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.

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

Speaker: Andrew Kuzovchikov (HSE, MSU, MI-RAS)

Title:  Spin models and flag manifolds

Date and time:  25.03.2026, 17:00 (GMT +03:00)

Abstract: We will consider a one-dimensional sigma model with the target space being an SU(3) full flag manifold, equipped with an arbitrary invariant metric. We explicitly describe all geodesics in terms of elliptic functions and demonstrate that the spectrum of the Laplace-Beltrami operator may be found by solving polynomial equations of a special type. These results are based on the previously discovered connection between sigma models and Gaudin models, which also holds in the SU(n) case.

The talk is based on joint works with D. Bykov:

- D. Bykov and A. Kuzovchikov. “The classical and quantum particle on a flag manifold”. arXiv:2404.15900 [hep-th]

- D. Bykov and A. Kuzovchikov. “Sigma models from Gaudin spin chains”. arXiv:2508.20889 [hep-th]

Video of the talk
https://rutube.ru/video/private/15c69c34e2074bb53896275e0a0a30b6/?p=NBLQqwEjX3ES-RW9mSwIiQ

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

Speaker: Vladimir Sokolov (MIPT, Moscow)

Title:  About linear deformations of matrix multiplication

Date and time:  25.02.2026, 17:00 (GMT +03:00)

Abstract: Two Lie algebras defined on the same vector space are called compatible if any linear combination of the corresponding brackets defines a Lie algebra. Compatible brackets have several important applications in the theory of integrable systems. A more rigid structure is a compatible family of associative algebras. Let one of the associative algebras be Mat(n). The problem of describing associative algebras compatible with it is considered. An algebraic structure is given, the representations of which describe such algebras. A wide class of examples generated by affine Dynkin diagrams of types A,D, and E is constructed.

The report will be held in Russian, the slides of the report will be in English, and any comments in English will be provided upon request.

Video of the talk
https://rutube.ru/video/private/1da22de000e83b8144a21993812374af/?p=D-D23J7n6qUL5bWuCZ_l0Q

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

Speaker: Andrei Zotov (Steklov Mathematical Institute RAS, ITMP MSU)

Title: Applications of associative Yang-Baxter equation for constructing integrable systems

Date and time:  28.01.2026, 17:00 (GMT +03:00)

Abstract: We review different applications of the associative Yang-Baxter equation (AYBE) to integrable systems. Namely, we study a class of quantum R-matrices in the fundamental representation which satisfy not only the standard quantum Yang-Baxter equation but also the quadratic relation called AYBE. It allows to propose constructions of the classical Lax pairs for integrable tops, quadratic r-matrix structures of Sklyanin type, classical spin chains and continuous 1+1 integrable field theories of Landau-Lifshitz type. One of the most general is the model of interacting tops. Another construction is an R-matrix valued Lax pair. With its help one can define a quantization for the model of interacting tops. By proceeding to half-quantum (hybrid) Lax equations we obtain a family of quantum long-range spin chains of the Haldane-Shastry type. Finally, we briefly discuss extension of the AYBE to BC_N root system, which involves the boundary K-matrices.

Video of the talk
https://rutube.ru/video/private/88e48e9bd4a3aa571b2e2b5026794b14/?p=2_QYPAPj8oadAflRn6ELFw

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

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