Dynamical Systems seminar - Parallel volumes and spectral counting functions for fractals

Speaker: Sabrina Kombrink (Birmingham University)

Abstract: We will discuss two applications of dynamical renewal theory in geometry. Firstly, we will look at asymptotic expansions of parallel volumes of fractal sets – aiming at introducing notions of “fractal volume”, “fractal surface area”, “fractal curvatures”. Secondly, by finding higher order asymptotic terms of eigenvalue counting functions of the Dirichlet Laplacian on domains with a fractal boundary, we will address the question which geometric features of a drum with a fractal boundary one can hear when listening to its sound. The proofs rely on spectral properties of Ruelle-Perron-Frobenius operators.

You are welcome to join earlier (1.45pm) for a chat.