Speaker: Anton Dzhamay (BIMSA)

Title: Discrete Painlevé equations from geometric deautonomization of QRT maps

Date and time:  14.01.2026, 17:00 (GMT +03:00)

Abstract: In this talk we consider some examples of discrete Painlevé equations that can be obtained from a given QRT map using the technique of geometric deautonomization. One common interesting feature of such equations is that they often correspond to quasi-translations, or the elements of infinite order in the corresponding affine Weyl group whose certain power is a translation. Such elements often become translations if one considers a smaller affine Weyl subgroup, the phenomena that is known as the projective reduction.

Video of the talk
https://rutube.ru/video/private/4908b37144ce978fb5cf5af06ee9c7d0/?p=xCjkb_qvP61G74KVb77b2Q

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

Speaker: Antons Pribitoks (BIMSA/YMSC)

Title: Boost Automorphic Symmetry and AdS Integrable Deformations

Date and time:  10.12.2025, 17:00 (GMT +03:00)

Abstract: We address the new structures arising in quantum and string integrable theories, as well as construct a method to find them. Initially we implement the automorphic symmetries on periodic lattice systems and exploit properties of an integrable hierarchy. This prescription is first applied for the new sl_2 sector, Generalised Hubbard type classes and more. We then construct a boost recursion for systems with R-/S-matrices that exhibit arbitrary spectral dependence, which is also an apparent property of the scattering in string theory integrable backgrounds. The generalised bottom-up approach based on coupled differential systems is derived to resolve for exact form of the associated R-matrices. In addition, we single out a class of quantum integrable models whose two-body S-matrices are of non-difference type and which induce a new integrable structure on AdS string backgrounds. These models can be rigorously realised as deformations of the AdS_3 and AdS_2 string worldsheet theories. We demonstrate that their R-matrices, among braiding unitarity and crossing symmetry, satisfy the free-fermion condition and give rise to deformed Hopf (super)algebra structures. The corresponding deformed algebraic structures closely parallel with integrable string models on AdS_3 x S^3b x M^4 and AdS_2 x S^2 x T^6, thereby providing a unified framework for their non-difference-form deformations. 

Video of the talk
https://rutube.ru/video/private/8149248b9964562fedd1f434bb4b2186/?p=zHL3KvwhrIk4eoGGmLxM4Q

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

Speaker: E. Yu. Bunkova (Steklov Mathematical Institute of Russian Academy of Sciences)

Title: Parametric Korteweg-de Vries hierarchy, polynomial dynamical systems and hyperelliptic sigma functions

Date and time:  12.11.2025, 17:00 (GMT +03:00)

Abstract: In our works with V. M. Buchstaber we have solved the problem of constructing dynamical systems corresponding to a hyperelliptic curve of infinite genus. In the talk the details of this construction will be presented. The dynamical systems in question are closely related to the famous Korteweg-de Vries hierarchy and a series of solutions of this hierarchy in terms of Kleinian hyperelliptic sigma functions. There are commutative diagrams giving embeddings of universal Jacobian bundles of hyperelliptic curves of any genus into a polynomial map of complex spaces of infinite dimension. The dynamical systems are explicit polynomial dynamical systems on these complex spaces, and the commutative diagrams bring them to differentiations of Abelian functions on the Jacobians of hyperelliptic curves.

Video of the talk
https://rutube.ru/video/private/ea1a3adad1aaf65b4ce8f01fc821cba7/?p=DlQbROeoY4hzvOgfnsKxcQ

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

Speaker: K.S. Sorokin (HSE St. Petersburg)

Title: Ricci flows in effective resistance metric for community detection in graphs

Date and time:  29.10.2025, 17:00 (GMT +03:00)

Abstract: Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the nodes. The latter computation is known to be done by pseudo-inverting the graph Laplacian matrix. At that, our approach is alternative to one based on Ollivier-Ricci geometric flow for community detection on graphs, significantly outperforming it in terms of computation time. In our proposed method, iterations of Foster-Ricci flow that highlight network regions of different curvature -- are followed by a Gaussian Mixture Model (GMM) separation heuristic. That allows to classify edges into ``strong'' (intra-community) and ``weak'' (inter-community) groups, followed by a systematic pruning of the former to isolate communities. We benchmark our algorithm on synthetic networks generated from the Stochastic Block Model (SBM), evaluating performance with the Adjusted Rand Index (ARI). Our results demonstrate that proposed framework robustly recovers the planted community structure of SBM-s, establishing Ricci-Foster Flow with GMM-clustering as a principled and computationally effective new tool for network analysis, tested against alternative Ricci–Ollivier flow coupled with spectral clustering.

Video of the talk
https://rutube.ru/video/3da3e87640b20b30b9dee45d39adbcf8/

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

Speaker: Dmitry Artamonov (MSU)

Title: Functional realization of the  Gelfand-Tselin base

Date and time:  15.10.2025, 17:00 (GMT +03:00)

Abstract: Consider a realization of finite-dimensional irreducible representations of gl(n) in the space of functions on the group GL(n). The question is: which functions on the group correspond to the Gelfand-Tsetlin basis vectors? The answer has been known since the 1960s for the first non-trivial case, n=3. In this case, the corresponding functions are written as the result of a substitution of  a certain expression involving determinants on the group into the Gauss hypergeometric function. In the  talk  a generalization of this result to the case of arbitrary n will be presented. To obtain such a generalization certain classes of functions and systems of hypergeometric type  (close to GKZ functions) will be constructed.

