Symmetry, heat kernels, and spectrum of infinite weighted graphs
by Radoslaw Wojciechowski (City University of New York, USA)
We will discuss how the symmetry of the geometry of a weighted graph can be characterized by the symmetry of the heat semigroup. We will then present some heat kernel comparisons and use these to study spectral properties of graphs. In particular, we will prove some estimates for the bottom of the spectrum and a condition for discreteness of the spectrum. Time permitting, we will illustrate our results with examples for the usual graph Laplacians. This is joint work with Matthias Keller and Daniel Lenz.