## Seminar: S.V. Smirnov "Discretisation of two-dimensional Toda Chains"

**Lecturer:** Sergei Smirnov, MSU**Talk title:** Discretisation of two-dimensional Toda Chains **Time: **February 20, at 16:00 **Venue:** 7th building YarSU, seminar room 427 (144 Soyuznaya str., 150007)

**Abstract:**

It is well known that, in the continuous case, the two-dimensional Toda chains corresponding to the Cartan matrices of simple Lie algebras are Darboux integrable, that is, integrable in an explicit form, and the chains corresponding to the generalised Cartan matrices are integrable by the inverse scattering method.

Although discrete versions of particular cases were considered earlier, in 2011 I.T. Khabibullin proposed a systematic method for the discretisation of the so-called exponential type systems (generalisation of Toda chains): the idea was to find a discretisation in which the characteristic integrals during the transition from the continuous to the semi-discrete model (and from the semi-discrete to the purely discrete) retain their form. The articles by Khabibullin et al. demonstrated that this method works for Toda chains of small length.

I will explain why this method works for discretising chains of arbitrary lengths of the series A and C and what is the progress in the question of the integrability of these discretisations in the general case.