal commutative subalgebras of the Yangian of a simple
Lie algebra\, parametrized by regular elements of the corresponding adjoin
t Lie group. We introduce an affine (Kirillov-Reshetikhin) crystal structu
re on the set of eigenlines for a Bethe subalgebra in a representation of
the Yangian (under certain conditions on the representation\, satisfied by
all tensor products of Kirillov-Reshetikhin modules in type A). This help
s to describe the monodromy of solutions of Bethe ansatz for the correspon
ding XXX Heisenberg magnet chain. \n\nThis is a joint project with Inna Ma
shanova-Golikova and Vasily Krylov.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huijun Fan (School of Mathematical Sciences\, Peking University)
DTSTART:20230324T090000Z
DTEND:20230324T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/8
DESCRIPTION:Title: On the Geometry of Landau-Ginzburg Model\nby Huijun Fan (Scho
ol of Mathematical Sciences\, Peking University) as part of BIMSA Integrab
le Systems Seminar\n\n\nAbstract\nAn LG model (M\, f) is given by a noncom
pact complex manifold M and the\nholomorphic function f defined on it\, wh
ich is an important model in string theory.\nBecause of the mirror symmetr
y conjecture\, the research on the geometric structure and\nquantization t
heory of LG model has attracted more and more attention. Given a Calabi-\n
Yau (CY) manifold\, we can define Gromov-Witten theory (A theory) on it\,
and also study\nthe variation of Hodge structure on its mirror manifold (B
theory). Accordingly\, LG model\nincludes A theory - FJRW theory and Hodg
e structure variational theory.\nThis report starts with some examples\, g
ives the geometric and topological\ninformation contained by a LG model\,
and derives the relevant Witten equation\n(nonlinear) and Schrodinger equa
tion (linear). The study of the solution space of these\ntwo sets of equat
ions will lead to different quantization theories. Secondly\, we give our\
nrecent correspondence theorem of Hodge structures between LG model and CY
\nmanifold. Finally\, we will discuss some relevant issues.\n\nBio: Huijun
Fan is the director of the Key Laboratory of Mathematics and Applied\nMat
hematics of the Ministry of Education of Peking University and the deputy
director of\nthe Sino-Russian Math Center. He has won national outstanding
youth grant\, Changjiang\nDistinguished Professor of the Ministry of Educ
ation\, and the second prize of the National\nNatural Science Award. He is
the plenary speaker of the 2021 annual meeting of the\nChinese Mathematic
al Society.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Nikitin (BIMSA)
DTSTART:20230210T090000Z
DTEND:20230210T103000Z
DTSTAMP:20260404T094912Z
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\
nLocally semisimple algebras (LS-algebras) are inductive limits of semisim
ple algebras\, and can be fully characterized by their Bratteli diagrams (
$\\mathbb{N}$-graded graphs). (Finite) harmonic functions on Bratteli diag
rams are a standard tool in the representation theory of LS-algebras and s
emifinite harmonic functions are a natural generalization. We plan to give
an overview of the subject\, starting with the classical results for the
infinite symmetric group\, followed by the recent results for the infinite
symmetric inverse semigroup. Joint work with N.Safonkin\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay (BIMSA)
DTSTART:20230303T090000Z
DTEND:20230303T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/10
DESCRIPTION:Title: Geometry of Discrete Integrable Systems: QRT Maps and Discrete P
ainlevé Equations\nby Anton Dzhamay (BIMSA) as part of BIMSA Integrab
le Systems Seminar\n\n\nAbstract\nMany interesting examples of discrete in
tegrable 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 maps) and\nnon-autonomous (discrete Painlevé equations). We introduc
e some geometric tools to study these systems\, such as the blowup procedu
re to construct algebraic surfaces on which the mappings are regularized\,
linearization of the mapping on the Picard lattice of the surface and\, f
or discrete Painlevé equations\, the decomposition of the Picard lattice
into complementary pairs of the surface and symmetry sub-lattices and cons
truction of a birational representation of affine Weyl symmetry groups tha
t gives a complete algebraic description of our non-linear dynamic. \n\nTh
is talk is based on joint work with Stefan Carstea (Bucharest) and Tomoyuk
i\nTakenawa (Tokyo).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigori Olshanski (IITP\, Skoltech\, and HSE Univ.)
DTSTART:20230317T090000Z
DTEND:20230317T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/11
DESCRIPTION:Title: The centralizer construction and Yangian-type algebras\nby G
rigori Olshanski (IITP\, Skoltech\, and HSE Univ.) as part of BIMSA Integr
able Systems Seminar\n\n\nAbstract\nIn the 1980s\, Vladimir Drinfeld intro
duced and 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 curr
ents g[x]. The general definition of Yangian is radically simplified for
the classical series A\, and it is even more convenient to work with the r
eductive algebra g=gl(n).\n\nIn the same 1980s\, it was discovered that th
e Yangian Y(gl(n)) can be constructed in an alternative way\, starting fro
m some centralizers in the universal enveloping algebra U(gl(n+N)) and the
n letting N go to infinity. This "centralizer construction" was then exte
nded to the classical series B\, C\, D\, which lead to the so-called twist
ed Yangians. The theory that arose from this is presented in Alexander Mol
ev's book "Yangians and classical Lie algebras"\, Amer. Math. Soc.\, 2007.
\n\nI will report on the recent work arXiv:2208.04809\, where another vers
ion of the centralizer construction is proposed. It produces a new family
of algebras and reveals new effects and connections.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youjin Zhang (Tsinghua University)
DTSTART:20230421T090000Z
DTEND:20230421T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/12
DESCRIPTION:Title: Linear reciprocal transformations of bihamiltonian integrable hi
erarchies\nby Youjin Zhang (Tsinghua University) as part of BIMSA Inte
grable Systems Seminar\n\n\nAbstract\nFor an integrable hierarchy which po
ssesses a bihamiltonian structure with semisimple hydrodynamic limit\, we
prove that the linear reciprocal transformation with respect to any of its
symmetry transforms it to another bihamiltonian integrable hierarchy. Mor
eover\, we show that the central invariants of the bihamiltonian structure
are preserved under the reciprocal transformation. The main tools that we
use to obtain this result are the bihamiltonian and variational bihamilto
nian cohomologies defined for a bihamiltonian structure of hydrodynamic ty
pe. We also apply this result to study the problem of classification of bi
hamiltonian integrable hierarchies.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhe Sheng (Jilin University\, Changchun)
DTSTART:20230331T090000Z
DTEND:20230331T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/13
DESCRIPTION:Title: Rota-Baxter groups\, post-groups and related structures\nby
Yunhe Sheng (Jilin University\, Changchun) as part of BIMSA Integrable Sys
tems Seminar\n\n\nAbstract\nRota-Baxter operators on Lie algebras were fir
st studied by Belavin\, Drinfeld and Semenov-Tian-Shansky as operator form
s of the classical Yang-Baxter equation.\n\nAs a fundamental tool in study
ing integrable systems\, the factorization theorem of Lie groups by Semeno
v-Tian-Shansky was obtained by integrating a factorization of Lie algebras
from solutions of the modified Yang-Baxter equation. Integrating the Rota
-Baxter operators on Lie algebras\, we introduce the notion of Rota-Baxter
operators on Lie groups and more generally on groups. Then the factorizat
ion theorem can be achieved directly on groups. As the underlying struct
ures of Rota-Baxter operators on groups\, the notion of post-groups was in
troduced. The differentiation of post-Lie groups gives post-Lie algebras.
Post-groups are also related to Lie-Butcher groups\, and give rise to solu
tions of Yang-Baxter equations. \n\nThe talk is based on the joint work wi
th Chengming Bai\, Li Guo\, Honglei Lang and Rong Tang.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ievgen Makedonskyi (BIMSA)
DTSTART:20230407T090000Z
DTEND:20230407T103000Z
DTSTAMP:20260404T094912Z
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 stu
dy some natural representations of current Lie algebras $g\\otimes \\Bbbk[
t]$\, called Weyl modules. They are natural analogues of irreducible repre
sentations of simple Lie algebras. There are several current analogues of
classical theorems about Lie algebras where these modules «play role» of
irreducible modules. In my talk I will explain analogues of duality theor
ems\, namely Peter-Weyl theorem\, Schur-Weyl duality etc.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d’Angers\, ITTP Moscow and IGAP Tr
ieste)
DTSTART:20230414T090000Z
DTEND:20230414T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/15
DESCRIPTION:Title: Symplectic and Contact Geometry of Monge– Ampère equation: In
troduction and application\nby Vladimir Rubtsov (Université d’Anger
s\, ITTP Moscow and IGAP Trieste) as part of BIMSA Integrable Systems Semi
nar\n\n\nAbstract\nI am going to present an introduction into the geometri
c approach to Monge– Ampère operators and equations based on contact an
d symplectic structures of cotangent and the 1st jet bundles of a smooth m
anifold. This approach was developed by V. Lychagin and goes back to the i
deas of E.Cartan and his successor T. Lepage. I shall try to make my talk
self-contained. I also plan to discuss various applications and links with
important geometric structures.\n
LOCATION:https://stable.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:20230519T090000Z
DTEND:20230519T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/16
DESCRIPTION:Title: Generalized Nijenhuis geometry and applications to Hamiltonian i
ntegrable 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 ne
w\, infinite family of tensor fields\, whose first representatives are the
classical Nijenhuis and Haantjes tensors. We prove that the vanishing of
a suitable higher-level Haantjes torsion is a sufficient condition for the
integrability of the eigen-distributions of an operator field on a differ
entiable manifold. This new condition\, which does not require the explici
t knowledge of the spectral properties of the considered operator\, genera
lizes the celebrated Haantjes theorem\, because it provides us with an eff
ective integrability criterion applicable to the generic case of non-Nijen
huis and non-Haantjes tensors. \nWe also propose a tensorial approach to t
he theory of classical Hamiltonian integrable systems\, based on the geome
try of Haantjes tensors. We introduce the family of symplectic-Haantjes ma
nifolds as a natural setting where the notion of integrability can be form
ulated. In particular\, the theory of separation of variables for classica
l Hamiltonian systems can also be formulated in the context of our new geo
metric structures.\n\nReferences:\nP. Tempesta\, G. Tondo\, Contemporary M
athematics\, AMS (2023) (to appear)\nD. Reyes\, P. Tempesta\, G. Tondo\, J
. Nonlinear Science 33\, 35 (2023)\nP. Tempesta\, G. Tondo\, Communication
s in Mathematical Physics 389\, 1647-1671 (2022)\nP. Tempesta\, G. Tondo\,
Annali Mat. Pura Appl. 201\, 57-90 (2022)\nP. Tempesta\, G. Tondo\, J. Ge
ometry and Physics 160\, 103968 (2021)\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto D'Onofrio (Università Bicocca and University of Surrey)
DTSTART:20230428T090000Z
DTEND:20230428T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/17
DESCRIPTION:Title: Singularities in geophysical fluid dynamics through Monge-Ampèr
e geometry\nby Roberto D'Onofrio (Università Bicocca and University o
f Surrey) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe s
emigeostrophic 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. Thi
s talk presents a new approach to classifying these singular structures us
ing the geometry of Monge-Ampère equations.\n\nIn the geometrical view\,
solutions are understood as Lagrangian submanifolds of a suitably defined
phase space equipped with a pseudo-Riemannian metric. We show the interpla
y between solution singularities\, elliptic-hyperbolic transitions of the
Monge-Ampère operator\, and the degeneracies of the metric on a few examp
les\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunfeng Jiang (Southeast University\, Nanjing)
DTSTART:20230526T090000Z
DTEND:20230526T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/18
DESCRIPTION:Title: Spin-s rational Q-system\nby Yunfeng Jiang (Southeast Univer
sity\, Nanjing) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\
nRational Q-system is an efficient method for solving Bethe ansatz equatio
ns (BAE). One important feature of this method is that\, unlike solving BA
E directly\, it gives only physical solutions of BAE. Therefore\, it is in
timately related to the completeness problem of Bethe ansatz. In this talk
\, I will first introduce the rational Q-system and discuss the completene
ss problem of the spin-$1/2$ Heisenberg spin chain. Then I will move to th
e discussion of the spin-$s$ Heisenberg spin chain where the situation is
more complicated. The key new feature here is that repeated roots are allo
wed. I will present the rational Q-system for the higher spin models and d
iscuss the completeness problem for the spin-$s$ Heisenberg spin chain. Th
e solution of the proposed Q-system gives precisely the all the physical s
olutions required by completeness of Bethe ansatz.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuyuki Kawahigashi (University of Tokyo)
