BIMSA > BIMSA Integrable Systems Seminar Singularities in geophysical fluid dynamics through Monge-Ampère geometry
Singularities in geophysical fluid dynamics through Monge-Ampère geometry
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Roberto D'Onofrio
Time
Friday, April 28, 2023 5:00 PM - 6:30 PM
Venue
Online
Abstract
The 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 understood as Lagrangian submanifolds of a suitably defined phase space equipped with a pseudo-Riemannian metric. We show the interplay between solution singularities, elliptic-hyperbolic transitions of the Monge-Ampère operator, and the degeneracies of the metric on a few examples