Graphs versus Manifolds in Eigenvalues and Distances Between Subsets
Professor of Mathematics
This talk presents a method to translate results concerning graph Laplacians to analogous theorems for Riemannian manifold Laplacians. It specifically demonstrates an improved upper bound for the first Laplacian eigenvalue on Riemannian manifolds, derived from graph theoretic bounds on subset distances and volumes.
Joel Friedman (University of British Columbia)
Beyond Graph Laplacians
We describe a method of converting results about graph Laplacians into analogous results about Laplacians of a Riemannian manifold. We illustrate this with an old result (from 2000), that gave a first Laplacian eigenvalue upper bound in terms of the distances between two subsets and their volumes. In this case the tightest graph theoretic bound lead to an improved bound for Riemannian manifolds. This is based on joint work with Jean-Pierre Tillich.