Abstract: Among the invariant characteristics of dynamical systems, an important role is played by the Lyapunov exponents and the Lyapunov dimension. The analysis of the spectrum of Lyapunov exponents is widely used to study complex dynamics in systems of ordinary differential equations and in models that reduce to mappings. In the finite-dimensional case, according to the Oseledets theorem, the system of ordinary differential equations linearized on an attractor is always Lyapunov stable, and thus the upper limit can be replaced by the ordinary one, which makes it possible to effectively calculate the Lyapunov exponents. In this talk, it is planned to consider the question of calculating Lyapunov exponents for systems of differential equations of argument with delay, for which the theorem in general does not work. The results of testing the developed algorithm for the Hutchinson equation will be presented and an application of the algorithm to some problems will be illustrated.

Location: Znam. tower, 3 Komsomol'skaya rd. (entrance inside the arch).

Abstract: TBA.

Location: Delone laboratory of "Discrete and Computational Geometry", 3 Komsomolskaya rd.

Abstract: Many interesting examples of discrete integrable systems can be studied from the geometric point of view. In this talk we will consider two classes of examples of such system: autonomous (QRT maps) and non-autonomous (discrete Painlevé equations). We introduce some geometric tools to study such systems, such as the blowup procedure to construct algebraic surfaces on which the mappings are regularized, linearization of the mapping on the Picard lattice of the surface and, for discrete Painlevé equations, the decomposition of the Picard lattice into complementary pairs of the surface and symmetry sub-lattices and construction of a birational representation of affine Weyl symmetry groups that gives a complete algebraic description of our non-linear dynamic. If time permits, we also explain the relationship between this picture and classical differential Painlevé equations.

Location: Znam. tower, 3 Komsomol'skaya rd. (entrance inside the arch).

Abstract: TBA.

Location: Znam. tower, 3 Komsomol'skaya rd. (entrance inside the arch).

We invite everyone to attend the lectures of Prof. V.V. Sokolov, Head Researcher of the Landau Institute for Theoretical Physics of the Russian Academy of Sciences.

The course of lectures is aimed at 1-st and 2-nd year students, but everyone is welcome.

In total, 2 meetings are planned:
The first meeting: Tuesday May 15, 16:00-17:30, lect. theatre 309, 7th building of YSU
The second meeting: Thursday May 17, 16:00-17:30, lect. theatre 309, 7th building of YSU

Abstract: By a quantum matrix algebra (QMA) I mean an algebra generated by the entries of a matrix subject to some relations. The best known QMAs are the RTT algebras and the Reflection Equation ones. Each of them is associated with an R-matrix (constant or depending on parameters). QMAs play a very important role in the Quantum Integrable System theory. I plan to exhibit some properties of the mentioned algebras and explain their role in this theory.

Location: Znamenskaya Tower, 3 Komsomolskaya St. (entrance inside the arch)