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BEGIN:VEVENT
SUMMARY:Anton Nazarov (Saint Petersburg State University)
DTSTART;VALUE=DATE-TIME:20230113T090000Z
DTEND;VALUE=DATE-TIME:20230113T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/1
DESCRIPTION:Title: Skew Howe duality\, limit shapes of Young diagrams and universal fluctua
tions\nby Anton Nazarov (Saint Petersburg State University) as part of
BIMSA Integrable Systems Seminar\n\n\nAbstract\nSchur-Weyl\, Howe and ske
w Howe dualities in representation theory of groups lead to multiplicity-f
ree decompositions of certain spaces into irreducible representations and
can be used to introduce probability measures on Young diagrams that param
eterize irreducible representations. It is interesting to study the behavi
or of such measures in the limit\, when groups become infinite or infinite
-dimensional. Schur-Weyl duality and GL(n)-GL(k) Howe duality are related
to classical works of Anatoly Vershik and Sergey Kerov\, as well as Logand
-Schepp\, Cohn-Larsen-Propp and Baik-Deift-Johannson. Skew GL(n)-GL(k) How
e duality was considered by Gravner\, Tracy and Widom\, who were intereste
d in the local fluctuations of the diagrams\, the limit shapes were studie
d Sniady and Panova. They demonstrated that results by Romik and Pittel on
limit shapes of rectangular Young tableaux are applicable in this case.\n
We consider skew Howe dualities for the actions of classical Lie group pai
rs: GL(n)-GL(k)\, Sp(2n)-Sp(2k)\, SO(2n)-O(2k) on the exterior algebras. W
e describe explicitly the limit shapes for probability measures defined by
the ratios of dimensions and demonstrate that they are essentially the sa
me for all classical Lie groups. Using orthogonal polynomials we prove cen
tral limit theorem for global fluctuations around these limit shapes. Usin
g free-fermionic representation we study local fluctuations for more gener
al measures given by ratios of representation characters for skew GL(n)-GL
(k) Howe duality. These fluctuations are described by Tracy-Widom distribu
tion in the generic case and in the corner by a certain discrete distribut
ion\, first obtained in papers by Gravner\, Tracy and Widom. Study of loca
l fluctuations for other classical series remains an open problem\, but we
present numerical evidence that these distributions are universal.\n\nBas
ed on joint works with Dan Betea\, Pavel Nikitin\, Olga Postnova\,\nDaniil
Sarafannikov and Travis Scrimshaw. See arXiv:2010.16383\,\n2111.12426\, 2
208.10331\, 2211.13728.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Talalaev (MSU\, YarSU\, ITEP)
DTSTART;VALUE=DATE-TIME:20230120T090000Z
DTEND;VALUE=DATE-TIME:20230120T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/2
DESCRIPTION:Title: The full Toda system\, QR decomposition and geometry of the flag varieti
es\nby Dmitry Talalaev (MSU\, YarSU\, ITEP) as part of BIMSA Integrabl
e Systems Seminar\n\n\nAbstract\nThe full Toda system is a generalization
of an open Toda chain\, which is one of the archetypal examples of integra
ble systems. The open Toda chain illustrates the connection of the theory
of integrable systems with the theory of Lie algebras and Lie groups\, is
a representative of the Adler-Kostant-Symes scheme for constructing and so
lving such systems. Until recently\, only some of the results from this li
st were known for the full Toda system. I will talk about the construction
\, the commutative family\, quantization and solution of the full Toda sys
tem by the QR decomposition method\, as well as about the application of t
his system to the geometry of flag vaireties. The material of my talk is b
ased on several joint works with A. Sorin\, Yu. Chernyakov and G. Sharygin
.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Yakubovich (Saint Petersburg State University)
DTSTART;VALUE=DATE-TIME:20230127T090000Z
DTEND;VALUE=DATE-TIME:20230127T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/3
DESCRIPTION:Title: Random growth of Young diagrams with uniform marginals\nby Yuri Yaku
bovich (Saint Petersburg State University) as part of BIMSA Integrable Sys
tems Seminar\n\n\nAbstract\nMany (random) growth procedures for integer pa
rtitions/Young diagrams has been introduced\nin the literature and intensi