DTSTART:20230616T090000Z
DTEND:20230616T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/19
DESCRIPTION:Title: $\\alpha$-induction\, tensor categories and operator algebras\nby Yasuyuki Kawahigashi (University of Tokyo) as part of BIMSA Integrab
le Systems Seminar\n\n\nAbstract\nTensor categories play an important role
in theory of subfactors in\noperator algebras in connection to conformal
field theory and condensed\nmatter physics. A certain induction procedure
called $\\alpha$-induction has\nbeen studied as a quantum version of the
classical induction in group\nrepresentation theory. I will present this
without assuming knowledge on\noperator algebras.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Matushko (Steklov MI RAS\, Moscow)
DTSTART:20230505T090000Z
DTEND:20230505T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/20
DESCRIPTION:Title: Anisotropic spin generalization of elliptic Ruijsenaars-Macdonal
d operators and related integrable long-range spin chains\nby Maria Ma
tushko (Steklov MI RAS\, Moscow) as part of BIMSA Integrable Systems Semin
ar\n\n\nAbstract\nWe propose commuting set of matrix-valued difference ope
rators in terms of the elliptic Baxter-Belavin R-matrix in the fundamental
representation of GL(M). In the scalar case M = 1 these operators are the
elliptic Ruijsenaars-Macdonald operators\, while in the general case they
can be viewed as anisotropic versions of the quantum spin Ruijsenaars Ham
iltonians. We show that commutativity of the operators for any M is equiva
lent to a set of R-matrix identities and prove them for the elliptic Baxte
r-Belavin R-matrix. We show that the Polychronakos freezing trick can be a
pplied to this model. It provides the commuting set of Hamiltonians for lo
ng-range 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:2201.05944 arXiv:2202.01177\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Roulstone (University of Surrey Guildford)
DTSTART:20230602T090000Z
DTEND:20230602T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/21
DESCRIPTION:Title: Applications of symplectic geometry in fluid dynamics\nby Ia
n Roulstone (University of Surrey Guildford) as part of BIMSA Integrable S
ystems Seminar\n\n\nAbstract\nWe present a brief history of the applicatio
n of methods from symplectic geometry to fluid dynamics\, and to geophysic
al systems in particular. The material will cover both analytical and nume
rical applications\, and emphasize the importance of geometric concepts in
operational weather prediction models. This seminar relates to others giv
en recently in this series by Rubtsov and by D'Onofrio\, and there will be
a focus on the role of partial differential equations of Monge—Ampere t
ype.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Sergeev (Australian National University and University of C
anberra\, Canberra)
DTSTART:20230609T090000Z
DTEND:20230609T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/22
DESCRIPTION:Title: Spectral equations for a class of entire $Q$-operators\nby S
ergey Sergeev (Australian National University and University of Canberra\,
Canberra) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nTher
e is a class of $\\mathcal{U}_q(\\widehat{sl}_2)$ models models where the
infinite dimensional evaluation representations lead to Baxter's $TQ=Q+Q$
equation where $Q$ is an entire function rather than a polynomial. I will
give a general introduction to the method of solving the Baxter equation i
n this case.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Lamers (Institut de Physique Théorique (IPhT))
DTSTART:20230512T090000Z
DTEND:20230512T103000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/23
DESCRIPTION:Title: Bethe ansatz inside Calogero--Sutherland models\nby Jules La
mers (Institut de Physique Théorique (IPhT)) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nThe Haldane--Shastry spin chain has long-ra
nge interactions and remarkable properties including Yangian symmetry at f
inite length and explicit highest-weight wave functions featuring Jack pol
ynomials. This stems from the trigonometric spin-Calogero--Sutherland mode
l\, which is intimately related to affine Hecke algebras\, already enjoys
these properties from affine Schur–Weyl duality and reduces to the Halda
ne--Shastry chain in the ‘freezing’ limit. I will present some new res
ults for these models\, including Heisenberg-like symmetries whose spectru
m can be characterised by Bethe ansatz.\n\nBased on recent work with D. Se
rban and ongoing work with G. Ferrando\, F. Levkovich-Maslyuk and D. Serba
n.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriy G. Bardakov (Sobolev Institute of Mathematics\, Novosibirs
k\, Russia)
DTSTART:20230919T080000Z
DTEND:20230919T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/24
DESCRIPTION:Title: Yang-Baxter equation\, relative Rota-Baxter operators and skew b
races\nby Valeriy G. Bardakov (Sobolev Institute of Mathematics\, Novo
sibirsk\, Russia) as part of BIMSA Integrable Systems Seminar\n\n\nAbstrac
t\nThe Yang-Baxter equation is a fundamental equation in mathematical\nph
ysics and statistical mechanics\, it has connections with knot\ntheory\,
braid theory and some algebraic systems. \n\nIn my talk I recall the defin
ition of the Yang-Baxter equation\, Braid equation\, skew brace and rela
tive Rota-Baxter operators on group. Further we discuss connections betw
een these objects\, suggest some way for construction of relative Rota-Bax
ter operators\, using known Rota-Baxter operators\, describe some of these
operators on 2-step nilpotent groups and construct some solutions to the
Yang-Baxter 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://stable.researchseminars.org/talk/BIMSA-ISS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Pochinka (HSE University)
DTSTART:20231017T080000Z
DTEND:20231017T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/25
DESCRIPTION:Title: Andronov School of Nonlinear Oscillations\nby Olga Pochinka
(HSE University) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract
\nAndronov's school began to take shape in 1931\, when Alexander Alexandro
vich himself\, together with his wife E.A. Leontovich\, moved from Moscow
to Nizhny Novgorod. \nBy the time of the move\, A.A. Andronov was an estab
lished scientist. Even then\, he introduced a number of new concepts into
science\, including self-oscillations\, concepts of the roughness of the s
ystem\, the bifurcation value of the parameter\, the phase portrait\, and
so on. This is a long-lived school in which a unified scientific program h
as been actively developed by several generations of scientists.\nIn my re
port\, I will touch upon the scientific direction of the school\, which is
associated with rough (structurally stable) dynamic systems. The simples
t of them - "Morse-Smale systems" got their name after the publication of
S. Smale's work "On gradient dynamical system // Ann. Math. 74\, 1961\, P.
199-206". He introduced a class of flows on manifolds of arbitrary dimensi
on 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 validity of inequalities similar to Morse inequalities for non-degene
rate functions\, after which such flows were called Morse-Smale flows. S.
Smale considered it extremely important to study such flows\, since he ass
umed that\, 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 multidimensio
nal structurally stable world is much wider\, and the Morse-Smale systems
represent only its regular part - structurally stable systems with a non-w
andering set consisting of a finite number of orbits. Due to the close con
nection of Morse-Smale systems with the carrier manifold\, various topolog
ical objects\, including wild ones\, are realized as invariant subsets of
such systems. This leads to a wide variety of Morse-Smale systems (especia
lly on multidimensional manifolds) and\, accordingly\, complicates their t
opological classification.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Appel (Dipartimento SMFI Università di Parma)
DTSTART:20231024T080000Z
DTEND:20231024T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/26
DESCRIPTION:Title: The R-matrix of the affine Yangian\nby Andrea Appel (Diparti
mento SMFI Università di Parma) as part of BIMSA Integrable Systems Semin
ar\n\n\nAbstract\nLet $\\mathfrak{g}$ be an affine Lie algebra with associ
ated Yangian $Y_h(\\mathfrak{g})$.\nWe prove the existence of two meromorp
hic $R$--matrices associated to any pair of representations of $Y_h(\\math
frak{g})$ in the category $\\mathcal{O}$. \nThey are related by a unitary
constraint and constructed as products of the form $\\mathcal R^{\\uparrow
/\\downarrow}(s)=\\mathcal R^+(s)\\cdot\\mathcal R^{0\,\\uparrow/\\downarr
ow}(s)\\cdot\\mathcal R^-(s)$\, where $\\mathcal R^+(s) = \\mathcal R^-_{2
1}(-s)^{-1}$. \nThe factors $\\mathcal R^{0\,\\uparrow/\\downarrow}(s)$ ar
e meromorphic\, 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
difference equation\nwhose difference operator is given in terms of the $q
$--Cartan matrix of $\\mathfrak g$.\nThe regularisation of this difference
equation gives rise to \n$\\mathcal R^{0\,\\uparrow/\\downarrow}(s)$ as
the\nexponentials of the two canonical fundamental solutions.\nThe second
key ingredient is\na higher order analogue of the adjoint action of \nthe
affine Cartan subalgebra $\\mathfrak h\\subset\\mathfrak g$ on $Y_h(\\math
frak g)$. This action has no classical counterpart\, and produces\na syste
m of linear equations from which $\\mathcal R^-(s)$\nis recovered as the u
nique solution. \nMoreover\, we show that both $\\mathcal R^{\\uparrow/\\d
ownarrow}(s)$\ngive rise to the same rational $R$--matrix \non the tensor
product of any two highest--weight representations.\n
LOCATION:https://stable.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:20230926T080000Z
DTEND:20230926T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/27
DESCRIPTION:Title: Yangian-type algebras and double Poisson brackets.\nby Nikit
a Safonkin (University of Reims Champagne-Ardenne\, Reims & Skolkovo Insti
tute of Science and Technology\, Moscow) as part of BIMSA Integrable Syste
ms Seminar\n\n\nAbstract\nLet A be an arbitrary associative algebra. With
the help of Olshanski’s centralizer construction one can define a sequen
ce Y_1(A)\, Y_2(A)\,... of "Yangian-type algebras" (they possess a numbe
r of properties of the Yangians of series A). I will discuss a link betwee
n these Yangian-type algebras and a class of double Poisson brackets on fr
ee associative algebras. The talk is based on the joint paper with Grigori
Olshanski arXiv:2308.13325.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis Napper (University of Surrey)
DTSTART:20231121T080000Z
DTEND:20231121T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/28
DESCRIPTION:Title: (Higher) Monge—Ampere Geometry of the Navier—Stokes Equation
s\nby Lewis Napper (University of Surrey) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nThe Poisson equation for the pressure of a
homogeneous\, incompressible Navier--Stokes flow is a key diagnostic relat
ion for understanding the formation of vortices in turbulence. Building on
the observation that\, in two dimensions\, the aforementioned equation is
a Monge--Amp{\\`e}re equation for the stream function\, this talk introdu
ces a framework for studying this relation from the perspective of (multi-
)symplectic geometry.\n\nWhile reviewing the geometry of Monge--Amp{\\`e}r
e equations presented by Rubtsov\, D'Onofrio\, and Roulstone in earlier se
minars of this series\, we demonstrate how an associated metric on the pha
se space of a two-dimensional fluid flow encodes the dominance of vorticit
y and strain. We then discuss how multi-symplectic geometry may be used to
generalise to fluid flows on Riemannian manifolds in higher dimensions\,
culminating in a Weiss--Okubo-type criterion in these cases. Throughout\,
we make comments on how the signatures and curvatures of our structures ma
y be interpreted in terms of the geometric and topological properties of v
ortices.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Kazakov (HSE University)
DTSTART:20231010T080000Z
DTEND:20231010T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/29
DESCRIPTION:Title: On robust chaos\nby Alexey Kazakov (HSE University) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nOne of the most fundame
ntal problems in multidimensional chaos theory is the study of strange att
ractors which are robustly chaotic (i.e.\, they remain chaotic after small
perturbations of the system). It was hypothesized in [1] that the robustn
ess of chaoticity is equivalent to the pseudohyperbolicity of the attracto
r. Pseudohyperbolicity is a generalization of hyperbolicity. The main char
acteristic property of a pseudohyperbolic attractor is that each of its or
bits has a positive maximal Lyapunov exponent. In addition\, this property
must be preserved under small perturbations. The foundations of the theor
y of pseudohyperbolic attractors were laid by Turaev and Shilnikov [2\,3]\
, who showed that the class of pseudohyperbolic attractors\, besides the c
lassical Lorenz and hyperbolic attractors\, also includes wild attractors
which contain orbits with a homoclinic tangency.\n\nIn this talk we
give a review on the theory of pseudohyperbolic attractors arising in both
systems with continuous and discrete time. At first\, we explain what is
meant under pseudohyperbolic attractors. Then\, we describe our methods fo
r the pseudohyperbolicity verification. We demonstrate the applicability o
f these methods for several well-known systems (with both pseudohyperbolic
and non-pseudohyperbolic attractors). Finally\, we present new examples o
