Symplectic and Contact Geometry of Monge– Ampère equation: Introduction and application

Time：2023-04-14 Fri 17:00-18:30

Venue：ZOOM:815 4690 4797（PW: BIMSA）

Organizer：Nicolai Reshetikhin, Andrey Tsiganov, Ivan Sechin

Speaker：Vladimir Rubtsov Université d’Angers, ITTP Moscow and IGAP Trieste

Abstract

I am going to present an introduction into the geometric approach to Monge– Ampère operators and equations based on contact and symplectic structures of cotangent and the 1st jet bundles of a smooth manifold. This approach was developed by V. Lychagin and goes back to the ideas of E. Cartan and his successor T. Lepage. I shall try to make my talk self-contained. I also plan to discuss various applications and links with important geometric structures.

DATEApril 14, 2023

Related News

0
Singularities in geophysical fluid dynamics through Monge-Ampère geometry
AbstractThe semigeostrophic equations are a mathematical model representing atmospheric motion on a subcontinental scale. Their remarkable mathematical features enable the equations to model singular behaviours like weather fronts. This talk presents a new approach to classifying these singular structures using the geometry of Monge-Ampère equations. In the geometrical view, solutions are under...
1
Algebraic Geometry Seminar | Contact loci of arcs
Abstract：Contact loci are sets of arcs on a variety with prescribed contact order along a fixed subvariety. They appear in motivic integration, where motivic zeta functions are generating series for classes of contact loci in appropriate Grothendieck groups. We give an overview of recent results relating the basic topology of contact loci of hypersurfaces with a Floer theory and with log minim...