vely studied. The examples include Pitman's `Chinese restaurant'\nconstruc
tion\, Kerov's Plancherel growth and many others. These procedures amount
to\ninsertion of a new box to a Young diagram on each step\, following ce
rtain Markovian procedure.\nHowever\, no such procedure leading to the uni
form measure on partitions of $n$ after $n$\nsteps is known. I will descr
ibe a Markiovian procedure of adding a rectangular block\nto a Young diagr
am with the property that given the growing chain visits some level $n$\,
it\npasses through each partition of $n$ with equal probabilities\, thus l
eading to the uniform\nmeasure on levels. I will explain connections to s
ome classical probabilistic objects.\nAlso I plan to discuss some aspects
of asymptotic behavior of this Markov chain and explain\nwhy the limit sha
pe is formed.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuancheng Xie (Peking University)
DTSTART;VALUE=DATE-TIME:20230203T090000Z
DTEND;VALUE=DATE-TIME:20230203T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/4
DESCRIPTION:Title: On the full Kostant-Toda lattice and the flag varieties\nby Yuanchen
g Xie (Peking University) as part of BIMSA Integrable Systems Seminar\n\n\
nAbstract\nIn 1967\, Japanese physicist Morikazu Toda proposed an integrab
le lattice model to\ndescribe motions of a chain of particles with exponen
tial interactions between nearest\nneighbors. Since then\, Toda lattice an
d its generalizations have become the test models\nfor various techniques
and philosophies in integrable systems and wide connections are\nbuilt wit
h many other branches of mathematics. In this talk\, I will characterize s
ingular\nstructure of solutions of the so-called full Kostant-Toda (f-KT)
lattices defined on simple\nLie algebras in two different ways: through th
e τ-functions and through the Kowalevski-\nPainlevé analysis. Fixing the
spectral parameters which are invariant under the f-KT flows\,\nwe build
a one to one correspondence between solutions of the f-KT lattices and poi
nts in\nthe corresponding flag varieties.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masatoshi Noumi (Rikkyo University\, Tokyo\, Japan)
DTSTART;VALUE=DATE-TIME:20230217T090000Z
DTEND;VALUE=DATE-TIME:20230217T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/5
DESCRIPTION:Title: Elliptic van Diejen difference operators and elliptic hypergeometric int
egrals of Selberg type\nby Masatoshi Noumi (Rikkyo University\, Tokyo\
, Japan) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nIn thi
s talk\, I propose a class of eigenfunctions for the elliptic van Diejen o
perators \n(Ruijsenaars operators of type BC) which are represented by ell
iptic hypergeometric \nintegrals of Selberg type. They are constructed fro
m simple seed eigenfunctions \nby integral transformations\, thanks to gau
ge symmetries and kernel function identities \nof the van Diejen operators
. \nBased on a collaboration with Farrokh Atai (University of Leeds\, UK)
.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Bobrova (National Research University Higher School of Econo
mics)
DTSTART;VALUE=DATE-TIME:20230224T090000Z
DTEND;VALUE=DATE-TIME:20230224T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/6
DESCRIPTION:Title: Different approaches for constructing non-abelian Painlevé equations\nby Irina Bobrova (National Research University Higher School of Economi
cs) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe famous
Painlevé equations play a significant role in modern mathematical physics
. The interest in their non-commutative extensions was motivated by the ne
eds of modern quantum physics as well as by natural attempts of mathematic
ians to extend ‘’classical’’ structures to the non-commutative cas
e.\n\nIn this talk we will consider several approaches that are useful for
detecting non-commutative analogs of the Painlevé equations. Namely\, th
e matrix Painlevé-Kovalevskaya test\, integrable non-abelian auxiliary au
tonomous systems\, and infinite non-commutative Toda equations. All of the
se methods allow us to find a finite list of non-abelian candidates for su
ch analogs. To provide their integrability\, one can present an isomonodro
