Mathematical Physics and Harmonic Analysis Seminar

Date: April 20, 2018

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: David Borthwick, Emory University

Title: Distribution of Resonances for Hyperbolic Surfaces

Abstract: For non-compact hyperbolic surfaces, the appropriate generalization of the eigenvalue spectrum is the resonance set, the set of poles of the resolvent of a meromoprhic continuation of the Laplacian. Hyperbolic surfaces serve as a model case for quantum theory when the underlying classical dynamics is chaotic. In this talk I’ll explain how the resonances are defined and discuss our current understanding of their distribution. I’ll introduce some conjectures inspired by the physics of quantum chaotic systems, and discuss numerical evidence for these conjectures and the partial progress that has been made recently.