Speaker: D. Talalaev (MSU, YarSU, ITEP)

Date and time: 28.10.2026, 17:00 (Moscow time, GMT +03:00)

Title: Exact Lie-Bianchi integrability of the full symmetric Toda system

Abstract: The talk will focus on a recent joint result with G. Sharygin and Y. Chernyakov, generalizing the Li-Bianchi integrability property of a complete symmetric Toda system. We have integrated the Lie algebra of symmetries of the full Toda system to an action of the stochastic Lie group ST(n) on the phase space commuting with the isospectral flows of the system. Moreover, we have identified the space of ST(n) orbits with the phase space of the open Toda chain and realized the projection as the famous Lanczos-Krylov map.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: A. Kazakov (HSE, YarSU, MIAN)

Date and time: 21.10.2026, 17:00 (Moscow time, GMT +03:00)

Title: Positivity in linear systems: combinatorial approach

Abstract: The main problem of electrical network theory is synthesis (finding the topology and values) of an electrical network from a given response matrix, such as a conductance or resistance matrix. However, not every matrix is realizable, which gives rise to the problem of fully characterizing the matrices that admit realization in a given class of networks. For planar resistive networks, such a characterization is given by the condition of complete circular nonnegativity of all minors of the response matrix. Remarkably, this result can be generalized to networks with controlled current sources (which are a linear approximation of networks with transistors) and Schrodinger networks. We will talk about these generalizations and how they are obtained using the general combinatorial theory of linear systems; we will also discuss the connection of these results with positive Grassmannians.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Rustem N. Garifullin (Institute of Mathematics, Ufa FRC RAS)

Date and time: 14.10.2026, 17:00 (Moscow time, GMT +03:00)

Title: On integrable quad equations

Abstract: The talk reviews the author’s results on higher symmetries and integrability of nonlinear discrete equations on the square lattice. We discuss a method for constructing higher symmetries and its application to the classification of multi-affine equations. Discrete equations with prescribed symmetries are considered as Bäcklund transformations for integrable differential-difference equations of Volterra and Toda type. Particular attention is paid to unusual symmetry structures and the role of periodic coefficients in nonautonomous equations. We also present families of Darboux integrable discrete equations with first integrals of arbitrarily high minimal order.

Video of the talk:
https://rutube.ru/video/private/a78a277512b853f27a6788a06a1185ec/?p=x8TyN4syrlbXRz95Mv_ViA

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Ian Marshall (HSE)

Date and time: 24.06.2026, 17:00 (Moscow time, GMT +03:00)

Title: Poisson reduction of the space of polygons

Abstract:  For some fixed positive integers N and n (with n < N), we consider the space S(n) of degree n shift operators on a one-dimensional lattice, having periodic coefficients, with period N. An analysis of the space S(n) naturally leads us to look at the space W of twisted polygons; these being sequences of vectors, satisfying v(i+N) = M v(i) for some matrix M. Looking at this from a Poisson point of view, confines us to a restricted class of Poisson structures on W, which in turn generate Possion structures on S(n), providing an alternative - and surprisingly simple - route to results of Frenkel, Reshetikhin, Semenov-Tian-Shansky and Sevostyanov, when they looked at the lattice analogue of the so-called Drinfeld--Sokolov reduction procedure.

It turns out that this slightly different approach to DS reduction generates a sequence of intermediate reductions, all of which yield spaces with bihamiltonian structures.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Jipeng Cheng (China University of Mining and Technology)

Date and time: 10.06.2026, 17:00 (Moscow time, GMT +03:00)

Title: Modified Toda Integrable Hierarchy

Abstract: This talk generalizes the modified Toda lattice equation to construct the corresponding integrable hierarchy within the Sato theoretical framework. We mainly focus on the fundamental properties of this hierarchy, including its bilinear equations and Lax equations. Furthermore, we discuss the systematic reductions of the proposed hierarchy and its intrinsic connections with classic integrable hierarchies, particularly the standard Toda hierarchy and other relevant integrable systems.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Chuanzhong Li, Shandong University of Science and Technology, China

Date and time: 27.05.2026, 17:00 (Moscow time, GMT +03:00)

Title: Classifications on soliton solutions of KP type systems

Abstract: In this talk, we will give a classification of the regular soliton solutions of the KP hierarchy, referred to as the KP solitons, under the Gel'fand-Dickey reductions in terms of the permutation of the symmetric group. As an example, we show that the regular soliton solutions of the (good) Boussinesq equation as the 3-reduction can have at most one resonant soliton. In particular, we show that the non-crossing permutation gives the regularity condition for the soliton solutions. Meanwhile the classification on singular soliton solutions of the Boussinesq equation is also interesting.