mic Lax pair.\n\nThis talk is based on a series of papers joint with Vladi
mir Sokolov and on arXiv:2205.05107 joint with Vladimir Retakh\, Vladimir
Rubtsov\, and Georgy Sharygin (publ. in J. Phys. A: Math. Theor.).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Rybnikov (National Research University Higher School of Eco
nomics)
DTSTART;VALUE=DATE-TIME:20230310T090000Z
DTEND;VALUE=DATE-TIME:20230310T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/7
DESCRIPTION:Title: Bethe subalgebras and Kirillov-Reshetikhin crystals\nby Leonid Rybni
kov (National Research University Higher School of Economics) as part of B
IMSA Integrable Systems Seminar\n\n\nAbstract\nBethe subalgebras form a fa
mily of maximal commutative subalgebras of the Yangian of a simple Lie alg
ebra\, parametrized by regular elements of the corresponding adjoint Lie g
roup. We introduce an affine (Kirillov-Reshetikhin) crystal structure on t
he set of eigenlines for a Bethe subalgebra in a representation of the Yan
gian (under certain conditions on the representation\, satisfied by all te
nsor products of Kirillov-Reshetikhin modules in type A). This helps to de
scribe the monodromy of solutions of Bethe ansatz for the corresponding XX
X Heisenberg magnet chain. \n\nThis is a joint project with Inna Mashanova
-Golikova and Vasily Krylov.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huijun Fan (School of Mathematical Sciences\, Peking University)
DTSTART;VALUE=DATE-TIME:20230324T090000Z
DTEND;VALUE=DATE-TIME:20230324T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/8
DESCRIPTION:Title: On the Geometry of Landau-Ginzburg Model\nby Huijun Fan (School of M
athematical Sciences\, Peking University) as part of BIMSA Integrable Syst
ems Seminar\n\n\nAbstract\nAn LG model (M\, f) is given by a noncompact co
mplex manifold M and the\nholomorphic function f defined on it\, which is
an important model in string theory.\nBecause of the mirror symmetry conje
cture\, the research on the geometric structure and\nquantization theory o
f LG model has attracted more and more attention. Given a Calabi-\nYau (CY
) manifold\, we can define Gromov-Witten theory (A theory) on it\, and als
o study\nthe variation of Hodge structure on its mirror manifold (B theory
). Accordingly\, LG model\nincludes A theory - FJRW theory and Hodge struc
ture variational theory.\nThis report starts with some examples\, gives th
e geometric and topological\ninformation contained by a LG model\, and der
ives the relevant Witten equation\n(nonlinear) and Schrodinger equation (l
inear). The study of the solution space of these\ntwo sets of equations wi
ll lead to different quantization theories. Secondly\, we give our\nrecent
correspondence theorem of Hodge structures between LG model and CY\nmanif
old. Finally\, we will discuss some relevant issues.\n\nBio: Huijun Fan is
the director of the Key Laboratory of Mathematics and Applied\nMathematic
s of the Ministry of Education of Peking University and the deputy directo
r of\nthe Sino-Russian Math Center. He has won national outstanding youth
grant\, Changjiang\nDistinguished Professor of the Ministry of Education\,
and the second prize of the National\nNatural Science Award. He is the pl
enary speaker of the 2021 annual meeting of the\nChinese Mathematical Soci
ety.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Nikitin (BIMSA)
DTSTART;VALUE=DATE-TIME:20230210T090000Z
DTEND;VALUE=DATE-TIME:20230210T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/9
DESCRIPTION:Title: Semifinite harmonic functions on Bratteli diagrams\nby Pavel Nikitin
(BIMSA) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nLocall
y semisimple algebras (LS-algebras) are inductive limits of semisimple alg
ebras\, and can be fully characterized by their Bratteli diagrams ($\\math
bb{N}$-graded graphs). (Finite) harmonic functions on Bratteli diagrams ar
e a standard tool in the representation theory of LS-algebras and semifini
te harmonic functions are a natural generalization. We plan to give an ove
rview of the subject\, starting with the classical results for the infinit
e symmetric group\, followed by the recent results for the infinite symmet
ric inverse semigroup. Joint work with N.Safonkin\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay (BIMSA)
