# Seminars & Colloquia Calendar

Nonlinear Analysis

## Morse theory and the resonant $$Q$$-curvature problem

#### Mohameden Ahmedou, Giessen University, Giessen, Germany

Location:  Hill 705
Date & time: Tuesday, 01 October 2019 at 1:40PM - 2:50PM

Abstract:  The Q-curvature is a scalar quantity which plays a central role in conformal geometry, in particular in the search of high order conformal invariants. In this talk we address the problem of finding conformal metrics of prescribed Q-curvature on four riemannian manifolds in the so called resonant case, that is when the total integral of the Q-curvature is a multiple of the one of the four-dimensional round sphere. This geometric problem has a variational structure with a lack of compactness. Using some topological tools of the theory of critical points at infinity of Abbas Bahri, combined with a refined blow-up analysis, we extend the full Morse theory, including Morse inequalities, to this non-compact geometric variational problem and derive existence and multiplicity results.

This is a joint work with C.B. Ndiaye (Howard University)

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