UW AGD Seminar: Stefan Steinerberger

There is an emerging interest in understanding the behavior of partial differential equations on graphs G=(V,E). The classic approach is to think of a graph as a (discretized) compact manifold without boundary (since there is no `complement', no place where the domain/graph ends, no boundary conditions are imposed). I will discuss an axiomatic definition of boundary on graphs that interacts well with classic ideas from Analysis and Probability Theory (including the isoperimetric inequality, exit time estimates for Brownian motion, the Faber-Krahn theorem, Hardy's inequality and the Alexandrov-Bakelman-Pucci estimate). I will not assume any prior knowledge and introduce all ideas from scratch, there will also be many pretty pictures.