DTSTART;VALUE=DATE-TIME:20230303T090000Z
DTEND;VALUE=DATE-TIME:20230303T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/10
DESCRIPTION:Title: Geometry of Discrete Integrable Systems: QRT Maps and Discrete Painlev
é Equations\nby Anton Dzhamay (BIMSA) as part of BIMSA Integrable Sys
tems Seminar\n\n\nAbstract\nMany interesting examples of discrete integrab
le systems can be studied from the geometric point of\nview. In this talk
we will consider two classes of examples of such system: autonomous (QRT m
aps) and\nnon-autonomous (discrete Painlevé equations). We introduce some
geometric tools to study these systems\, such as the blowup procedure to
construct algebraic surfaces on which the mappings are regularized\, linea
rization of the mapping on the Picard lattice of the surface and\, for dis
crete Painlevé equations\, the decomposition of the Picard lattice into c
omplementary pairs of the surface and symmetry sub-lattices and constructi
on of a birational representation of affine Weyl symmetry groups that give
s a complete algebraic description of our non-linear dynamic. \n\nThis tal
k is based on joint work with Stefan Carstea (Bucharest) and Tomoyuki\nTak
enawa (Tokyo).\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grigori Olshanski (IITP\, Skoltech\, and HSE Univ.)
DTSTART;VALUE=DATE-TIME:20230317T090000Z
DTEND;VALUE=DATE-TIME:20230317T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/11
DESCRIPTION:Title: The centralizer construction and Yangian-type algebras\nby Grigori
Olshanski (IITP\, Skoltech\, and HSE Univ.) as part of BIMSA Integrable Sy
stems Seminar\n\n\nAbstract\nIn the 1980s\, Vladimir Drinfeld introduced a
nd studied the notion of Yangian Y(g) associated with an arbitrary simple
complex Lie algebra g. The Yangian Y(g) is a deformation of U(g[x])\, the
universal enveloping algebra for the Lie algebra of polynomial currents g[
x]. The general definition of Yangian is radically simplified for the cla
ssical series A\, and it is even more convenient to work with the reductiv
e algebra g=gl(n).\n\nIn the same 1980s\, it was discovered that the Yangi
an Y(gl(n)) can be constructed in an alternative way\, starting from some
centralizers in the universal enveloping algebra U(gl(n+N)) and then letti
ng N go to infinity. This "centralizer construction" was then extended to
the classical series B\, C\, D\, which lead to the so-called twisted Yang
ians. The theory that arose from this is presented in Alexander Molev's bo
ok "Yangians and classical Lie algebras"\, Amer. Math. Soc.\, 2007.\n\nI w
ill report on the recent work arXiv:2208.04809\, where another version of
the centralizer construction is proposed. It produces a new family of alge
bras and reveals new effects and connections.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youjin Zhang (Tsinghua University)
DTSTART;VALUE=DATE-TIME:20230421T090000Z
DTEND;VALUE=DATE-TIME:20230421T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/12
DESCRIPTION:Title: Linear reciprocal transformations of bihamiltonian integrable hierarchi
es\nby Youjin Zhang (Tsinghua University) as part of BIMSA Integrable
Systems Seminar\n\n\nAbstract\nFor an integrable hierarchy which possesses
a bihamiltonian structure with semisimple hydrodynamic limit\, we prove t
hat the linear reciprocal transformation with respect to any of its symmet
ry transforms it to another bihamiltonian integrable hierarchy. Moreover\,
we show that the central invariants of the bihamiltonian structure are pr
eserved under the reciprocal transformation. The main tools that we use to
obtain this result are the bihamiltonian and variational bihamiltonian co
homologies defined for a bihamiltonian structure of hydrodynamic type. We
also apply this result to study the problem of classification of bihamilto
nian integrable hierarchies.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhe Sheng (Jilin University\, Changchun)
DTSTART;VALUE=DATE-TIME:20230331T090000Z
DTEND;VALUE=DATE-TIME:20230331T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/13
DESCRIPTION:Title: Rota-Baxter groups\, post-groups and related structures\nby Yunhe S
heng (Jilin University\, Changchun) as part of BIMSA Integrable Systems Se