f pseudohyperbolic 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.\, & Shiln
ikov\, L. P. (1998). An example of a wild strange attractor. Sbornik: Math
ematics\, 189(2)\, 291.\n[3] Turaev\, D. V.\, & Shilnikov\, L. P. (2008\,
February). Pseudohyperbolicity and the problem on periodic perturbations o
f Lorenz-type attractors. In Doklady Mathematics (Vol. 77\, pp. 17-21).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Basalaev (HSE University)
DTSTART:20231107T080000Z
DTEND:20231107T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/30
DESCRIPTION:Title: Integrable systems of A\,D and B-type Dubrovin-Frobenius manifol
ds\nby Alexey Basalaev (HSE University) as part of BIMSA Integrable Sy
stems Seminar\n\n\nAbstract\nGiven a series of WDVV or open-WDVV equation
solutions satisfying the certain stabilization conditions\, one can constr
uct an infinite system of commuting partial differential equations.\nWe il
lustrate these fact on the examples of A and D type Dubrovin--Frobenius ma
nifolds and their "open extensions". These give KP\, a reduction of a 2-c
omponent BKP and 2D Toda hierarchies respectively. Following D.Zuo to a B_
n type Coxeter group one can associate n different WDVV solutions that ar
e not necessarily polynomial. We will prove that these Dubrovin--Frobeniu
s structures stabilize too and present the integrable systems associated t
o them.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bart Vlaar (BIMSA)
DTSTART:20231113T053000Z
DTEND:20231113T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/31
DESCRIPTION:Title: Baxter Q-operators for open spin chains\nby Bart Vlaar (BIMS
A) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe discuss s
ome recent progress on Baxter Q-operators for the XXZ spin chain with diag
onal boundary conditions. A key tool is the universal K-matrix for affine
quantum groups. Joint work with Alec Cooper and Robert Weston.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (University of Angers)
DTSTART:20231128T080000Z
DTEND:20231128T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/32
DESCRIPTION:Title: Kontsevich and Buchstaber polynomials\, multiplication kernels a
nd Calabi–Yau Differential operators\nby Vladimir Rubtsov (Universit
y of Angers) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe
discuss several result on ongoing work in collaboration (with I. Gaiur &
D. Van Straten and with V. Buchstaber & I. Gaiur) on interesting properti
es of multiplicative generalized Bessel kernels\, which include the famous
Clausen and Sonine –Gegenbauer formulas\, examples of polynomials for
Kontsevich discriminant locus given as addition laws for special 2-valued
formal groups (Buchstaber–Novikov–Veselov) as well as connections with
«period functions» solving some Picard–Fuchs type equations and assoc
iated with analogues of Landau–Ginzburg superpotentials.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Georgy Sharygin (Sino-Russian Mathematics Center\, Moscow State Un
iversity)
DTSTART:20231031T080000Z
DTEND:20231031T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/33
DESCRIPTION:Title: Argument shift method for the universal enveloping algebras\
nby Georgy Sharygin (Sino-Russian Mathematics Center\, Moscow State Univer
sity) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nArgument
shift method is a construction that produces a commutative subalgebra of a
Poisson algebra by differentiating its central elements along a suitable
vector field. An important particular case of this situation is when the P
oisson algebra is equal to the space of (polynomial) functions on a dual s
pace of a Lie algebra $g$. In my talk I will discuss an attempt to raise t
his procedure to the universal enveloping algebra of $g$. Based on a joint
work with Y.Ikeda and A.Molev\n
LOCATION:https://stable.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:20231016T053000Z
DTEND:20231016T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/34
DESCRIPTION:Title: Loop-gas formulation of two-dimensional integrable models\nb
y Ivan Kostov (BIMSA & Institut de physique théorique\, Université Paris
-Saclay\, CNRS and CEA) as part of BIMSA Integrable Systems Seminar\n\nLec
ture held 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 rel
ativistic loops. The loops interact through scattering factors associated
with their intersections. For the doubly periodic spacetime\, after decoup
ling the pairwise interactions by a Hubbard-Stratonovich transformation\,
the sum over loops can be performed explicitly. The resulting effective th
eory becomes mean field type in the limit when one of the periods becomes
asymptotically large. The mean field obeys the Thermodynamical Bethe Ansat
z equations.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hrachya Babujian (BIMSA & Yerevan Physics Institute\, Armenia)
DTSTART:20231023T053000Z
DTEND:20231023T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/35
DESCRIPTION:Title: The form factor program: asymptotic factorization of n-particle
SU(N) form factors\nby Hrachya Babujian (BIMSA & Yerevan Physics Insti
tute\, Armenia) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\
nWe investigate the high energy behavior of the SU(N) chiral Gross-Neveu m
odel in 1 + 1 dimensions. The model is integrable and matrix elements of s
everal local operators (form factors) are known exactly. The form factors
show rapidity space clustering\, which means factorization\, if a group of
rapidities is shifted to infinity. We analyze this phenomenon for the SU(
N) model. For several operators the factorization formulas are presented e
xplicitly.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaomeng Xu (Beijing International Center for Mathematical Researc
h (BICMR))
DTSTART:20231026T030000Z
DTEND:20231026T040000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/36
DESCRIPTION:Title: Integrability in Stokes phenomenon.\nby Xiaomeng Xu (Beijing
International Center for Mathematical Research (BICMR)) as part of BIMSA
Integrable Systems Seminar\n\n\nAbstract\nIt is well known that for a mero
morphic linear system with only regular singularities\, any formal solutio
n is necessarily convergent. It is less well known that for meromorphic li
near systems with irregular singularities\, a prescribed asymptotics at an
irregular singular point determine different fundamental solutions in dif
ferent sectorial regions surrounding the singular point. The transition ma
trices between the preferred solutions in the different sectoral regions a
re known as the Stokes matrices. This talk shows a relation between Stokes
matrices and various structures appearing in integrability. It then expla
ins that how the theory of quantum groups\, Yangians\, crystal basis and s
o on can be used to study the Stokes phenomenon.\n\nWorkshop on Lie theory
and integrable systems at BIMSA\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Zhedanov (Renmin University of China\, Beijing. School of
Mathematics)
DTSTART:20231026T020000Z
DTEND:20231026T030000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/37
DESCRIPTION:Title: Heun operators from different points of view: quantum and classi
cal\nby Oleksiy Zhedanov (Renmin University of China\, Beijing. School
of Mathematics) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract
\nWe discuss recent construction of Heun operators as bilinear combination
s of two generators of the Askey-Wilson algebra (as well as of its degener
ate cases). This construction is related to an important "band and time li
miting" problem in Fourier analysis. Classical mechanical analogs of the H
eun operators give rise to several families of dynamical systems having ex
plicit solutions in terms of elliptic functions.\n\nWorkshop on Lie theory
and integrable systems at BIMSA\n
LOCATION:https://stable.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:20231026T053000Z
DTEND:20231026T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/38
DESCRIPTION:Title: Local analog of the Deligne-Riemann-Roch isomorphism for line bu
ndles on a family of curves.\nby Denis Osipov (Visitor of Sino-Russian
mathematical center of PKU\, Steklov Mathematical Institute of RAS\, HSE
University) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nI w
ill speak about a local analog of the Deligne-Riemann-Roch theorem for li
ne bundles on a family of smooth projective curves. First\, I recall the D
eligne-Riemann-Roch theorem. Then I will speak about its local analog. The
two parts for this local analog of the Deligne-Riemann-Roch theorem consi
st of the 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
multiplicative group. The theorem is that these central extensions are eq
uivalent over the ground field of rational numbers. \nThe talk is based on
my reсent preprint arXiv:2308.0649.\n\nWorkshop on Lie theory and integ
rable systems at BIMSA\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov (Moscow State University\, now a visitor of SRMC
in PKU)
DTSTART:20231026T063000Z
DTEND:20231026T073000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/39
DESCRIPTION:Title: Commuting scalar partial differential (and not only) operators a
nd moduli spaces of torsion-free sheaves.\nby Alexander Zheglov (Mosco
w State University\, now a visitor of SRMC in PKU) as part of BIMSA Integr
able Systems Seminar\n\n\nAbstract\nIn my talk I’ll give an overview of
the results obtained by me\, as well as jointly with co-authors\, related
to the problem of classifying commuting (scalar) differential\, or more ge
nerally\, differential-difference or integral-differential operators in se
veral variables. The problem\, under some reasonable restrictions\, essent
ially reduces to the description of projective algebraic varieties that ha
ve a non-empty moduli space of torsion-free sheaves with a fixed Hilbert p
olynomial. \n\nMore precisely\, it turns out to be possible to classify th
e so-called quasi-elliptic rings\, which describe a wide class of operator
rings appeared in the theory of (quantum) integrable systems. They are co
ntained in a certain non-commutative “universal” ring - a purely algeb
raic analogue of the ring of pseudodifferential operators on a manifold an
d admit (under some weak restrictions) a convenient algebraic-geometric de
scription. This description is a natural generalization of the classificat
ion of rings of commuting ordinary differential or difference operators\,
described in the works of Krichever\, Novikov\, Drinfeld\, Mumford\, Mulas
e. Moreover\, already in the case of dimension two there are significant r
estrictions on the geometry of spectral manifolds.\n\nWorkshop on Lie theo
ry and integrable systems at BIMSA\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Belousov (Steklov Mathematical Institute\, St. Petersburg\,
Russia)
DTSTART:20231114T080000Z
DTEND:20231114T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/40
DESCRIPTION:Title: Baxter Q-operators in Ruijsenaars hyperbolic system\nby Niki
ta Belousov (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. Ruijsenaars in 2012. \n\nRecently in the joint work with S. Derkachov\,
S. Kharchev and S. Khoroshkin we proved some properties of these eigenfun
ctions using the so-called Baxter Q-operators. In the talk I will explain
the motivation behind these operators\, their key properties and how they
are used to prove the bispectral symmetry\, orthogonality and completeness
of the eigenfunctions.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takashi Takebe (BIMSA)
DTSTART:20231106T053000Z
DTEND:20231106T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/41
DESCRIPTION:Title: Dispersionless integrable hierarchies and Loewner type equations
\nby Takashi Takebe (BIMSA) as part of BIMSA Integrable Systems Semina
r\n\n\nAbstract\nDispersionless integrable hierarchies are obtained as cer
tain limits of classical integrable hierarchies such as the KP hierarchy a
nd 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 o
f conformal mappings. I shall talk about the relation of dispersionless hi
erarchies and the Loewner equations for conformal mappings.\n
LOCATION:https://stable.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:20231205T080000Z
DTEND:20231205T093000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/42
DESCRIPTION:Title: Quantum intersection numbers and the Gromov-Witten invariants of
the Riemann sphere.\nby Alexandr Buryak (National Research University
Higher School of Economics\, Skolkovo Institute of Science and Technology
) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nQuantum inter
section numbers were introduced through a natural quantization of the KdV
hierarchy in a work of Buryak\, Dubrovin\, Guere\, and Rossi. Because of t
he Kontsevich-Witten theorem\, a part of the quantum intersection numbers
coincides with the classical intersection numbers of psi-classes on the mo
duli spaces of stable algebraic curves. I will talk about our joint work i
n progress with Xavier Blot\, where we relate the quantum intersection num
bers to the stationary relative Gromov-Witten invariants of the Riemann sp
here\, with an insertion of a Hodge class. Using the Okounkov-Pandharipand
e approach to such invariants (with the trivial Hodge class) through the i
nfinite wedge formalism\, we then give a short proof of an explicit formul
a for the ``purely quantum'' part of the quantum intersection numbers\, fo
und before by Xavier\, which in particular relates these numbers to the on
e-part double Hurwitz numbers.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Reshetikhin (YSMC\, Tsinghua University & BIMSA)
DTSTART:20231126T013000Z
DTEND:20231126T023000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/43
DESCRIPTION:Title: Hybrid integrable systems\nby Nicolai Reshetikhin (YSMC\, Ts
