Morse theory at infinity: an abstract approach and applications

Mohameden Ahmedou (University Giessen)
Morse theory at infinity: an abstract approach and applications

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).