Liouville Equations and Functional Determinants

Workshop on Geometric Functionals: Analysis and Applications
Topic:Liouville Equations and Functional Determinants
Speaker:Andrea Malchiodi
Affiliation:Scuola Normale Superiore
Date:Tuesday, March 5
Time/Room:4:00pm - 5:00pm/Simonyi Hall 101
Video Link:https://video.ias.edu/ws/2019/0305-AndreaMalchiodo

Abstract:  Functional Determinants are quantities constructed out of spectra of conformally covariant operators, and are explicit in dimension two and four, due to formulas by Polyakov and Branson-Oersted. Extremizing them in a conformal class amounts to solving Liouville equations with principal parts of different order but all scaling invariant. We discuss some existence, uniqueness, non-uniqueness results and some open problems. This is joint work with M.Gursky and P.Esposito.