minar\n\n\nAbstract\nRota-Baxter operators on Lie algebras were first stud
ied by Belavin\, Drinfeld and Semenov-Tian-Shansky as operator forms of th
e classical Yang-Baxter equation.\n\nAs a fundamental tool in studying int
egrable systems\, the factorization theorem of Lie groups by Semenov-Tian-
Shansky was obtained by integrating a factorization of Lie algebras from s
olutions of the modified Yang-Baxter equation. Integrating the Rota-Baxter
operators on Lie algebras\, we introduce the notion of Rota-Baxter operat
ors on Lie groups and more generally on groups. Then the factorization the
orem can be achieved directly on groups. As the underlying structures of
Rota-Baxter operators on groups\, the notion of post-groups was introduce
d. The differentiation of post-Lie groups gives post-Lie algebras. Post-gr
oups are also related to Lie-Butcher groups\, and give rise to solutions o
f Yang-Baxter equations. \n\nThe talk is based on the joint work with Chen
gming Bai\, Li Guo\, Honglei Lang and Rong Tang.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ievgen Makedonskyi (BIMSA)
DTSTART;VALUE=DATE-TIME:20230407T090000Z
DTEND;VALUE=DATE-TIME:20230407T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/14
DESCRIPTION:Title: Duality theorems for current algebras\nby Ievgen Makedonskyi (BIMSA
) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe study some
natural representations of current Lie algebras $g\\otimes \\Bbbk[t]$\, c
alled Weyl modules. They are natural analogues of irreducible representati
ons of simple Lie algebras. There are several current analogues of classic
al theorems about Lie algebras where these modules «play role» of irredu
cible modules. In my talk I will explain analogues of duality theorems\, n
amely Peter-Weyl theorem\, Schur-Weyl duality etc.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Rubtsov (Université d’Angers\, ITTP Moscow and IGAP Tr
ieste)
DTSTART;VALUE=DATE-TIME:20230414T090000Z
DTEND;VALUE=DATE-TIME:20230414T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/15
DESCRIPTION:Title: Symplectic and Contact Geometry of Monge– Ampère equation: Introduct
ion and application\nby Vladimir Rubtsov (Université d’Angers\, ITT
P Moscow and IGAP Trieste) as part of BIMSA Integrable Systems Seminar\n\n
\nAbstract\nI am going to present an introduction into the geometric appro
ach to Monge– Ampère operators and equations based on contact and sympl
ectic structures of cotangent and the 1st jet bundles of a smooth manifold
. This approach was developed by V. Lychagin and goes back to the ideas of
E.Cartan and his successor T. Lepage. I shall try to make my talk self-co
ntained. I also plan to discuss various applications and links with import
ant geometric structures.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Piergiulio Tempesta (Universidad Complutense de Madrid and Institu
to de Ciencias Matemáticas (ICMAT) – Madrid\, Spain)
DTSTART;VALUE=DATE-TIME:20230519T090000Z
DTEND;VALUE=DATE-TIME:20230519T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/16
DESCRIPTION:Title: Generalized Nijenhuis geometry and applications to Hamiltonian integrab
le systems\nby Piergiulio Tempesta (Universidad Complutense de Madrid
and Instituto de Ciencias Matemáticas (ICMAT) – Madrid\, Spain) as part
of BIMSA Integrable Systems Seminar\n\n\nAbstract\nWe propose a new\, inf
inite family of tensor fields\, whose first representatives are the classi
cal Nijenhuis and Haantjes tensors. We prove that the vanishing of a suita
ble higher-level Haantjes torsion is a sufficient condition for the integr
ability of the eigen-distributions of an operator field on a differentiabl
e manifold. This new condition\, which does not require the explicit knowl
edge of the spectral properties of the considered operator\, generalizes t
he celebrated Haantjes theorem\, because it provides us with an effective
integrability criterion applicable to the generic case of non-Nijenhuis an
d non-Haantjes tensors. \nWe also propose a tensorial approach to the theo
ry of classical Hamiltonian integrable systems\, based on the geometry of
Haantjes tensors. We introduce the family of symplectic-Haantjes manifolds
as a natural setting where the notion of integrability can be formulated.
