AWM-MAA Etta Z. Falconer Lecture 2009

Lecturer: Kate Okikiolu, University of California, San Diego

Title: The Sum of Squares of Wavelengths of a Closed Surface

For the Laplacian on a closed manifold, we define a spectral invariant which is heuristically the sum of squares of the wavelengths which is a regularized trace of the inverse of the Laplacian. On a technical level, this is an analog for surfaces of the ADM mass from general relativity. We discuss a negative mass theorem for surfaces of positive genus, and give a probabilistic interpretation.