Video of the talk
https://rutube.ru/video/private/413acecf71ae650fcec87fea3e576998/?p=isOUQJjXU5_a3cE2B-_wUg

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Sergey M. Sergeev (Faculty of Science and Technology, University of Canberra, Australia and Department of Fundamental & Theoretical Physics, Research School of Physics, Australian National University, Canberra, Australia.)

Title:  Quantum Dilogarithms and New Integrable Lattice Models in Three Dimensions

Date and time: 13.05.2026, 12:00 (GMT +03:00)

Abstract: In this talk I will describe a class of integrable 3D lattice models (related to solution of Zamolodchikov tetrahedron equation) related to a class of so called quantum dilogarithic functions. The partition function per site in these models can be exactly calculated in the limit of an infinite lattice by using the functional relations, symmetry and factorization properties of the transfer matrix. The results of such calculations for 3D models associated with the Faddeev modular quantum dilogarithm are briefly presented.

Please note the non-standard time of the seminar 12:00 (GMT +03:00), it is due to the time difference with Australia.

Video of the talk
https://rutube.ru/video/private/28143014f1c9a0a7fa30434e1bf8a9d2/?p=caiyt8dc2c6iG9A6vg7FjA

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Maxim Pavlov, Shandong University of Science and Technology, China

Title:  Lagrangian formulation of the Darboux system

Date and time: 29.04.2026, 17:00 (GMT +03:00)

Abstract: The classical Darboux system governing the rotation coefficients of three-dimensional metrics of diagonal curvature admits an equivalent formulation as a sixth-order partial differential equation for a scalar potential associated with the corresponding τ-function. In this talk, we show that this equation possesses a Lagrangian structure and can be interpreted as an explicit scalar representation of the generating PDE of the KP hierarchy, in the sense recently proposed by Frank Nijhoff within the Lagrangian multiform framework. We further construct scalar Lagrangian formulations for differential-difference and fully discrete analogues of the Darboux system. In the continuous and semi-discrete settings, the Lagrangians can be written in terms of elementary functions, specifically logarithms, whereas in the fully discrete case they naturally involve special functions, notably dilogarithms. An additional outcome of this approach is that the dispersionless limits of these Lagrangians yield a complete classification of three-dimensional second-order integrable Lagrangians of certain form.

Video of the talk
https://rutube.ru/video/private/050294e6db36c6890625496f19ba7a33/?p=Sy09n05pfJBY0Wadr7fv3A

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Anton Sutulin (BLTP, JINR, Dubna)

Title:  Integrability of supersymmetric Calogero Moser models (Continuation)

Date and time:  15.04.2026, 17:00 (GMT +03:00)

Abstract: We analyze the integrability of the N-extended supersymmetric Calogero{Moser model. We explicitly construct the Lax pair fL;Ag for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solving dU/dt = AU for the time evolution operator U(t). The bosonic variables, however, evolve independently of U on closed trajectories, as is required for superintegrability. To visualize the structure of the conserved currents we derive the complete set of Liouville charges up to the 5-th power in the momenta, for the N=2 supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com

Speaker: Anton Sutulin (BLTP, JINR, Dubna)

Title:  Integrability of supersymmetric Calogero Moser models

Date and time:  1.04.2026, 17:00 (GMT +03:00)

Abstract: We analyze the integrability of the N-extended supersymmetric Calogero-Moser model. We explicitly construct the Lax pair for this system, which properly reproduces all equations of motion. After adding a supersymmetric oscillator potential we reduce the latter to solving dU/dt = AU for the time evolution operator U(t). The bosonic variables, however, evolve independently of U on closed trajectories, as is required for superintegrability. To visualize the structure of the conserved currents we derive the complete set of Liouville charges up to the 5-th power in the momenta, for the N=2 supersymmetric model. The additional, non-involutive, conserved charges needed for a maximal superintegrability of this model are also found.

Video of the talk
https://rutube.ru/video/private/17797e646b8c105dca5613b925952664/?p=WYzuY45uErumTHg2fLylxw

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com