inghua University & BIMSA) as part of BIMSA Integrable Systems Seminar\n\n
\nAbstract\nWorkshop Kirillov–75. Combinatorics and Bethe ansatz. Novemb
er 26–27\n\nThis talk is focused on quantum integrable systems on a clas
sical background. In physics such systems are known as Born-Oppenheimer ap
proximations\, when heavy atoms are classical and electrons are quantum. I
n mathematics\, perhaps\, most known structures of this type are Azumaya a
lgebras (an algebra that is finite dimensional over the center) and quantu
m groups at roots of unity. After the description of general mathematical
framework several natural examples will be given\, such as spin chains\, s
pin Calogero-Moser systems and isomonodromic deformations. The talk is bas
ed on joint work with A. Liashyk and I. Sechin.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Smirnov (Independent University of Moscow and GTIIT)
DTSTART:20231126T023000Z
DTEND:20231126T033000Z
DTSTAMP:20260404T094912Z
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 Inte
grable Systems Seminar\n\n\nAbstract\nWorkshop Kirillov–75. Combinatoric
s and Bethe ansatz. November 26–27\n\nI will speak about a new combinato
rial description for stable Grothendieck polynomials and Lascoux polynomia
ls in terms of cellular decompositions of Gelfand-Zetlin polytopes. This g
eneralizes an earlier result on key polynomials (aka characters of Demazur
e modules) by Kiritchenko\, Timorin and myself. The talk is based on a joi
nt work with Ekaterina Presnova.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleksiy Zhedanov (Renmin University of China)
DTSTART:20231126T050000Z
DTEND:20231126T060000Z
DTSTAMP:20260404T094912Z
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\nWorksho
p Kirillov–75. Combinatorics and Bethe ansatz. November 26–27\n\nFor S
zego polynomials on the unit circle we present explicit examples of bispec
trality which makes these polynomials similar to "classical" orthogonal po
lynomials. These examples admit extension to much wider class of special B
axter polynomials. Affine and double affine Hecke algebras of rank 1 arise
naturally in this approach from first principles.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhuoke Yang (BIMSA)
DTSTART:20231126T060000Z
DTEND:20231126T070000Z
DTSTAMP:20260404T094912Z
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\nWorksh
op Kirillov–75. Combinatorics and Bethe ansatz. November 26–27\n\nIn t
his talk we introduce a universal weight system (a function on chord diagr
ams satisfying the 4-term relation) taking values in the ring of polynomia
ls in infinitely many variables\, whose particular specialisations are wei
ght systems associated with the Lie algebras gl(N) and Lie superalgebras g
l(M|N). We extend this weight system to permutations and provide an effici
ent recursion for its computation.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Feigin (Hebrew university in Jerusalem)
DTSTART:20231126T070000Z
DTEND:20231126T080000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/47
DESCRIPTION:Title: Tolya and fermionic formulas\nby Boris Feigin (Hebrew univer
sity in Jerusalem) as part of BIMSA Integrable Systems Seminar\n\n\nAbstra
ct\nWorkshop Kirillov–75. Combinatorics and Bethe ansatz. November 26–
27\n\nI explain what are the fermionic formulas and why they are interesti
ng and important and present some relatively new results — fermionic for
mulas related with triplet-like vertex algebras.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Shapiro (Stockholm University & BIMSA)
DTSTART:20231127T053000Z
DTEND:20231127T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/48
DESCRIPTION:Title: Zonotopal algebras of graphs and their generalizations\nby B
oris Shapiro (Stockholm University & BIMSA) as part of BIMSA Integrable Sy
stems Seminar\n\n\nAbstract\nWorkshop Kirillov–75. Combinatorics and Bet
he ansatz. November 26–27\n\nIn the late 1990s motivated by a question o
f V.Arnold the speaker and M.Shapiro have studied the algebra generated by
the curvature forms of the standard linear bundles over the space of comp
lete flags in C^n. This was the first example of the so-called external zo
notopal algebra associated to the complete graph K_n. Since then a number
of modifications and generalizations of this algebra defined for all undir
ected graphs has been introduced. I will briefly survey the field many adv
ances in which were inspired by suggestions and ideas of Anatol Kirillov.\
n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruijie XU (BIMSA)
DTSTART:20231127T063000Z
DTEND:20231127T073000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/49
DESCRIPTION:Title: Lattice walk as an exactly solvable model\nby Ruijie XU (BIM
SA) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWorkshop Ki
rillov–75. Combinatorics and Bethe ansatz. November 26–27\n\nIn this t
alk\, I will introduce the research of lattice walk in analytic combinator
ics. Starting from simple one dimensional discrete random walks\, I will s
how how algebraic structures affect the the solution. The result in two di
mensional walks is most attracting. We will meet many concepts such as alg
ebraic curves\, conformal mapping and Riemann surface in solving two dimen
sional walks. In the last part of this talk\, I will talk about the relati
on between lattice walk and integrable phase model.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (University of Angers)
DTSTART:20231212T080000Z
DTEND:20231212T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/50
DESCRIPTION:Title: Kontsevich and Buchstaber polynomials\, multiplication kernels a
nd Calabi–Yau Differential operators II\nby Vladimir Rubtsov (Univer
sity 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 sev
eral result on ongoing work in collaboration (with I. Gaiur & D. Van Strat
en and with V. Buchstaber & I. Gaiur) on interesting properties of multip
licative generalized Bessel kernels\, which include the famous Clausen and
Sonine –Gegenbauer formulas\, examples of polynomials for Kontsevich d
iscriminant locus given as addition laws for special 2-valued formal group
s (Buchstaber–Novikov–Veselov) as well as connections with «period fu
nctions» solving some Picard–Fuchs type equations and associated with a
nalogues of Landau–Ginzburg superpotentials.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenwei Ruan (University of Wisconsin - Madison)
DTSTART:20231222T053000Z
DTEND:20231222T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/51
DESCRIPTION:Title: A uniform approach to the Damiani\, Beck\, and alternating PBW b
ases for the positive part of $U_q(\\hat{\\mathfrak{sl}}_2)$\nby Chenw
ei Ruan (University of Wisconsin - Madison) as part of BIMSA Integrable Sy
stems Seminar\n\n\nAbstract\nThe $q$-deformed enveloping algebra $U_q(\\ha
t{\\mathfrak{sl}}_2)$ and its positive part $U^+_q$\nare studied in both m
athematics and mathematical physics. The literature contains at least thre
e\nPBW bases for $U^+_q$\, called the Damiani\, the Beck\, and the alterna
ting PBW bases.\nThese PBW bases are related via exponential formulas. In
this talk\, we will introduce\nan exponential generating function whose ar
gument is a power series involving the\nBeck PBW basis and an integer para
meter $m$. The cases $m = 2$ and $m = −1$ yield the\nknown exponential f
ormulas for the Damiani and alternating PBW bases\, respectively.\nWe will
give present two results on the generating function for an arbitrary inte
ger m.\nThe first result gives a factorization of the generating function.
In the second result\,\nwe express the coefficients of the generating fun
ction in closed form.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov
DTSTART:20231219T053000Z
DTEND:20231219T063000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/52
DESCRIPTION:Title: Kontsevich and Buchstaber polynomials\, multiplication kernels a
nd Calabi–Yau Differential operators III\nby Vladimir Rubtsov as par
t of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIt is continuation of
the previous talk at November 28 and December 12.\n\nWe discuss several r
esult on ongoing work in collaboration (with I. Gaiur & D. Van Straten an
d with V. Buchstaber & I. Gaiur) on interesting properties of multiplicati
ve generalized Bessel kernels\, which include the famous Clausen and Sonin
e –Gegenbauer formulas\, examples of polynomials for Kontsevich discrim
inant locus given as addition laws for special 2-valued formal groups (Buc
hstaber–Novikov–Veselov) as well as connections with «period function
s» solving some Picard–Fuchs type equations and associated with analogu
es of Landau–Ginzburg superpotentials.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tao Gui (Peking University)
DTSTART:20240227T080000Z
DTEND:20240227T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/53
DESCRIPTION:Title: Asymptotic Log-concavity of Dominant Lower Bruhat Intervals via
the Brunn--Minkowski Inequality\nby Tao Gui (Peking University) as par
t of BIMSA Integrable Systems Seminar\n\n\nAbstract\nBj\\"orner and Ekedah
l [Ann. of Math. (2)\, 170(2): 799-817\, 2009] pioneered the study of leng
th-enumerating sequences associated with parabolic lower Bruhat intervals
in crystallographic Coxeter groups. In this talk\, we study the asymptotic
behavior of these sequences in affine Weyl groups. We prove that the leng
th-enumerating sequences associated with the dominant intervals correspond
ing to a dominant coroot lattice element are ``asymptotically'' log-concav
e. More precisely\, we prove that a certain sequence of discrete measures
naturally constructed from the length-enumerating sequences converges weak
ly to a continuous measure constructed from a certain polytope. Moreover\,
a certain sequence of step functions naturally constructed from the lengt
h-enumerating sequences uniformly converges to the density function of tha
t continuous measure\, which implies the weak convergence and that the seq
uences of numbers of elements in each layer of the dilated dominant interv
al converges to a sequence of volumes of hyperplane sections of the polyto
pe. By the Brunn--Minkovski inequality\, the density function is log-conca
ve. Our approach relies on the ``dominant lattice formula''\, which yields
a new bridge between the discrete nature of Betti numbers of parabolic af
fine Schubert varieties and the continuous nature of the geometry of conve
x polytopes. Our technique can be seen as a refinement in our context of t
he classical Ehrhart's theory relating the volume of a polytope and the nu
mber of lattice points the polytope contains\, by replacing the volume by
volumes of transversal sections and the number the total lattice points by
the number of lattice points of a given length. Joint with Gaston Burrull
and Hongsheng Hu.\n\nShort bio: I got my Ph. D. in 2023 from the Academy
of Mathematics and Systems Science\, Chinese Academy of Sciences. Currentl
y I am a postdoc of the Beijing International Center for Mathematical Rese
arch\, Peking University. My research interests are Lie theory\, geometric
/combinatorial representation theory\, and combinatorial Hodge theory. And
I have broad interests in topological\, geometric\, and combinatorial pro
blems related to representation theory.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando (HSE University\, Skolkovo Institute of Science and
Technology)
DTSTART:20240305T080000Z
DTEND:20240305T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/54
DESCRIPTION:Title: Inducing graph invariants from the universal gl-weight system\nby Sergei Lando (HSE University\, Skolkovo Institute of Science and Te
chnology) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWeigh
t systems\, which are functions on chord diagrams satisfying certain 4-\nt
erm relations\, appear naturally in Vassiliev's theory of \nnite type knot
invariants.\nIn particular\, a weight system can be constructed from any
\nnite dimensional\nLie algebra endowed with a nondegenerate invariant bil
inear form. Recently\,\nM. Kazarian suggested to extend the gl(N)-weight s
ystem from chord diagrams\n(treated as involutions without \nxed point) to
arbitrary permutations\, which\nled to a recurrence formula allowing for
an eective computation of its values\,\nelaborated by Zhuoke Yang. In tur
n\, the recurrence helped to unify the gl(N)\nweight systems\, for N = 1\,
2\, 3\, . . . \, into a universal gl-weight system. The\nlatter takes val
ues in the ring of polynomials C[N][C1\, C2\, . . . ] in in\nnitely many\n
variables C1\, C2\, . . . (Casimir elements)\, whose coe\ncients are polyn
omials in N.\nThe universal gl-weight system carries a lot of information
about chord\ndiagrams and intersection graphs. The talk will address the q
uestion which graph\ninvariants can be extracted from it. We will discuss
the interlace polynomial\,\nthe enhanced skew-characteristic polynomial\,
and the chromatic polynomial. In\nparticular\, we show that the interlace
polynomial of the intersection graphs can\nbe obtained by a speci\nc subst
itution for the variables N\, C1\, C2\, . . . . This allows\none to extend
it from chord diagrams to arbitrary permutations.\nQuestions concerning o
ther graph and delta-matroid invariants and their\npresumable extensions w
ill be formulated.\nThe talk is based on a work of the speaker and a PhD s
tudent Nadezhda\nKodaneva.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Oblezin (BIMSA)
DTSTART:20240312T080000Z
DTEND:20240312T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/55
DESCRIPTION:Title: On matrix element representation of the GKZ hypergeometric funct
ions\nby Sergey Oblezin (BIMSA) as part of BIMSA Integrable Systems Se
minar\n\n\nAbstract\nIn the talk\, I shall present our joint paper with A.
