# Colloquium

Professor Floyd Williams, University of Massachusetts Amherst

Colloquium Title: Fourier analysis, scattering, and mock zeta function of certain black hole vacua

Abstract: We consider Fourier expansions of functions invariant under the action of some discrete group. Such functions therefore are a generalization of ordinary periodic functions on the real line R, where the discrete group is the group of integers. Our interest is in hyperbolic space - the upper 1/2 plane, for example. In particular we focus on some group actions that are quite simple in character and which define a black hole, or a ground state vacuum, and an associated zeta function, whose zeros are related to scattering theory. Since we will focus only on concrete examples, the talk would be largely self-contained, with the requirement of a good background in advanced real and complex calculus. No knowledge of scattering theory nor of black holes will be assumed.