Seminář z diferenciální geometrie pokračuje 12.11.2018 od 10:00 v učebně M5

Artur Sergyeyev (SU Opava)

Hydrodynamic Integrability: from Symplectic to Contact Geometry

Abstrakt:

We begin with a brief introduction to integrable systems in general and a review of known results on the construction of integrable hydrodynamic-type partial differential systems in three independent variables with Lax pairs involving Hamiltonian vector fields. Then we present a generalization of this construction to the case of four independent variables, where Hamiltonian vector fields are replaced by contact ones, and show that this approach gives rise to a large new class of integrable hydrodynamic-type systems.

Přednášky od 5. 11. do 8. 11. 2018, zasedací mistnost ÚMS (první patro u schodů), od 12:00 do 14:00

Gian Maria Dall'Ara (University of Vienna)

An invitation to PDE methods in several complex variables

Abstract:

In these lectures I will present the point of view on complex analysis in several variables originated in the '60s from the seminal work of Hörmander and Kohn (among others) on the d-bar problem and some of the most interesting applications. A tentative list of the topics I will discuss is:

1) one versus several complex variables: domains of holomorphy and failure of Riemann mapping theorem;

2) the problem of smooth extension to the boundary of biholomorphisms (Fefferman and Bell-Ligocka theorems);

3) existence and compactness in the d-bar problem: a review of some ideas of Hörmander, Kohn and Catlin;

4) Kohn-Nirenberg regularity and recent work on necessary and sufficient conditions for compactness.

The lectures will be suited (and hopefully interesting) for master students and researchers alike.