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BEGIN:VEVENT
SUMMARY:Hjalmar Rosengren (Chalmers University)
DTSTART:20220308T170000Z
DTEND:20220308T180000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/1
DESCRIPTION:Title: Deformed Ruijsenaars operators\nby Hjalmar Rosengren (Chalmers Un
iversity) as part of 2022 Workshop on Elliptic Integrable Systems\n\n\nAbs
tract\nThe Ruijsenaars operators are a commuting family of difference oper
ators with elliptic coefficients\, which define an integrable system of re
lativistic quantum particles. In the trigonometric limit\, they have Macdo
nald polynomials as joint eigenfunctions. Through the work of Chalykh\, Fe
igin\, Silantyev\, Veselov and others\, it has become apparent that even m
ore general "deformed" or "super" operators exist. We will describe how to
obtain the main properties of such operators in a direct way\, which work
s also in the elliptic setting. In particular\, we can prove that the defo
rmed elliptic Ruijsenaars model is integrable\, in the sense of constructi
ng a sufficiently large family of algebraically independent operators that
commute with the Hamiltonian. The talk is based on joint work with Martin
Hallnäs\, Edwin Langmann and Masatoshi Noumi.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Ruijsenaars (University of Leeds)
DTSTART:20220308T180000Z
DTEND:20220308T190000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/2
DESCRIPTION:Title: Around Razamat's A_2 and A_3 kernel identities\nby Simon Ruijsena
ars (University of Leeds) as part of 2022 Workshop on Elliptic Integrable
Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Felipe van Diejen (Universidad de Talca)
DTSTART:20220308T190000Z
DTEND:20220308T200000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/3
DESCRIPTION:Title: Eigenfunctions of a discrete elliptic integrable particle model with
hyperoctahedral symmetry\nby Jan Felipe van Diejen (Universidad de Tal
ca) as part of 2022 Workshop on Elliptic Integrable Systems\n\n\nAbstract\
nI report on joint work with Tamás Görbe (University of Groningen) conce
rning the eigenfunctions of a finite-dimensional truncation of the $BC_n$
elliptic Ruijsenaars type quantum hamiltonian. In the trigonometric limit
the eigenfunctions in question reproduce a well-known $q$-Racah type reduc
tion of the Koornwinder-Macdonald polynomials. When the interaction betwee
n the particles degenerates to a Pauli repulsion of free fermions\, the or
thogonal eigenbasis can be expressed in terms of generalized Schur polynom
ials on the spectrum that are associated with recently found elliptic Raca
h polynomials.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Etingof (Massachusetts Institute of Technology)
DTSTART:20220309T010000Z
DTEND:20220309T020000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/4
DESCRIPTION:Title: Hecke operators over local fields and an analytic approach to the geo
metric Langlands correspondence.\nby Pavel Etingof (Massachusetts Inst
itute of Technology) as part of 2022 Workshop on Elliptic Integrable Syste
ms\n\n\nAbstract\nI will review an analytic approach to the geometric Lang
lands correspondence\, following my work with E. Frenkel and D. Kazhdan\,
arXiv:1908.09677\, arXiv:2103.01509\, arXiv:2106.05243. This approach was
developed by us in the last couple of years and involves ideas from previo
us and ongoing works of a number of mathematicians and mathematical physic
ists\, Kontsevich\, Langlands\, Teschner\, and Gaiotto-Witten. One of the
goals of this approach is to understand single-valued real analytic eigenf
unctions of the quantum Hitchin integrable system. The main method of stud
ying these functions is realizing them as the eigenbasis for certain compa
ct normal commuting integral operators the Hilbert space of L2 half-densit
ies on the (complex points of) the moduli space Bun_G of principal G-bundl
es on a smooth projective curve X\, possibly with parabolic points. These
operators actually make sense over any local field\, and over non-archimed
ian fields are a replacement for the quantum Hitchin system. We conjecture
them to be compact and prove this conjecture in the genus zero case (with
parabolic points) for G=PGL(2). I will first discuss the simplest non-tri
vial example of Hecke operators over local fields\, namely G=PGL(2) and ge
nus 0 curve with 4 parabolic points. In this case the moduli space of semi
stable bundles Bun_G^{ss} is P^1\, and the situation is relatively well un
derstood\; over C it is the theory of single-valued eigenfunctions of the
Lame operator with coupling parameter -1/2 (previously studied by Beukers
and later in a more functional-analytic sense in our work with Frenkel and
Kazhdan). I will consider the corresponding spectral theory and then expl
ain its generalization to N>4 points and conjecturally to higher genus cur
ves.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junichi Shiraishi (University of Tokyo)
DTSTART:20220309T020000Z
DTEND:20220309T030000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/5
DESCRIPTION:Title: Quantization of Discrete Sixth Painlev\\'e Equation and Shakirov's C
onjecture\nby Junichi Shiraishi (University of Tokyo) as part of 2022
Workshop on Elliptic Integrable Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wenbin Yan (Tsinghua University)
DTSTART:20220309T030000Z
DTEND:20220309T040000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/6
