Calculus of Variations and Geometric Measure Theory

Morse theory at infinity: an abstract approach and applications

Mohameden Ahmedou

created by malchiodi on 15 Oct 2024

31 oct 2024 -- 11:00   [open in google calendar]

Scuola Normale Superiore, Aula Bianchi

Abstract.

In this talk, we introduce a new abstract framework that allows the application of Morse theory to certain non-compact variational problems. This is achieved by analyzing the topological changes induced by the so-called 'critical points at infinity.' As an application, we show how this approach can be used to study the Nirenberg problem on spheres and the resonant prescribed Q-curvature problem on four-dimensional manifolds.

This is a joint work with Thomas Bartsch (University of Giessen).