Gerasimov and D.Lebedev. In this paper\, we develop a representation theor
y approach to the study of generalized hypergeometric functions of Gelfand
\, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric func
tions may be identified with matrix elements of non-reductive Lie algebras
L(N) of oscillator type. The Whittaker functions associated with princip
al series representations of gl(n\,R) being special cases of GKZ hyperge
ometric functions\, thus admit along with a standard matrix element repres
entations associated with reductive Lie algebra gl(n\,R)\, another matrix
element representation in terms of L(n(n-1)).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shuai Guo (Peking University)
DTSTART:20240319T080000Z
DTEND:20240319T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/56
DESCRIPTION:Title: Birkhoff Factorization\, Givental’s Quantization\, and BCOV’
s Feynman Rule\nby Shuai Guo (Peking University) as part of BIMSA Inte
grable Systems Seminar\n\n\nAbstract\nBCOV’s Feynman rule is a conjectur
al algorithm used to compute the higher genus Gromov-Witten invariants of
Calabi-Yau threefolds. The Feynman graph that appears in BCOV’s rule can
be interpreted as a form of geometric quantization. In this presentation\
, I will attempt to extract it from the A-model perspective and realize it
as Givental’s R-matrix quantization action. Finally\, I will explain ho
w 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://stable.researchseminars.org/talk/BIMSA-ISS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chenglang Yang (Chinese Academy of Sciences)
DTSTART:20240326T080000Z
DTEND:20240326T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/57
DESCRIPTION:Title: A connection between the topological vertex and multi-component
KP hierarchy\nby Chenglang Yang (Chinese Academy of Sciences) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe topological vertex\
, developed by Aganagic\, Klemm\, Marino and Vafa\, provides an explicit a
lgorithm to compute the open Gromov-Witten invariants of smooth toric Cala
bi-Yau threefolds in mathematics\, as well as the A-model topological stri
ng amplitudes in physics. In this talk\, I will introduce our recent work
on the connection between the topological vertex and multi-component KP hi
erarchy. \n\nThis talk is based on a joint work with Zhiyuan Wang and Jian
Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Limeng Xia (Jiangsu University)
DTSTART:20240412T133000Z
DTEND:20240412T143000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/58
DESCRIPTION:Title: GIM algebras and their modules\nby Limeng Xia (Jiangsu Unive
rsity) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIn this
talk\, we mainly introduce some background of the structure\, the represen
tation and the quantization of the generalized intersection matrix algebra
s. Then we introduce a result on finite dimensional modules over indefini
te type Kac-Moody Lie algebras. It is given in a joint work with Hongmei H
u and Yilan Tan.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Mishnyakov (Nordita)
DTSTART:20240409T080000Z
DTEND:20240409T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/59
DESCRIPTION:Title: Superintegrability of matrix models and BPS algebras\nby Vic
tor Mishnyakov (Nordita) as part of BIMSA Integrable Systems Seminar\n\n\n
Abstract\nThe prominent role of matrix models in physics and mathematics i
s well known. It is especially interesting that some of those models are e
xactly solvable\, meaning the one can find explicit formulas for correlati
on functions. This phenomenon has also been called superintegrability of m
atrix models. I will present some recent attempt to study it systematicall
y and search for its algebraic origins. It leads to an interesting connect
ion with the rapidly developing field of BPS algebras and their representa
tions.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Glutsyuk Alexey (CNRS\, ENS de Lyon\; HSE University and IITP (Mos
cow))
DTSTART:20240416T080000Z
DTEND:20240416T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/60
DESCRIPTION:Title: Model of Josephson junction\, dynamical systems on $\\mathbb T^2
$\, isomonodromic deformations and Painleve 3 equations\nby Glutsyuk A
lexey (CNRS\, ENS de Lyon\; HSE University and IITP (Moscow)) as part of B
IMSA Integrable Systems Seminar\n\n\nAbstract\nThe tunneling effect predic
ted by B.Josephson (Nobel \nPrize\, 1973) concerns the Josephson junctio
n: two superconductors \nseparated by a narrow dielectric. It states exis
tence of a supercurrent through it and equations governing it. The overda
mped Josephson junction \nis modeled by a family of differential equation
s 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-loc
k areas are those level sets $L_r:=\\{\\rho=r\\}$ that have non-empty \ni
nteriors. They exist only for integer rotation number values $r$: this is
the rotation number quantization effect discovered by Buchstaber\, Karpov
and Tertychnyi. They are \nanalogues of the famous Arnold tongues. \nEach
$L_r$ is an infinite chain of domains going vertically to infinity \n
and separated 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
presentation.\n\nWe show that: 1) all constrictions in $L_r$ lie in the
vertical line $\\{ B=\\omega r\\}$\; \n2) each constriction is positive
\, that is\, some its punctured neighborhood in \nthe vertical line lies i
n $\\operatorname{Int}(L_r)$. These results\, obtained in collaboration wi
th Yulia Bibilo\, confirm experiences of physicists (pictures from physica
l books of 1970-th) \nand two mathematical conjectures.\n\nThe proof uses
an equivalent description of model by linear systems of differential eq
uations on $\\oc$ (found by Buchstaber\, Karpov and Tertychnyi)\, their
isomonodromic deformations described by \nPainleve 3 equations and me
thods of the theory of slow-fast systems.\n\nIf the time allows we will d
iscuss new results and open questions.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuantong Qu (Nottingham University)
DTSTART:20240423T080000Z
DTEND:20240423T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/61
DESCRIPTION:Title: Special functions over finite Chevalley groups\nby Xuantong
Qu (Nottingham University) as part of BIMSA Integrable Systems Seminar\n\n
\nAbstract\nMany special functions appearing in the study of integrable sy
stems have their finite field counterparts with extensive connections with
number theory and algebraic geometry. For instance\, it is well known tha
t Gauss sums are finite field analogues of Gamma-functions and Kloosterman
sums are finite field analogues of Bessel functions. In this talk I will
present a new approach of studying certain special functions over finite f
ields using representation theory of finite Chevalley groups. Namely\, I w
ill first define finite field analogues of Gamma-functions and Whittaker f
unctions and then identify them as matrix elements of representations of (
subgroups of) general linear groups over a finite field and compare them w
ith their counterparts defined over real groups.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luyao Wang (School of Mathematical Sciences\, Capital Normal Unive
rsity)
DTSTART:20240402T080000Z
DTEND:20240402T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/62
DESCRIPTION:Title: W-representation for multi-character partition function\nby
Luyao Wang (School of Mathematical Sciences\, Capital Normal University) a
s part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe discuss sever
al results on work in collaboration (with V.Mishnyakov\, A.Popolitov\, F.L
iu\, R.Wang and with B. Kang\, K.Wu\, W.Z. Zhao).\nWe construct W-represen
tations for multi-character expansions\, which involve a generic number of
sets of time variables. We propose integral representations for such kind
of partition functions which are given by tensor models and multi-matrix
models with multi-trace couplings. In addition\, we present the W-represen
tation for a two-tensor model with order-3. We derive the compact expressi
ons of correlators from the W-representation\, and analyze the free energy
in the large N limit. By establishing the correspondence between the two-
color Dyck order in Fredkin spin chain and the tree operator on the ring\,
we prove that the entanglement scaling of Fredkin spin chain beyond the l
ogarithmic scaling in ordinary critical systems.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wen-Li Yang (Physics School\, Northwest University\, Xian)
DTSTART:20240507T080000Z
DTEND:20240507T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/63
DESCRIPTION:Title: Off-diagonal Bethe ansatz approach to quantum integrable models<
/a>\nby Wen-Li Yang (Physics School\, Northwest University\, Xian) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nApplying the recent de
veloped method-the off-diagonal Bethe ansatz method\, we construct the exa
ct solutions of the Heisenberg spin chain with various boundary conditions
. The results allow us to calculate the boundary energy of the system in t
he thermodynamic limit. The method used here can be generalized to study t
he thermodynamic properties and boundary energy of other high rank models
with non-diagonal boundary fields.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masashi Hamanaka (Nagoya University)
DTSTART:20240521T080000Z
DTEND:20240521T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/65
DESCRIPTION:Title: Anti-Self-Dual Yang-Mills Equations and a Unification of Integra
ble Systems\nby Masashi Hamanaka (Nagoya University) as part of BIMSA
Integrable Systems Seminar\n\n\nAbstract\nAnti-self-dual Yang-Mills (ASDYM
) equations have played important roles in quantum field theory (QFT)\, ge
ometry and integrable systems for more than 50 years. In particular\, inst
antons\, global solutions of them\, have revealed nonperturbative aspects
of QFT ['t Hooft\,...] and have given a new insight into the study of the
four-dimensional geometry [Donaldson]. Furthermore\, it is well known as t
he Ward conjecture that the ASDYM equations can be reduced to many integra
ble systems\, such as the KdV eq. and Toda eq. Integrability aspects of th
em can be understood from the viewpoint of the twistor theory [Mason-Woodh
ouse\,...]. The ASDYM equation is realized as the equation of motion of th
e four-dimensional Wess-Zumino-Witten (4dWZW) model in Yang's form. The 4
dWZW model is analogous to the two dimensional WZW model and possesses asp
ects of conformal field theory and twistor theory [Losev-Moore-Nekrasov-Sh
atashvili\,...]. \n\nOn the other hand\, 4d Chern-Simons (CS) theory has c
onnections to many solvable models such as spin chains and principal chira
l models [Costello-Witten-Yamazaki\, ...]. These two theories (4dCS and 4d
WZW) have been derived from a 6dCS theory like a ``double fibration'' [Cos
tello\, Bittleston-Skinner].\n\nThis suggests a nontrivial duality corresp
ondence between the 4dWZW model and the 4dCS theory. \nWe note that the Wa
rd conjecture holds mostly in the split signature (+\,+\,−\,−) and the
n the 4dWZW model describes the open N=2 string theory in the four-dimensi
onal space-time. Hence a unified theory of integrable systems (6dCS-->4dCS
/4dWZW) can be proposed in this context with the split signature. \n\nIn t
his talk\, I would like to discuss integrability aspects of the ASDYM equa
tion and construct soliton/instanton solutions of it by the Darboux/ADHM p
rocedures\, respectively. We calculate the 4dWZW action density of the sol
utions and found that the soliton solutions behaves as the KP-type soliton
s\, that is\, the one-soliton solution has localized action (energy) densi
ty on a 3d hyperplane in 4-dimensions (soliton wall) and the N-soliton sol
ution describes N intersecting soliton walls with phase shifts. Our solito
n solutions would describe a new-type of physical objects (3-brane) in the
N=2 string theory. If time permits\, I would mention reduction to lower-d
imensions and extension to noncommutative spaces. \n\nThis talk is based o
n our works: [arXiv:2212.11800\, 2106.01353\, 2004.09248\, 2004.01718] and
forthcoming papers.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Chalykh (University of Leeds)
DTSTART:20240416T092000Z
DTEND:20240416T102000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/66
DESCRIPTION:Title: Elliptic complex reflection groups and Seiberg–Witten integrab
le systems\nby Oleg Chalykh (University of Leeds) as part of BIMSA Int
egrable Systems Seminar\n\n\nAbstract\nFor any abelian variety $X$ with an
action of a finite complex reflection group $W$\, Etingof\, Felder\, Ma a
nd Veselov constructed a family of integrable systems on $T^*X$. When $X$
is a product of $n$ copies of an elliptic curve $E$ and $W=S_n$\, this rep
roduces the usual elliptic Calogero-Moser system. Recently\, together
with Philip Argyres (Cincinnati) and Yongchao Lü (KIAS)\, we proposed tha
t many of these integrable systems at the classical level can be interpret
ed as Seiberg-Witten integrable systems of certain supersymmetric qu
antum field theories. I will describe our progress in understanding this c
onnection for the case $X=E^n$ where $E$ is an elliptic curve with the sym
metry group $Z_m$ (of order $m=2\,3\,4\,6$)\, and $W$ is the wreath produc
t of $Z_m$ and $S_n$. I will mostly talk about $n=1$ case\, which is alrea
dy rather interesting. Based on: arXiv 2309.12760.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Veselov (Loughborough\, UK)
DTSTART:20240521T092000Z
DTEND:20240521T102000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/67
DESCRIPTION:Title: Delay Painleve-I equation and Masur-Veech volumes\nby Alexan
der Veselov (Loughborough\, UK) as part of BIMSA Integrable Systems Semina
r\n\n\nAbstract\nThe subject of the talk is the delay version of the Painl
eve-I equation obtained as a delay periodic reduction of Shabat's dressing
chain. We study the formal entire solutions to this equation and introduc
e a new family of interesting polynomials (called Bernoulli-Catalan polyno
mials). Using the recent results by Di Yang\, Don Zagier and Youjin Zhang\
, we apply the theory of these polynomials to the problem of calculation o
f the Masur-Veech volumes of the moduli spaces of meromorphic quadratic di
fferentials.\n \nThe talk is based on a joint work with John Gibbons and
Alex Stokes.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Sechin (BIMSA\, China)
DTSTART:20240604T080000Z
DTEND:20240604T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/68
DESCRIPTION:Title: Ruijsenaars duality for B\, C\, D Toda chains\nby Ivan Sechi
n (BIMSA\, China) as part of BIMSA Integrable Systems Seminar\n\n\nAbstrac
t\nWe use the Hamiltonian reduction method to construct the Ruijsenaars du
al systems to generalized Toda chains associated with the classical Lie al
gebras 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 explain how both types of systems emerge in the reduction of the cotan
gent bundle of a Lie group and provide the formulae for dual Hamiltonians.