Video of the talk
https://rutube.ru/video/d4f429fff185e32ed243438270f9fe95/

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

Speaker: Dmitry Timashev (MSU)

Title: Maximal Poisson commutative subalgebras and 2-splittings of semisimple Lie algebras

Date and time:  1.10.2025, 17:00 (GMT +03:00)

Abstract: A fundamental problem in the theory of integrable systems is to construct a complete involutive set of first integrals for a Hamiltonian dynamical system. Algebraically the problem amounts to construction of a commutative subalgebra of maximal transcendence degree in a given Poisson algebra. A powerful method of constructing Poisson commutative subalgebras in the symmetric algebra S(g) of a semisimple Lie algebra g, known as the Lenard-Magri scheme, is based on including the Lie-Poisson bracket on S(g) in a pencil of compatible Poisson brackets. If all Poisson brackets in the pencil are linear, i.e., come from a pencil of Lie brackets on g, then the Lenard-Magri scheme yields a Poisson commutative subalgebra of maximal transcendence degree if and only if all values of the parameter in the pencil are regular, i.e. the indices of the Lie algebras corresponding to different values of the parameter are one and the same. Panyushev and Yakimova (2021) suggested an implementation of the Lenard-Magri scheme by considering a pencil of Lie brackets associated to a 2-splitting of g, i.e., a decomposition into a direct sum of Lie subalgebras g = f + h. The possible singular values of the parameter correspond to the Inönü-Wigner contractions of g along f and h. Extending the results of Panyushev and Yakimova, we prove a formula for the index of an Inönü-Wigner contraction of g and deduce that the resulting Poisson commutative subalgebra of S(g) has maximal transcendence degree if and only if both f and h are spherical Lie subalgebras.

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

Speaker: Mikhail Chirkov (HSE University, YarSU)

Title: Quantisation ideals and canonical parametrisations of the unipotent group

Date and time:  17.09.2025, 17:00 (GMT +03:00)

Abstract: Quantisation ideals for dynamical systems on the free associative algebra have proven to be an effective tool for solving the problem of deformation quantisation, as well as for obtaining non-deformation quantisation. This talk will provide a brief overview of the history and motivation behind this approach. In our joint work with A.V. Mikhailov and D.V. Talalaev, we generalize this approach to the case of discrete dynamics on the free associative algebra A. This dynamics is defined by a well-known solution of the tetrahedron equation (Case α from Sergeev's list), which is related to the problem of re-parameterisation of the unipotent group N(3, A). As a result, we construct several families of quantisations, analyze their classical limit and obtain canonical integrable systems compatible with re-parameterisations. We have to mention that the charts and re-parameterisations (mutations) form a cluster-like structure, with Poisson brackets that represent a deformation of the log-canonical type.

Video of the talk
https://rutube.ru/video/private/6ffa6d381300f213c7e5024e3fbf1c3c/?p=GIt1GsJfJbBgqJhQPAIgFg

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

Speaker: Yunhe Sheng (Jilin University, Changchun, China)

Title: Leibniz 2-algebras, linear 2-racks and the Zamolodchikov Tetrahedron equation

Date and time:  9.07.2025, 17:00 (GMT +03:00)

Abstract: First we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show that a linear 2-rack also gives rise to a solution of the Zamolodchikov Tetrahedron equation. We show that a central Leibniz 2-algebra gives rise to a linear 2-rack if the underlying 2-vector space is splittable. Finally we discuss the relation between linear 2-racks and 2-racks, and show that a linear 2-rack gives rise to a 2-rack structure on the group-like category. A concrete example of strict 2-racks is constructed from an action of a strict 2-group.

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

Speaker: Leonid Chekhov (Steklov Mathematical Institute and Michigan State University)

Title: Symplectic groupoid: geometry, networks, and moduli spaces of closed Riemann surfaces

Date and time:  25.06.2025, 17:00 (GMT +03:00)

Abstract: I will describe the Bondal's symplectic groupoid: a set of pairs (B,A) with A unipotent upper-triangular matrices and B an element of GL(n) being such that the matrix B A B^T is itself unipotent upper triangular. Since works of J.Nelson, T.Regge, B.Dubrovin,  and M.Ugaglia it was known that entries of A can be identified with geodesic functions on a Riemann surface with holes; these entries then enjoy a closed Poisson algebra (reflection equation) expressible in the r-matrix form. In our recent work with M.Shapiro, we solved the symplectic groupoid in terms of planar networks; we used this solution to construct a complete set of geodesic functions for a closed Riemann surface of genus 2; all geodesic functions are elements of the upper cluster algebra whereas Dehn twists are described by cluster mutations. This is a joint work with M.Shapiro.

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

Speaker: G.I. Sharygin (MSU, MIPT)

Title: Symmetries of the full symmetric Toda system and Li-Bianchi integrability

Date and time:  11.06.2025, 17:00 (GMT +03:00)

Abstract: The full symmetric Toda system is an integrable Hamiltonian system on the space of symmetric real matrices, similar to the open Toda chain. In this report, I will talk about how to build vector fields that preserve this system. In particular, it follows that this system is integrable in the sense of the Li-Bianchi theorem (that is, it has a solvable algebra of symmetries of maximum dimension).

Video of the talk
https://rutube.ru/video/private/7a03bddb8b8e25ca6c2bbb261532c550/?p=UtuEJV79owNeV2L6a2uh5w

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