There will be two additional contributed talks, to be announced later.
David Borthwick (Emory University) Resonances in Geometric Scattering Theory
Hyperbolic manifolds (i.e., manifolds of constant negative sectional
curvature) provide a "laboratory" for conjectures about the distribution
of scattering resonances in the complex plane and their relationship
with classical dynamics, i.e., geodesic flow. In these lectures we'll
discuss the geometric scattering theory of a distinguished class of
hyperbolic manifolds, the convex co-compact manifolds. We'll begin by
developing scattering theory on convex co-compact surfaces and study the
associated Selberg zeta function that encodes the relationship between
geodesic flow (the length spectrum of closed orbits) and quantum flow
(the scattering resonances of the Laplacian). We'll then discuss
higher-dimensional analogues and more detailed questions such as
spectral gaps and the relationship between the distribution of
resonances and the Hausdorff dimension of the trapped set of geodesics.