We compute explicitly the higher Hamiltonians of Goldfish models using th
e Cauchy-Binet theorem. \n\nJoint work with Mikhail Vasilev\, arXiv:2405.0
8620.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Feher (University of Szeged and Wigner Research Centre for
Physics\, Hungary)
DTSTART:20240611T080000Z
DTEND:20240611T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/69
DESCRIPTION:Title: Bi-Hamiltonian structures of integrable many-body models from Po
isson reduction\nby Laszlo Feher (University of Szeged and Wigner Rese
arch Centre for Physics\, Hungary) as part of BIMSA Integrable Systems Sem
inar\n\n\nAbstract\nWe review our results on bi-Hamiltonian structures of
trigonometric spin Sutherland\nmodels built on collective spin variables.
Our basic observation was that the cotangent\nbundle $T^∗U(n)$ and its h
olomorphic analogue $T^∗GL(n\,\\mathbb C)$\, as well as $T^∗GL(n\,\\ma
thbb C)_{\\mathbb R}$\, carry\na natural quadratic Poisson bracket\, which
is compatible with the canonical linear one.\nThe quadratic bracket arise
s by change of variables and analytic continuation from\nan associated Hei
senberg double. Then\, the reductions of $T^∗U(n)$ and $T^∗GL(n\,\\mat
hbb C)$ by\nthe conjugation actions of the corresponding groups lead to th
e real and holomorphic\nspin Sutherland models\, respectively\, equipped w
ith a bi-Hamiltonian structure. The\nreduction of $T^∗GL(n\,\\mathbb C)_
{\\mathbb R}$ by the group $U(n) \\times U(n)$ gives a generalized Sutherl
and\nmodel coupled to two $u(n)^∗$-valued spins. We also show that a bi-
Hamiltonian structure\non the associative algebra $gl(n\,\\mathbb R)$ that
appeared in the context of Toda models can be\ninterpreted as the quotien
t of compatible Poisson brackets on $T^∗GL(n\,\\mathbb R)$. Before our\n
work\, all these reductions were studied using the canonical Poisson struc
tures of the\ncotangent bundles\, without realizing the bi-Hamiltonian asp
ect.\n\nReferences\n\n[1] L. Feher\, Reduction of a bi-Hamiltonian hierarc
hy on $T^∗U(n)$ to spin Ruijsenaars–\nSutherland models\, Lett. Math.
Phys. 110\, 1057-1079 (2020).\n\n[2] L. Feher\, Bi-Hamiltonian structure o
f spin Sutherland models: the holomorphic case\,\nAnn. Henri Poincar´e 22
\, 4063-4085 (2021).\n\n[3] L. Feher\, Bi-Hamiltonian structure of Sutherl
and models coupled to two $u(n)^∗$-valued\nspins from Poisson reduction\
, Nonlinearity 35\, 2971-3003 (2022).\n\n[4] L. Feher and B. Juhasz\, A no
te on quadratic Poisson brackets on $gl(n\,\\mathbb R)$ related to\nToda l
attices\, Lett. Math. Phys. 112:45 (2022).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Khoroshkin (HSE University)
DTSTART:20241008T080000Z
DTEND:20241008T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/70
DESCRIPTION:Title: Ruijsenaars spectral transform\nby Sergey Khoroshkin (HSE
University) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nRec
ent success in the study of Baxter $Q$ operators in Ruijsenaars \nhyperbol
ic system led to establishing\, besides of bispectral duality\, of \nth
e duality concerning reflection of the coupling constant. It \nalso give
s a way to prove orthogonality and completeness of the wave \nfunctions. T
he corresponding integral transform\, defined for complex valued parameter
s\,\ncan be regarded as a generalization of Laplace transform. We prove
an analog of classical inversion\nformula and apply it for establishing $L
_2$ isomorphisms of Ruijsenaars spectral transform in 4 regimes of unitar
ity of the system.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filipp Uvarov (Skoltech\, HSE University)
DTSTART:20241029T080000Z
DTEND:20241029T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/71
DESCRIPTION:Title: Deligne's category\, monodromy-free pseudo-differential operator
s and Gaudin model for the Lie superalgebra $gl(m|n)$.\nby Filipp Uvar
ov (Skoltech\, HSE University) as part of BIMSA Integrable Systems Seminar
\n\n\nAbstract\nThe Deligne's category is a formal way to define an interp
olation of the category of finite-dimensional representations of the Lie g
roup $GL(n)$ to any complex number $n$. It is used in various construction
s\, which all together can be named as representation theory in complex ra
nk. In the talk\, I will present one of such constructions\, namely\, the
interpolation of the algebra of higher Gaudin Hamiltonians (the Bethe alge
bra) associated with the Lie algebra $gl(n)$.\n \nOne can also interpolate
monodromy-free differential operators of order $n$ desribing eigenvectors
of Gaudin Hamiltonians\, obtaining "monodromy-free" pseudo-differential o
perators. In joint work with L. Rybnikov and B. Feigin arXiv:2304.04501\,
we prove that the Bethe algebra in Deligne's category is isomorphic to the
algebra of functions on certain pseudo-differential operators. Our work i
s motivated by the Bethe ansatz conjecture for the case of Lie superalgebr
a $gl(m|n)$. The conjecture says that eigenvectors in this case are descri
bed by ratios of differential operators of orders $m$ and $n$. We prove th
at such ratios are "monodromy-free" pseudo-differential operators.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Povolotsky (JINR Dubna)
DTSTART:20241022T080000Z
DTEND:20241022T090000Z
DTSTAMP:20260404T094912Z
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 A
lexander Povolotsky (JINR Dubna) as part of BIMSA Integrable Systems Semin
ar\n\n\nAbstract\nThe percolation problem provides one of the basic exampl
es of phase transition and critical behavior manifested in the statistics
of percolation clusters. The critical bond percolation model on a square l
attice is closely related to the $O(1)$ dense loop model\, which\, in turn
\, can be mapped on the exactly solvable six-vertex model at special value
s of the Boltzmann weights\, known as the Razumov-Stroganov combinatorial
point. This point is known for providing the possibility to obtain exact
results in finite-size systems. I will review the latest results on calcul
ating the exact densities of percolation clusters in critical percolation\
, as well as loops in the $O(1$) dense loop model on an infinite cylinder
of a finite circumference.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Pribytok (BIMSA)
DTSTART:20241015T080000Z
DTEND:20241015T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/73
DESCRIPTION:Title: Superdeformed CP $\\sigma$-models\, RG-flow and Conformal limits
\nby Anton Pribytok (BIMSA) as part of BIMSA Integrable Systems Semina
r\n\n\nAbstract\nWe prove that the supersymmetric deformed $\\mathbb{CP}^1
$ sigma model (the generalization of the Fateev-Onofri-Zamolodchikov model
) admits an equivalent description as a generalized Gross-Neveu model. Thi
s formalism is useful for the study of renormalization properties and part
icularly for calculation of the one- and two-loop $\\beta$-function. Remar
kably we find new Nahm-type conditions\, which guarantee renormalizability
and supersymmetric invariance. We show that in the UV the superdeformed m
odel flows to the super-Thirring CFT\, for which we also develop a supersp
ace approach. It is then demonstrated that the super-Thirring model is equ
ivalent to a sigma model with the cylinder $\\mathbb{R}\\times S^1$ target
space by an explicit computation of the correlation functions on both sid
es. Apart from that\, we observe that the original model has another inter
esting conformal limit\, given by the supercigar model\, for which we also
find a chiral dual and explicitly demonstrate agreement of the four-point
functions 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 o
f $\\cl{N}=2$ Liouville (Landau-Ginzburg class)\, as well as topological t
heories in higher $D$.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Gaiur (University of Geneva)
DTSTART:20241112T080000Z
DTEND:20241112T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/74
DESCRIPTION:Title: Higher Bessel Product Formulas\nby Ilia Gaiur (University of
Geneva) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nHigher
Bessel functions are the solutions to the quantum differential equations
for $\\mathbb{P}^{N-1}$. These functions are connected to the periods of t
he Dwork families via the Laplace transform\, and the functions themselves
are exponential integrals. In my talk\, I will show how product formulas
for these irregular special functions lead to other geometric differential
equations associated with higher-dimensional families of algebraic variet
ies. I will discuss the geometric and algebraic properties of the periods
for these families and later provide further perspectives on these corresp
ondences.\n\nWork in collaboration with V.Rubtsov and D. van Straten.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavlo Gavrylenko (SISSA\, International School for Advanced Studie
s\, Trieste)
DTSTART:20241105T080000Z
DTEND:20241105T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/75
DESCRIPTION:Title: Zeros of isomonodromic tau functions\, spectral problems\, and h
olomorphic anomaly\nby Pavlo Gavrylenko (SISSA\, International School
for Advanced Studies\, Trieste) as part of BIMSA Integrable Systems Semina
r\n\n\nAbstract\nIsomonodromic tau functions have explicit expressions as
sums of conformal blocks (or Nekrasov functions)\, so-called Kyiv formulas
\, found by Gamayun\, Iorgov\, Lisovyy. Zeros of these tau functions corre
spond to the situation when 2*2 isomonodromic problem becomes the quantum
mechanical problem\, e.g.\, with potential $\\cosh x$. This way we get exa
ct quantization conditions for the latter. Expansion around zero of the ta
u function is also worth studying\, since its modular properties are well-
defined and imply the so-called holomorphic anomaly equation for $E_2$ dep
endence of conformal block. \n\nThe talk will be partially based on the pa
pers https://arxiv.org/abs/2410.17868 and https://arxiv.org/abs/2105.00985
.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kohei Motegi (Tokyo University of Marine Science and Technology)
DTSTART:20241119T080000Z
DTEND:20241119T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/76
DESCRIPTION:Title: An odd two-dimensional and a three-dimensional realization of Sc
hur functions\nby Kohei Motegi (Tokyo University of Marine Science and
Technology) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe
present unconventional constructions of Schur/Grothendieck polynomials fr
om the viewpoint of quantum integrability.\nFirst\, we present a construct
ion of Schur/Grassmannian Grothendieck polynomials using a degeneration of
higher rank rational/quantum R-matrices\, which is different from the Bet
he vector or Fomin-Kirillov type constructions.\n\nSecond\, using the q=0
version of the three-dimensional $R$-matrix satisfying the tetrahedron equ
ation introduced by\nBazhanov-Sergeev and further studied by Kuniba-Maruya
ma-Okado\, we show that a class of three-dimensional partition functions\n
can be expressed as Schur polynomials. Keys of our derivation in both cons
tructions are the multiple commutation relations between quantum algebras.
