Spectral Geometry

Objectifs:
The aim of the course is to give an introduction to Spectral geometry covering several methods of harmonic analysis and partial differential equations. 

Contents:

 Possible topics include harmonic functions, spectrum of the Laplace operator, eigenvalues, Weyl’s Law, PDE,  elliptic regularity, compact operators and Fredholm’s theorem,  minimax methods, Courant’s theorem, Faber-Krahn’s inequality, co-area formula, monotonicity formulas for elliptic partial differential equations, geometry of zero sets, exponential sums.

Prerequisites: Measure theory, Functional analysis are obligatory.