Jonathan Rohleder: From "Hearing the Shape of a Drum" to Shape Optimization: An Introduction to Spectral Geometry

Abstract

Spectral geometry deals with relations between eigenvalues of a differential operator and the geometry of the underlying space, e.g. a domain in Euclidean space, a manifold or a graph. In this talk I will give a gentle introduction to the topic and will discuss questions related to, amongst others, isospectrality ("Can one hear the shape of a drum?") and shape optimization problems (the famous Faber-Krahn inequality). I plan to proceed from more classical results to recent research and some open problems.