In particular\, the theory of separation of variables for classical Hamil
tonian systems can also be formulated in the context of our new geometric
structures.\n\nReferences:\nP. Tempesta\, G. Tondo\, Contemporary Mathemat
ics\, AMS (2023) (to appear)\nD. Reyes\, P. Tempesta\, G. Tondo\, J. Nonli
near Science 33\, 35 (2023)\nP. Tempesta\, G. Tondo\, Communications in Ma
thematical Physics 389\, 1647-1671 (2022)\nP. Tempesta\, G. Tondo\, Annali
Mat. Pura Appl. 201\, 57-90 (2022)\nP. Tempesta\, G. Tondo\, J. Geometry
and Physics 160\, 103968 (2021)\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto D'Onofrio (Università Bicocca and University of Surrey)
DTSTART;VALUE=DATE-TIME:20230428T090000Z
DTEND;VALUE=DATE-TIME:20230428T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/17
DESCRIPTION:Title: Singularities in geophysical fluid dynamics through Monge-Ampère geome
try\nby Roberto D'Onofrio (Università Bicocca and University of Surre
y) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThe semigeos
trophic equations are a mathematical model representing atmospheric motion
on a subcontinental scale. Their remarkable mathematical features enable
the equations to model singular behaviours like weather fronts. This talk
presents a new approach to classifying these singular structures using the
geometry of Monge-Ampère equations.\n\nIn the geometrical view\, solutio
ns are understood as Lagrangian submanifolds of a suitably defined phase s
pace equipped with a pseudo-Riemannian metric. We show the interplay betwe
en solution singularities\, elliptic-hyperbolic transitions of the Monge-A
mpère operator\, and the degeneracies of the metric on a few examples\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunfeng Jiang (Southeast University\, Nanjing)
DTSTART;VALUE=DATE-TIME:20230526T090000Z
DTEND;VALUE=DATE-TIME:20230526T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/18
DESCRIPTION:Title: Spin-s rational Q-system\nby Yunfeng Jiang (Southeast University\,
Nanjing) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nRation
al Q-system is an efficient method for solving Bethe ansatz equations (BAE
). One important feature of this method is that\, unlike solving BAE direc
tly\, it gives only physical solutions of BAE. Therefore\, it is intimatel
y related to the completeness problem of Bethe ansatz. In this talk\, I wi
ll first introduce the rational Q-system and discuss the completeness prob
lem of the spin-$1/2$ Heisenberg spin chain. Then I will move to the discu
ssion of the spin-$s$ Heisenberg spin chain where the situation is more co
mplicated. The key new feature here is that repeated roots are allowed. I
will present the rational Q-system for the higher spin models and discuss
the completeness problem for the spin-$s$ Heisenberg spin chain. The solut
ion of the proposed Q-system gives precisely the all the physical solution
s required by completeness of Bethe ansatz.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasuyuki Kawahigashi (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20230616T090000Z
DTEND;VALUE=DATE-TIME:20230616T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/19
DESCRIPTION:Title: $\\alpha$-induction\, tensor categories and operator algebras\nby Y
asuyuki Kawahigashi (University of Tokyo) as part of BIMSA Integrable Syst
ems Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/815469047
97?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9SUT09\nPassword hint: BIMSA\nView-only l
ivestream: https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9
S3jij\n\nAbstract\nTensor categories play an important role in theory of s
ubfactors in\noperator algebras in connection to conformal field theory an
d condensed\nmatter physics. A certain induction procedure called $\\alph
a$-induction has\nbeen studied as a quantum version of the classical induc
tion in group\nrepresentation theory. I will present this without assumin
g knowledge on\noperator algebras.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/19/
URL:https://us02web.zoom.us/j/81546904797?pwd=T1hjVFNzNEU4V3hiMUpGbVpqbE9S
UT09
URL:https://youtube.com/playlist?list=PLLGkFbxve670e0PsiNklMW2Ntkh9S3jij
