Center Seminar on Mondays / Spring2021

Center for Advanced Studies
Seminar on Mondays at 17.00 via Zoom

January 25, 2021 / Alexander Bobenko (Inst. Mathematik, TU Berlin)
= = On a discretization of confocal quadrics: Geometric parametrizations, integrable systems and incircular nets
February 1, 2021 / Andrei Smilga (Subatech, Univ. de Nantes)
= = Group manifolds and homogeneous spaces with HKT geometry: the role of automorphisms
February 8, 2021 / Sergey Cherkis (Univ. of Arizona)
= = Instantons and bow varieties, I
February 15, 2021 Sergei Korotkikh (MIT)
= = Vertex models and (non)symmetric functions
February 22, 2021 / Sergei Lukyanov (Rutgers Univ., Kharkevich Inst.)
= = Density of states for the (Euclidean) black hole NLSM
March 1, 2021 / Andrey Gelash (Skoltech, Inst. of Automation and Electrometry, Novosibirsk)
= = Spontaneous modulation instability and exact multi-soliton solutions of the nonlinear Schrodinger equation
March 8, 2021 / Sergey Cherkis (Univ. of Arizona)
= = Instantons and bow varieties, II
March 15, 2021 / Vladlen Timorin (HSE Univ.)
= = The Mandelbrot set and its topological models
March 22, 2021 / Alexei Glutsyuk (ENS de Lyon, HSE Univ.)
= = Dynamical systems on torus modeling the dynamics of Josephson junction, isomonodromic deformations, and Painlevé 3 equation
March 29, 2021 / Alexander Tsymbaliuk (Purdue Univ.)
= = Shifted Yangians and quantum affine algebras
April 5, 2021 / Vadim Prokofev (Skoltech, MIPT)
= = Integrable hierarchies of nonlinear differential equations and many body systems. Elliptic case
[ link to access the Seminar ]

April 12, 2021

Shamil Shakirov
(Univ. of Geneva)
Quantum DELL system and around

It has been long expected that trigonometric Ruijsenaars-Schneider integrable system should admit a generalization elliptic both in coordinates and in momenta, the so-called double elliptic system or DELL for short. In this talk we review the recent development of 1906.10354 by P.Koroteev and the speaker, where a candidate for such a system has been put forward. An advantage of this proposal is that it is fully explicit at quantum level, i.e. formulated as a set of commuting difference operators. We cover the basic properties of the resulting system and its eigenfunctions, comment on relation to the previous proposals for DELL, and discuss relation to other double-elliptic constructions in mathematical physics

April 19, 2021
Andrei Grekov
(Stony Brook Univ.)

April 26, 2021
Taras Panov
(Moscow State Univ., Kharkevich Inst.)
Complex geometry of manifolds with torus action