DESCRIPTION:Title: Tetrahedron Instantons\nby Wenbin Yan (Tsinghua University) as pa
rt of 2022 Workshop on Elliptic Integrable Systems\n\n\nAbstract\nWe intro
duce and analyze tetrahedron instantons\, which can be realized in string
theory by D0-branes probing a configuration of intersecting D6-branes with
a nonzero constant background B-field. Physically they capture instantons
in six-dimensional gauge theories with the most general intersecting codi
mention-two supersymmetric defects. We study the properties of the moduli
space of tetrahedron instantons. We compute the instanton partition functi
on\, which lies between the higher-rank Donaldson-Thomas invariants and th
e partition function of the magnificent four model. Remarkably the instant
on partition function has a closed-form expression in terms of the plethys
tic exponential\, and matches the index of M-theory on a Calabi-Yau fivefo
ld. Our computations provide evidence of the duality between M-theory and
type IIA string theory on more general grounds.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykola Dedushenko (Simons Center for Geometry and Physics)
DTSTART:20220309T170000Z
DTEND:20220309T180000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/7
DESCRIPTION:Title: Interfaces and Quantum Algebras\nby Mykola Dedushenko (Simons Cen
ter for Geometry and Physics) as part of 2022 Workshop on Elliptic Integra
ble Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yegor Zenkevich (SISSA)
DTSTART:20220309T180000Z
DTEND:20220309T190000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/8
DESCRIPTION:Title: Pentagon identity in DIM algebra\nby Yegor Zenkevich (SISSA) as p
art of 2022 Workshop on Elliptic Integrable Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Zotov (MI RAS)
DTSTART:20220309T190000Z
DTEND:20220309T200000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/9
DESCRIPTION:Title: Spin generalization of the elliptic Macdonald-Ruijsenaars operators a
nd elliptic version of q-deformed Haldane-Shastry model\nby Andrey Zot
ov (MI RAS) as part of 2022 Workshop on Elliptic Integrable Systems\n\n\nA
bstract\nWe describe anisotropic spin generalization of the elliptic Macdo
nald-Ruijsenaars operators. Commutativity of the operators follows from a
set of R-matrix identities. Then the obtained spin operators are used for
constructing elliptic generalization of q-deformed Haldane-Shastry long-ra
nge spin chain. It is derived by the freezing trick and elliptic function
identities.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Krichever (Columbia University)
DTSTART:20220310T010000Z
DTEND:20220310T020000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/10
DESCRIPTION:Title: Turning points of elliptic integrable systems\nby Igor Krichever
(Columbia University) as part of 2022 Workshop on Elliptic Integrable Sys
tems\n\n\nAbstract\nThe notion of turning points of the elliptic Calogero-
Moser system was introduced in the recent work of N.Nekrasov and the autho
r where\, in particular\, the quasi-holomorphic solutions of the double pe
riodic O(2n+1) – sigma model were constructed. These solutions are expre
ssed in terms of the Riemann theta-functions of the spectral curves corres
ponding to the turning points. Lately\, in our joint works with Zabrodin t
he notion of turning points was extended to the case of the elliptic Ruijs
enaars-Schneider system. As it turned out\, the theory of the correspondin
g finite-dimensional systems is isomorphic to the theory of elliptic solut
ions of some basic (2+1)-dimensional hierarchies with symmetries. Among th
em CKP hierarchy\, Constrained 2D Toda hierarchy.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Smirnov (UNC)
DTSTART:20220310T020000Z
DTEND:20220310T030000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/11
DESCRIPTION:Title: Difference equations arising from elliptic stable envelopes\nby
Andrey Smirnov (UNC) as part of 2022 Workshop on Elliptic Integrable Syste
ms\n\n\nAbstract\nIn my talk I explain how certain class of q-difference e
quations can be constructed from the elliptic stable envelope. In this app
roach\, the elliptic R-matrices are identified with monodromy of differenc
e equations. The difference equations are arising from the monodromy via v
arious limiting procedures. For quiver varieties such approach leads to qu
antum difference equations\, playing role in enumerative geometry.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hee-Cheol Kim (POSTECH)
DTSTART:20220310T030000Z
DTEND:20220310T040000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/12
DESCRIPTION:Title: Elliptic quantum curves of 6d SCFTs\nby Hee-Cheol Kim (POSTECH)
as part of 2022 Workshop on Elliptic Integrable Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Chalykh (University of Leeds)
DTSTART:20220310T170000Z
DTEND:20220310T180000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/13
DESCRIPTION:Title: Twisted Ruijsenaars models\nby Oleg Chalykh (University of Leeds
) as part of 2022 Workshop on Elliptic Integrable Systems\n\n\nAbstract\nT
he quantum Ruijsenaars model is a q-analogue of the Calogero—Moser model
\, described by n commuting partial difference operators (quantum hamilton
ians) h_1\,...\, h_n. It turns out that for each natural number m>1\, ther
e exists an integrable system whose quantum hamiltonians loosely resemble
the m-th powers of h_1\,...\, h_n. I will discuss several ways of arriving
