SPEAKER:  Mark Kempton  (Harvard)

TITLE:  Curvature and homology on graphs

ABSTRACT: 

A popular theme in graph theory today is to take ideas and theorems from the "continuous world" (e.g. geometry of Riemannian manifolds) and reformulate them in the "discrete world" (e.g. on a graph). In recent
years, much work has been done defining notions of Ricci curvature for
discrete graphs, as well as developing homology theories for graphs. In
this talk, I will connect these two areas by proving a homology vanishing theorem for graphs with positive curvature. This result is analogous to a classical theorem of Bochner on Riemannian manifolds. The proof draws on several different areas of graph theory.