Sergei Igonin will give lectures on "English for mathematicians" for everyone.

The lectures will be taking place on Thursdays (November 29, December 6, December 13) from 14:15 to 15:45.
The lectures are also planned to be continued in the next semester.

Venue: Lecture theatre 317, 7th building YarSU (144 Soyuznaya str.).

Learning materials can be found on the website.
https://vk.com/ma3333

Abstract:
Discussion of the following topics is planned.
1. Effective ways to learn English.
2. Features of the use of English in communicating about mathematics.
3. How to make reports and write mathematical texts in English.

Materials from leading universities in Moscow and the UK will be used.
The lecturer has working experience in English at the University of Leeds (United Kingdom).

Boris Bychkov (Higher School of Economics) will give a lecture on "Symmetric polynomials" for 1st and 2nd year students and school students.

The lecture will take place on November 21, 2018, at 17:30.

Venue: 8/10 Kirova st. (2nd building of YarSU), aud. 202.

Abstract: A polynomial in several variables is called symmetric if it is invariant with respect to any permutations of variables. The main theorem on symmetric polynomials asserts that any symmetric polynomial can be expressed in terms of elementary ones, and in a unique way. We shall obtain several more such sets of polynomials, and then we shall define Schur polynomials, a basis in the space of symmetric polynomials, parametrised by partitions (Young diagrams), and will discuss some interesting properties of this basis.

Vladimir Nikolaevich Rubtsov from the University of Angers will give lectures for first and second year students and school students.

1nd and 2nd lecture: November 22, 2018, at 16:00

3rd and 4th lecture: November 23, 2018, at 16:00

Venue: 2nd corpus, YarSU, aud. 106.

Mini-course title: "Complex numbers, their generalisations, geometry and applications."

Abstract: In my lectures, I will talk about various extensions of natural and real numbers, the basic algebraic structures and operations associated with these extensions, as well as the conditions of complexity and their applications.

2nd lecture on this topic.

Abstract: I will talk about  continuous limits, normal forms, possibly symmetries, etc. The course is suitable for 2d year students in general or above.

The lecture will be in English.

Venue: Laboratory 419, 7-th corpus, YarSU.

I will talk about  continuous limits, normal forms, possibly symmetries, etc. The course is suitable for 2d year students in general or above.

The lecture will be in English.

Venue: Room 419, 7th corpus, YarSU.

Abstract: Integrability in statistical physics models usually means that the partition function can be represented in terms of the transfer matrix included in the "large" commutative family. The last property for two-dimensional models is traditionally accompanied by the structure of a vertex model with a weight matrix satisfying the Yang-Baxter equation. This talk is about the generalisation of this idea to a larger dimension, in particular, I will consider the three-dimensional Ising model, as well as the Hopfield neural network model on a 2-dimensional triangular lattice in the memory phase. It turns out that both these models have a vertex representation, with a matrix of weights that satisfies the deformation of the generalization of the Yang-Baxter equation in 3 dimensions, the so-called twisted equation of tetrahedra. In both cases, the combinatorics of the hypercube is essentially used to construct the matrix of weights.

Location: 3 Komsomol'skaya st., B. Delaunay "Discrete and computational geometry" laboratory.

Abstract: All Painlevé equations can be written as a time-dependent Hamiltonian system, and as such they admit a natural generalization to the case of several particles with an interaction of Calogero type (rational, trigonometric or elliptic). Recently, these systems of interacting particles have been proved to be relevant the study of β-models.

An almost two decade old open question by Takasaki asks whether these multi-particle systems can be understood as isomonodromic equations, thus extending the Painlevé correspondence. I shall give an (afrmative ) answer by displaying explicitly suitable isomonodromic Lax pair formulations. As an application of the isomonodromic representation we provide a construction based on discrete Schlesinger transforms, to produce solutions for these systems for special values of the coupling constants, starting from uncoupled ones; the method is illustrated for the case of the second Painlevé equation.

This is a joint work with Marco Bertola (SISSA-CRM, Montreal) and Mattia Cafasso (LAREMA, Angers).

References

[1] M. Bertola, M. Cafasso, V. Roubtsov, Non-commutative Painlevé equations and systems of Calogero type, arXiv:1710.00736, 25 pp.

[2] K. Takasaki. Painlevé-Calogero correspondence revisited. J. Math. Phys., 42(3):1443–1473, 2001.

Location: 3 Komsomol'skaya st., B. Delaunay "Discrete and computational geometry" laboratory.

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).