\n\nPartly based on joint work with Shinsuke Iwao and Ryo Ohkawa.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhuoke Yang (BIMSA)
DTSTART:20241126T080000Z
DTEND:20241126T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/77
DESCRIPTION:Title: Chromatic polynomial and the $\\mathfrak{so}$ weight system\
nby Zhuoke Yang (BIMSA) as part of BIMSA Integrable Systems Seminar\n\n\nA
bstract\nWeight systems are functions on chord diagrams satisfying the so-
called Vassiliev 4-term relations. They are closely related to finite-type
knot invariants. Certain weight systems can be derived from graph invaria
nts and Lie algebra. \nIn a recent paper by M. Kazarian and the speaker\,
a recurrence for the Lie algebras $\\mathfrak{so}(N)$ weight systems has
been suggested\; the recurrence allows one to construct the universal $\\m
athfrak{so}$ weight system. The construction is based on an extension of t
he $\\mathfrak{so}$ weight systems to permutations.\n\nAnother recent pape
r\, by M. Kazarian\, N. Kodaneva\, and the S. Lando\, shows that under the
specific substitution for the Casimir elements\, the leading term in $N$
of the universal $\\mathfrak{gl}$ weight system becomes the chromatic poly
nomial of the intersection graph of the chord diagram.\nIn this talk\, we
establish a similar result for the universal $\\mathfrak{so}$ weight syste
m. that is the leading term of the universal $\\mathfrak{so}$ weight syste
m also becomes the chromatic polynomial under a specific substitution.\n\n
The talk is based on a joint work arxiv: 2411.01128 with Sergei Lando.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mizuki Yamaguchi (Graduate School of Arts and Sciences\, The Unive
rsity of Tokyo)
DTSTART:20241203T080000Z
DTEND:20241203T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/78
DESCRIPTION:Title: Classification of integrability and non-integrability for some q
uantum spin chains\nby Mizuki Yamaguchi (Graduate School of Arts and S
ciences\, The University of Tokyo) as part of BIMSA Integrable Systems Sem
inar\n\n\nAbstract\nQuantum non-integrability\, or the absence of local co
nserved quantity\, is a necessary condition for various empirical laws obs
erved in macroscopic systems. Examples are thermal equilibration\, the Kub
o formula in linear response theory\, and the Fourier law in heat conducti
on\, all of which require non-integrability. From these facts\, it is wide
ly believed that integrable systems are highly exceptional\, and non-integ
rability is ubiquitous in generic quantum many-body systems. Many numerica
l simulations also support this expectation. Nevertheless\, conventional a
pproaches in mathematical physics cannot address this belief\, and establi
shing non-integrability of vast majority of generic quantum many-body syst
ems is left as an open problem.\n\nIn this study\, we address this problem
and provide an affirmative result for a wide class of quantum many-body s
ystems. Precisely\, we rigorously classify the integrability and non-integ
rability of all spin-1/2 chains with symmetric nearest-neighbor interactio
ns [1]. Our classification demonstrates that except for the known integrab
le models\, all systems are indeed non-integrable. This result provides a
rigorous proof of the ubiquitousness of non-integrability\, as well as the
absence of undiscovered integrable systems which remains to be discovered
. Moreover\, it is proved that there is no partially integrable systems wi
th finite number of local conserved quantities.\n\nIn addition\, recent ex
tensions of non-integrability proofs to spin-1 systems [2] and others will
be presented.\n\n[1] M. Yamaguchi\, Y. Chiba\, N. Shiraishi\, ``Complete
Classification of Integrability and Non-integrability for Spin-1/2 Chain w
ith Symmetric Nearest-Neighbor Interaction\,'' arXiv:2411.02162\n\n[2] A.
Hokkyo\, M. Yamaguchi\, Y. Chiba\, ``Proof of the absence of local conserv
ed quantities in the spin-1 bilinear-biquadratic chain and its anisotropic
extensions\,'' arXiv:2411.04945\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kun Zhang (Northwest University\, China)
DTSTART:20241210T080000Z
DTEND:20241210T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/79
DESCRIPTION:Title: Yang-Baxter gates and integrable circuit\nby Kun Zhang (Nort
hwest University\, China) as part of BIMSA Integrable Systems Seminar\n\n\
nAbstract\nBrickwork circuits composed of the Yang-Baxter gates are integr
able. It becomes an important tool to study the quantum many-body system o
ut of equilibrium. I will talk about the properties of Yang-Baxter gates v
ia the quantum information theory. We find that only certain two-qubit gat
es can be converted to the Yang-Baxter gates via the single-qubit gate ope
rations. I will also talk about some possible extensions of the integrable
circuits. Numerical analysis suggests that there is a broad class of circ
uits that are integrable\, which are beyond the standard algebraic Bethe a
nsatz method. \n\nReference:\n[1] K. Zhang\, K. Hao\, K. Yu\, V. Korepin\,
and W.-L. Yang\, Geometric representations of braid and Yang-Baxter gates
\, J. Phys. A: Math. Theor. 57 445303\, arXiv:2406.08320 (2024).\n\n[2] K.
Zhang\, K. Yu\, K. Hao\, and V. Korepin\, Optimal realization of Yang-Bax
ter gate on quantum computers\, Adv. Quantum Technol. 2024\, 2300345\, arX
iv:2307.16781 (2024).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xin Zhang (Institute of Physics\, Chinese Academy of Sciences)
DTSTART:20241217T080000Z
DTEND:20241217T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/80
DESCRIPTION:Title: Chiral coordinate Bethe ansatz for anisotropic spin chains\n
by Xin Zhang (Institute of Physics\, Chinese Academy of Sciences) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIn this talk\, I will i
ntroduce the chiral coordinate Bethe ansatz for anisotropic spin chains wi
th periodic boundaries\, including the XYZ\, XY\, and XX models. First\, w
e construct a set of factorized chiral vectors with a fixed number of kink
s\, which form an invariant subspace of the Hilbert space. Next\, we propo
se a modified coordinate Bethe ansatz method to solve the XYZ model\, base
d on the action of the Hamiltonian on the chiral vectors. For the XY and X
X models\, we demonstrate that our Bethe ansatz yields all normalized eige
nstates and the complete spectrum of the Hamiltonian. The differences betw
een our approach and other methods are also discussed.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Zinn-Justin (University of Melbourne)
DTSTART:20250218T080000Z
DTEND:20250218T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/81
DESCRIPTION:Title: Generic pipe dreams\, lower-upper varieties\, and Schwartz–Mac
Pherson classes\nby Paul Zinn-Justin (University of Melbourne) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nI will describe some a
pplications of solvable lattice models to various problems in enumerative
geometry. I will focus on so-called "pipe dreams"\, which are lattice mode
l configurations in disguise\, and various generalisations (generic\, hybr
id\, etc).\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Matushko (Steklov Mathematical Institute of Russian Academy
of Sciences)
DTSTART:20250225T080000Z
DTEND:20250225T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/82
DESCRIPTION:Title: A trigonometric solution of the associative Yang-Baxter equation
related to the queer Lie superalgebra\nby Maria Matushko (Steklov Mat
hematical Institute of Russian Academy of Sciences) as part of BIMSA Integ
rable Systems Seminar\n\n\nAbstract\nI will show that the rational solutio
n of the quantum Yang-Baxter equation related to the queer Lie superalgebr
a satisfies the associative Yang-Baxter equation. Then I will tell about t
he construction of such a trigonometric solution of the associative Yang-B
axter equation. The talk is based on arXiv:2412.19214\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arthur Hutsalyuk (SISSA)
DTSTART:20250311T080000Z
DTEND:20250311T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/84
DESCRIPTION:Title: Exact Spin Correlators of Integrable Quantum Circuits from Algeb
raic Geometry\nby Arthur Hutsalyuk (SISSA) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nWe calculate the correlation functions of
strings of spin operators for integrable quantum circuits exactly. These o
bservables can be used for calibration of quantum simulation platforms. We
use algebraic Bethe Ansatz\, in combination with computational algebraic
geometry to obtain analytic results for medium-size (around 10-20 qubits)
quantum circuits. The results are rational functions of the quantum circui
t parameters. We obtain analytic results for such correlation functions bo
th in the real space and Fourier space. In the real space\, we analyze the
short time and long time limit of the correlation functions. In Fourier s
pace\, we obtain analytic results in different parameter regimes\, which e
xhibit qualitatively different behaviors. Using these analytic results\, o
ne can easily generate numerical data to arbitrary precision.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jue Hou (Shing-Tung Yau Center\, Southeast University)
DTSTART:20250318T080000Z
DTEND:20250318T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/85
DESCRIPTION:Title: Spin-s Q-systems: Twist and Open Boundaries\nby Jue Hou (Shi
ng-Tung Yau Center\, Southeast University) as part of BIMSA Integrable Sys
tems Seminar\n\n\nAbstract\nIn this talk\, I will explore the eigenvalue p
roblem of integrable spin chains using the Bethe ansatz. I will begin with
a review of the rational Q-system\, a powerful tool for solving Bethe equ
ations. Then\, I will demonstrate how Bethe solutions evolve under twist b
oundaries. Most importantly\, I will highlight our key findings: the disco
very of hidden symmetries and magnetic strings under specific open boundar
y parameters. These novel phenomena provide new insights into the interpla
y between symmetries and boundary conditions.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jirui Guo (Tongji University)
DTSTART:20250325T080000Z
DTEND:20250325T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/86
DESCRIPTION:Title: Quantum integrable model for the quantum cohomology/K-theory of
flag varieties and the double β-Grothendieck polynomials\nby Jirui Gu
o (Tongji University) as part of BIMSA Integrable Systems Seminar\n\n\nAbs
tract\nThe $GL(N)$ asymmetric five vertex model is a quantum integrable sy
stem that generalizes the spin-1/2 five vertex model. In this talk\, I wil
l explain why the Bethe ansatz equations of this model encode the ring rel
ations of the equivariant quantum cohomology and $K$-theory ring of flag v
arieties\, and how the Bethe ansatz states generate the double β-Grothend
ieck polynomials.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Nijhoff (University of Leeds)
DTSTART:20250401T080000Z
DTEND:20250401T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/87
DESCRIPTION:Title: The Elliptic lattice KdV system: a curious discrete integrable s
ystem\nby Frank Nijhoff (University of Leeds) as part of BIMSA Integra
ble Systems Seminar\n\n\nAbstract\nThe elliptic lattice KdV was introduced
in 2003 as a system that \ngeneralises the lattice potential KdV equation
. It is a rather complicated system \nfor 3 components which contains an e
lliptic curve in the fixed parameters (in addition \nto the lattice parame
ters). It was constructed on the basis of a `direct linearisation scheme'
\nwith an elliptic Cauchy kernel. \n\nIn the talk I will highlight some
newly discovered aspects: \na reformulation in terms of a 2-component mult
iquartic system\, an associated \nelliptic Yang-Baxter map\, aan associate
d system of 2x2 matrix equations and \nand a 6-component elliptic generali
sation of the Ernst equations which forms the \n`generating PDE system' fo
r the related continuous hierarchy of integrable PDEs.\n \n(This work is i
n collaboration with Cheng Zhang and Da-jun Zhang.)\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Chalykh (University of Leeds)
DTSTART:20250415T080000Z
DTEND:20250415T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/88
DESCRIPTION:Title: Integrability of the Inozemtsev spin chain\nby Oleg Chalykh
(University of Leeds) as part of BIMSA Integrable Systems Seminar\n\n\nAbs
tract\nWe show that the Inozemtsev spin chain is integrable. The conserved
quantities (commuting Hamiltonians) are constructed using elliptic Dunkl
operators. We also suggest a generalisation.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Matushko (Steklov Mathematical Institute of Russian Academy
of Sciences)
DTSTART:20250331T090000Z
DTEND:20250331T100000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/89
DESCRIPTION:Title: The associative Yang-Baxter equation and R-matrix Lax pairs for
Calogero models\nby Maria Matushko (Steklov Mathematical Institute of
Russian Academy of Sciences) as part of BIMSA Integrable Systems Seminar\n
\n\nAbstract\nThe elliptic Calogero-Moser system admits the so-called R-ma
trix Lax pair presentation\, the matrix elements are expressed in terms o
f the quantum GL_N Baxter-Belavin elliptic R-matrices. For N = 1 this con
struction reproduces the Krichever’s Lax pair with spectral parameter. T
he equations of motion follow from the associative Yang-Baxter equation fo
r the elliptic Baxter-Belavin R-matrix.\n\nI will tell how to extend the K
irillov's B-type associative Yang-Baxter equations to the similar relation
s depending on the spectral parameters and to construct an $R$-matrix val
