Colloquium

Speaker: Joan Lind, UTK

Title: Convergence Via Discrete Modulus 

Abstract: Discrete modulus provides a useful framework for studying a variety of graph theoretic objects. In this talk, we will be interested in objects that approximate continuous counterparts. For instance, we show that there is a family of discrete paths that approximate the extremal curves for the (continuous) modulus of the curve family connecting two arcs in a Jordan domain. Moreover, the discrete paths carry a natural probability measure deriving from the theory of discrete modulus, and these measures converge to a natural measure on the set of extremal curves. One key ingredient is the convergence of certain discrete harmonic functions to continuous harmonic functions. As a second example, we will look at the convergence of Peano curves associated with certain random spanning trees. This is joint work with Nathan Albin and Pietro Poggi-Corradini.