at this generalisation. In the elliptic case\, the deformation parameter
(“twisting”) is an arbitrary $m$-torsion point c on the underlying ell
iptic curve\; when c=0 one gets precisely the m-th powers of h_1\,...\, h_
n.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Bullimore (University of Durham)
DTSTART:20220310T180000Z
DTEND:20220310T190000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/14
DESCRIPTION:Title: 3d Supersymmetric Gauge Theory on an Elliptic Curve\nby Matthew
Bullimore (University of Durham) as part of 2022 Workshop on Elliptic Inte
grable Systems\n\n\nAbstract\nThere are beautiful connections between supe
rsymmetric gauge theory in various dimensions and generalised cohomology t
heories. In this talk\, I will discuss the ground states of 3d supersymmet
ric theories on an elliptic curve\, focussing on the mathematical structur
e of the Berry connection that encodes their dependence on background flat
connections for global symmetries. I will explain connections to generali
sed doubly periodic monopoles\, equivariant elliptic cohomology and equiva
riant K-theory. Based on https://arxiv.org/abs/2109.10907 and work in prog
ress with Daniel Zhang.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shlomo Razamat (Technion)
DTSTART:20220310T190000Z
DTEND:20220310T200000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/15
DESCRIPTION:Title: Comments on modularity of Schur indices\nby Shlomo Razamat (Tech
nion) as part of 2022 Workshop on Elliptic Integrable Systems\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shamil Shakirov (University of Geneva)
DTSTART:20220311T170000Z
DTEND:20220311T180000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/16
DESCRIPTION:Title: Nonstationary difference equation for q-Virasoro conformal blocks\nby Shamil Shakirov (University of Geneva) as part of 2022 Workshop on E
lliptic Integrable Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Gorsky (IITP\, Moscow)
DTSTART:20220311T180000Z
DTEND:20220311T190000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/17
DESCRIPTION:Title: Dualities in the integrable many-body systems and integrable probabi
lities\nby Alexander Gorsky (IITP\, Moscow) as part of 2022 Workshop o
n Elliptic Integrable Systems\n\n\nAbstract\nWe shall discuss several dual
ities in the realm of integrable many-body systems which involve two famil
ies. One family involves inhomogeneous XXZ spin chain and its degeneration
s while the second involves Calogero-Moser-Ruijsenaars-Schneider (CM-RS) i
ntegrable models. First type of duality-so called spectral duality acts wi
thin families and relates two different many-body systems when the coordin
ates and action variables get interchanged. The second QC duality acts bet
ween the families and maps the quantum spin chain system to the classical
CM-RS models with nontrivial identification of variables and parameters. I
t can be generalized to the QQ duality when both dual systems are quantum.
We shall map the dualities observed in the framework of integrable probab
ilities into the spectral and QQ dualities . As an example\, we will show
a new duality between the discrete-time inhomogeneous multispecies TASEP m
odel on the circle and the quantum Goldfish model from the RS family.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Spiridonov (HSE\, Moscow & JINR\, Dubna)
DTSTART:20220311T190000Z
DTEND:20220311T200000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/18
DESCRIPTION:Title: Limits of the elliptic hypergeometric equation and integrable system
s\nby Vyacheslav Spiridonov (HSE\, Moscow & JINR\, Dubna) as part of 2
022 Workshop on Elliptic Integrable Systems\n\n\nAbstract\nWe describe som
e new rational degenerations of the elliptic hypergeometric equation and i
ts solutions. They lead to new rational degenerations of the Ruijsenaars a
nd van Diejen elliptic integrable systems. \n\nThis is a joint work with G
or Sarkissian.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Gaiotto (Perimeter Institute)
DTSTART:20220311T010000Z
DTEND:20220311T020000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/19
DESCRIPTION:Title: Algebras from twisted M-theory\nby Davide Gaiotto (Perimeter Ins
titute) as part of 2022 Workshop on Elliptic Integrable Systems\n\n\nAbstr
act\nI will describe the relations between twisted M-theory\, the affine Y
angian and Calogero models. \nThese constructions govern many aspects of t
he theory of W-algebras\, including degenerate modules\, the Miura transfo
rm and Coulomb gas constructions.\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ole Warnaar (University of Queensland)
DTSTART:20220311T020000Z
DTEND:20220311T030000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/20
DESCRIPTION:Title: Generalised Elliptic Selberg Integrals\nby Ole Warnaar (Universi
ty of Queensland) as part of 2022 Workshop on Elliptic Integrable Systems\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Heckman (University of Pensilvania)
DTSTART:20220311T030000Z
DTEND:20220311T040000Z
DTSTAMP:20260410T064617Z
UID:Elliptic2022/21
DESCRIPTION:Title: 6D SCFTs\, 4D SCFTs\, Conformal Matter and Spin Chains\nby Jonat
han Heckman (University of Pensilvania) as part of 2022 Workshop on Ellipt
ic Integrable Systems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Elliptic2022/21/
END:VEVENT
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