# Variational Techniques for the Prescribed $Q$-Curvature Equation

 MINI-COURSE IN GEOMETRIC PDE Topic: Variational Techniques for the Prescribed $Q$-Curvature Equation Speaker: Andrea Malchiodi Affiliation: Scuola Internazionale Superiore di Studi Avanzati, Italy and Member, School of Mathematics Date: Tuesday, October 28 Time/Room: 1:30pm - 3:30pm/S-101

After recalling the definition of $Q$-curvature and some applications, we will address the question of prescribing it through a conformal deformation of the metric. We will address some compactness issues, treated via blow-up analysis, and then study the problem, which has variational structure, using a Morse-theoretical approach.