EVENT DETAILS AND ABSTRACT

Title: Feynman diagrams and the Inverse Spectral Problem
Speaker: Steve Zelditch
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

My talk concerns the well-known question, Can you hear the shape of a drum? There are well-known counterexamples of Gordon et al, but they are not real analytic. Can one hear the shape of an analytic drum (I.e. an analytic simply connected plane domain)? The answer is "yes" if the drums additionally have an up-down symmetry: roughly speaking, a simply connected analytic plane domain with an up-down symmetry symmetry is determined by its Dirichlet or Neumann spectrum among other such domains. The proof is based on the study of Feynman diagrams and amplitudes for trace of the wave group.