Jozef Dodziuk spoke in the Queens College Mathematics Colloquium on October 8, 2009.

Title: Combinatorial Laplacian on Graphs.

Abstract: I will talk about a certain difference operator acting on real-valued functions on vertices of a graph. I will try to motivate how “Combinatorial Laplacian” is a reasonable name for this operator by exploring its similarities with the Laplace operator in Euclidean spaces and Riemannian manifolds. We will consider, for example, the maximum principle, Harnack inequality, and isoperimetric inequalities.