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Matushko (Steklov MI RAS\, Moscow)
DTSTART;VALUE=DATE-TIME:20230505T090000Z
DTEND;VALUE=DATE-TIME:20230505T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/20
DESCRIPTION:Title: Anisotropic spin generalization of elliptic Ruijsenaars-Macdonald opera
tors and related integrable long-range spin chains\nby Maria Matushko
(Steklov MI RAS\, Moscow) as part of BIMSA Integrable Systems Seminar\n\n\
nAbstract\nWe propose commuting set of matrix-valued difference operators
in terms of the elliptic Baxter-Belavin R-matrix in the fundamental repres
entation of GL(M). In the scalar case M = 1 these operators are the ellipt
ic Ruijsenaars-Macdonald operators\, while in the general case they can be
viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonia
ns. We show that commutativity of the operators for any M is equivalent to
a set of R-matrix identities and prove them for the elliptic Baxter-Belav
in R-matrix. We show that the Polychronakos freezing trick can be applied
to this model. It provides the commuting set of Hamiltonians for long-rang
e spin chain. We also discuss the trigonometric degenerations based on the
XXZ R-matrix. \nThe talk is based on joint work with Andrei Zotov arXiv:2
201.05944 arXiv:2202.01177\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Roulstone (University of Surrey Guildford)
DTSTART;VALUE=DATE-TIME:20230602T090000Z
DTEND;VALUE=DATE-TIME:20230602T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/21
DESCRIPTION:Title: Applications of symplectic geometry in fluid dynamics\nby Ian Rouls
tone (University of Surrey Guildford) as part of BIMSA Integrable Systems
Seminar\n\n\nAbstract\nWe present a brief history of the application of me
thods from symplectic geometry to fluid dynamics\, and to geophysical syst
ems in particular. The material will cover both analytical and numerical a
pplications\, and emphasize the importance of geometric concepts in operat
ional weather prediction models. This seminar relates to others given rece
ntly in this series by Rubtsov and by D'Onofrio\, and there will be a focu
s on the role of partial differential equations of Monge—Ampere type.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Sergeev (Australian National University and University of C
anberra\, Canberra)
DTSTART;VALUE=DATE-TIME:20230609T090000Z
DTEND;VALUE=DATE-TIME:20230609T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/22
DESCRIPTION:Title: Spectral equations for a class of entire $Q$-operators\nby Sergey S
ergeev (Australian National University and University of Canberra\, Canber
ra) as part of BIMSA Integrable Systems Seminar\n\n\nAbstract\nThere is a
class of $\\mathcal{U}_q(\\widehat{sl}_2)$ models models where the infinit
e dimensional evaluation representations lead to Baxter's $TQ=Q+Q$ equatio
n where $Q$ is an entire function rather than a polynomial. I will give a
general introduction to the method of solving the Baxter equation in this
case.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jules Lamers (Institut de Physique Théorique (IPhT))
DTSTART;VALUE=DATE-TIME:20230512T090000Z
DTEND;VALUE=DATE-TIME:20230512T103000Z
DTSTAMP;VALUE=DATE-TIME:20230610T050318Z
UID:BIMSA-ISS/23
DESCRIPTION:Title: Bethe ansatz inside Calogero--Sutherland models\nby Jules Lamers (I
nstitut de Physique Théorique (IPhT)) as part of BIMSA Integrable Systems
Seminar\n\n\nAbstract\nThe Haldane--Shastry spin chain has long-range int
eractions and remarkable properties including Yangian symmetry at finite l
ength and explicit highest-weight wave functions featuring Jack polynomial
s. This stems from the trigonometric spin-Calogero--Sutherland model\, whi
ch is intimately related to affine Hecke algebras\, already enjoys these p
roperties from affine Schur–Weyl duality and reduces to the Haldane--Sha
stry chain in the ‘freezing’ limit. I will present some new results fo
r these models\, including Heisenberg-like symmetries whose spectrum can b
e characterised by Bethe ansatz.\n\nBased on recent work with D. Serban an
d ongoing work with G. Ferrando\, F. Levkovich-Maslyuk and D. Serban.\n
LOCATION:https://researchseminars.org/talk/BIMSA-ISS/23/
END:VEVENT
END:VCALENDAR