PhD Course: Spectral theory of Partial Differential Equations

Brief description

We learn some fundamental properties of the spectra, in particular eigenvalues and eigenfunctions, of partial differential equations such as the Laplace or Schrödinger equations on Euclidean domains and manifolds. After a thorough introduction we focus on the relation between the spectrum and the geometry of the underlying space and go through classical results such as the Faber–Krahn inequality or the counter example to Mark Kac' famous question “Can one hear the shape of a drum?”. The course does not require any preknowledge on spectral theory or any deeper prerequisites on partial differential equations. Everything will be introduced on the spot as it is needed.

See course web page  for full details.