ued Lax pair in terms of the 8-vertex elliptic R-matrix for the Calogero-I
nozemtsev system.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hrachya Babujian (BIMSA and Alikhanyan National Science Laboratory
\, Yerevan\, Armenia)
DTSTART:20250422T080000Z
DTEND:20250422T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/90
DESCRIPTION:Title: Factorization in deep inelastic scattering at Bj\\"orken limit:
Reduction to (1+1)D integrable models\nby Hrachya Babujian (BIMSA and
Alikhanyan National Science Laboratory\, Yerevan\, Armenia) as part of BIM
SA Integrable Systems Seminar\n\n\nAbstract\nWe investigate structure func
tions in deep inelastic scattering processes (DIS) at Bj\\"orken limit\nan
d found that they are factorized into the longitudinal and transversal par
ts. We see\, that the\nlongitudinal part can be linked to exact form facto
rs calculated earlier in 1+1 dimensional integrable\nquantum field theorie
s\, such as sine-Gordon model. We extract asymptotic of Form-factors at sm
all\nBj\\"orken parameter $x$ and compare it with experimental data of HER
A and ZEUS collaborations\non Deep inelastic lepton-proton scattering. We
observe the factorization of the structure functions\n$F_2(x\, q_2$) and f
ind out its power behavior on scaling parameter $x$.\n\nBased on arXiv:250
3.11735\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoyue Sun (BIMSA)
DTSTART:20250520T080000Z
DTEND:20250520T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/91
DESCRIPTION:Title: Tetrahedron equation\, cluster algebra and quantum field theorie
s\nby Xiaoyue Sun (BIMSA) as part of BIMSA Integrable Systems Seminar\
n\n\nAbstract\nThe Zamolodchikov tetrahedron equation is a fundamental rel
ation for integrability of quantum field theories in (2+1)-D and of statis
tical mechanical models on 3D lattices\, much in the same way as its lower
-dimensional analog\, the Yang–Baxter equation\, is a fundamental relati
on in integrable (1+1)-D quantum field theories and 2D lattice models. Com
pared to the Yang–Baxter equation\, however\, our understanding of the t
etrahedron equation is still limited despite its obvious importance and re
latively long history. This talk will explore constructing solutions to th
e tetrahedron equation using cluster algebra\, based on collaborations wit
h Junya Yagi [arXiv: 2211.10702]\, and Rei Inoue\, Atsuo Kuniba\, Yuji Ter
ashima\, and Junya Yagi [arXiv:2403.08814]. Our cluster algebraic approach
recovers most known solutions as special limits and links these solutions
to some partition functions of 3D N=2 gauge theories on a 3D ellipsoid\,
unveiling the first connection between 3D integrable systems and supersymm
etric gauge theories. If time permits\, I will also talk about an ongoing
work collaborated with Myungbo Shim\, Hao Wang and Junya Yagi. In this ong
oing work\, we use a topological field theory-based method to construct ne
w solutions of the modified tetrahedron equation.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Litvinov (Skoltech\, Landau Institute)
DTSTART:20250513T080000Z
DTEND:20250513T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/92
DESCRIPTION:Title: Integrable structures in conformal field theory\, affine Yangian
s and Bethe ansatz equations\nby Alexey Litvinov (Skoltech\, Landau In
stitute) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIn thi
s talk\, I will discuss the affine Yangian approach to conformal field the
ories. The affine Yangian symmetry appears naturally in conformal field th
eories whose symmetry algebras admit representations as commutant of scree
ning operators\, including but not limited to Toda field theories of the B
CD type.\n\nI will follow certain examples and explain how this constructi
on works\, with special emphasis on the construction of off-shell/on-shell
Bethe vectors.\n\nMy talk is based on the results obtained in collaborati
on with Ilya Vilkoviskiy\, Elizaveta Chistyakova\, Pavel Orlov\, Dmitry Ko
lyaskin\, Arkady Zhukov and Nikita Ignatyuk\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Litvinov (Skoltech\, Landau Institute)
DTSTART:20250527T080000Z
DTEND:20250527T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/93
DESCRIPTION:Title: Integrable structures in conformal field theory\, affine Yangian
s and Bethe ansatz equations\nby Alexey Litvinov (Skoltech\, Landau In
stitute) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIt is
the second part of the previous talk on the 13th of May.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akihiro Hokkyo (Ueda Group\, Department of Physics\, The Universit
y of Tokyo)
DTSTART:20251125T080000Z
DTEND:20251125T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/94
DESCRIPTION:Title: Integrability from a Single Conservation Law in Quantum Spin Cha
ins\nby Akihiro Hokkyo (Ueda Group\, Department of Physics\, The Unive
rsity of Tokyo) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\
nIdentifying integrable systems has been one of the central problems in ri
gorous statistical mechanics. In this talk\, I will discuss a recent resul
t [1] on the mathematical structure of integrability in quantum spin chain
s with finite-range interactions. We prove that the existence of a specifi
c conservation law\, known as the Reshetikhin condition\, implies the pres
ence of infinitely many local conserved quantities—that is\, integrabili
ty. This result shows that the entire hierarchy of conservation laws assoc
iated with solutions of the Yang–Baxter equation is already encoded in t
he lowest nontrivial conservation law. Combined with recent progress on th
e absence of integrability in generic systems [2]\, I will also discuss th
e sharp boundary between integrable and nonintegrable quantum spin chains.
\n\n[1] A.Hokkyo\, "Integrability from a Single Conservation Law in Quantu
m Spin Chains"\, arXiv:2508.20713.\n \n\n[2] A.Hokkyo\, "Rigorous Test for
Quantum Integrability and Nonintegrability"\, arXiv:2501.18400.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Safonkin (Leipzig University)
DTSTART:20251202T080000Z
DTEND:20251202T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/95
DESCRIPTION:Title: Deformation quantization of double Poisson algebras\nby Niki
ta Safonkin (Leipzig University) as part of BIMSA Integrable Systems Semin
ar\n\n\nAbstract\nDouble Poisson brackets\, introduced by M. Van den Bergh
in 2004\, are noncommutative analogs of the usual Poisson brackets in the
sense of the Kontsevich–Rosenberg principle: for any $N$\, they induce
Poisson structures on the space of $N$-dimensional representations $\\math
rm{Rep}_N(A)$ of an associative algebra $A$. The problem of deformation qu
antization of double Poisson brackets was raised by D. Calaque in 2010 and
has remained open since then. In the talk\, I will discuss a solution to
this problem and present a structure on $A$ that induces a star-product un
der the representation functor and therefore\, according to the Kontsevich
–Rosenberg principle\, can be viewed as an analog of star-products in no
ncommutative geometry. I will also discuss an analog of the famous formali
ty theorem of M.Kontsevich in this context. \n\nThe talk is based on arXiv
:2506.00699.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuancheng Xie (Shenzhen-MSU-BIT University)
DTSTART:20251118T080000Z
DTEND:20251118T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/96
DESCRIPTION:Title: Commuting ring of differential operators with more than three ge
nerators\nby Yuancheng Xie (Shenzhen-MSU-BIT University) as part of BI
MSA Integrable Systems Seminar\n\n\nAbstract\nIn 1920s\, Burchnall and Cha
undy studied when two ordinary differential operators commute\, and this l
eads to deep connection with the theory of plane algebraic curves. This th
eory was later developed and used by Krichever to construct algebro-geomet
ric solutions for KP hierarchy.\n\nIn this talk\, I will associate a famil
y of singular space curves indexed by the numerical semigroups $\\langle l
\, lm+1\, \\dots\, lm+k \\rangle$ where $m \\ge 1$ and $1 \\le k \\le l-1$
with a class of generalized KP solitons. Some of these curves can be defo
rmed into smooth ``space curves"\, and they provide canonical models for t
he $l$-th generalized KdV hierarchies (KdV hierarchy corresponds to the ca
se $l = 2$). We will see how to construct the space curves from a commuta
tive ring of differential operators with more than three generators. \n\nT
his talk is based on a joint work with Yuji Kodama.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Solovyev (Tsinghua University)
DTSTART:20251216T080000Z
DTEND:20251216T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/97
DESCRIPTION:Title: Limit shapes of probability measures in representation theory of
U_q(sl_2) at roots of unity\nby Dmitry Solovyev (Tsinghua University)
as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nLimit shape ph
enomenon emerges in systems with random behavior. It manifests a formation
of the most probable state\, where all other macroscopically different st
ates are exponentially improbable. In this talk\, we explore such phenomen
a in the Grothendieck ring of the category of tilting modules for the quan
tum group U_q(sl_2) with divided powers\, where q is an even root of unity
. Considering large tensor powers of the defining representation\, we desc
ribe the most probable trajectory in the main Weyl chamber with respect to
the character probability measure and analyze fluctuations around this li
mit shape. \n\nThis talk is based on arXiv:2404.03933\, a joint work with
A. Lachowska\, O. Postnova and N. Reshetikhin.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Alfimov (Lebedev Physics Institute / Higher School of Econ
omics)
DTSTART:20251223T080000Z
DTEND:20251223T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/98
DESCRIPTION:Title: On RG flow and dual description of N=2 supersymmetric 2d integra
ble sigma models\nby Mikhail Alfimov (Lebedev Physics Institute / High
er School of Economics) as part of BIMSA Integrable Systems Seminar\n\n\nA
bstract\nThere are several known examples of integrable deformations of 2D
sigma models\, including N=2 supersymmetric ones\, for which there exist
dual descriptions in terms of Toda-type theories. For such deformations th
ere is a system of screening charges\, depending on the continuous paramet
er b\, which determines deformed sigma model in the limit b to infinity an
d certain quantum field theory of Toda type in the limit b to 0. In the l
atter regime one can see that the 2-particle scattering matrix coincides w
ith the expansion of the trigonometric S-matrix of the corresponding defor
med sigma model. In the sigma model regime it can be shown that the leadin
g ultraviolet asymptotic of the deformed sigma model coincides with pertur
bed Gaussian theory. We study the regularization scheme dependence of Kaeh
ler (N = 2) supersymmetric sigma models. At the one-loop order the metric
beta-function is the same as in the\nnon-supersymmetric case and it coinci
des with the Ricci tensor. The first correction in the MS scheme is known
to appear in the fourth loop in both cases. Also for the N=2 case the fift
h loop contribution was previously calculated. We show that for certain in
tegrable Kähler backgrounds\, such as the complete T-dual of eta-deformed
CP(n) sigma models and lambda-deformed ones\, there is a renormalization
scheme in which the fourth and fifth loop contributions vanish. This poten
tially paves the way for the all-loop dual description of such sigma model
s in terms of Toda type theories.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Didina Serban (Institut de Physique Théorique\, Saclay)
DTSTART:20260106T080000Z
DTEND:20260106T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/99
DESCRIPTION:Title: The fermionic point of the q-deformed Haldane-Shastry model\
nby Didina Serban (Institut de Physique Théorique\, Saclay) as part of BI
MSA Integrable Systems Seminar\n\n\nAbstract\nThe talk will present an int
egrable anisotropic (XXZ-like) deformation of the Haldane-Shastry spin cha
in. Thanks to the long-range nature of the spin-spin interaction\, the cha
in possesses quantum affine symmetry that q-deforms the Yangian symmetry.
At q=i the model can be written in terms of non-unitary fermions\, and the
symmetry becomes extended gl(1|1) symmetry. The spectrum is radically dif
ferent for even and odd lengths of the chain. In the former case all the c
onserved quantities are nilpotent\, in the latter the dispersion relation
is linear and the spectrum displays features of fractional statistics.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilia Danilin (Weizmann Institute of Science)
DTSTART:20260113T080000Z
DTEND:20260113T090000Z
DTSTAMP:20260404T094912Z
UID:BIMSA-ISS/100
DESCRIPTION:Title: Algebraic topology of Shuffle algebras and Nichols algebras
\nby Ilia Danilin (Weizmann Institute of Science) as part of BIMSA Integra
ble Systems Seminar\n\n\nAbstract\nI will discuss the ongoing work on the
classification of so-called Nichols algebras of diagonal type and explain
how they are connected to quantum groups. This problem is naturally dual t
o the description of relations in the generalized shuffle algebra\, which
can be reformulated in homological terms. I will state a theorem relating
the shuffle algebra's homology to the homology of a local system on a conf
iguration space. Finally\, I will suggest a conjecture regarding the latte
r.\n
LOCATION:https://stable.researchseminars.org/talk/BIMSA-ISS/100/
END:VEVENT
END:VCALENDAR