Topology, Geometry and Data Seminar - Michael Catanzaro

Title: Stochastic dynamics of cellular cycles

Speaker: Michael Catanzaro (University of Florida)

Abstract: In this talk, we will explore stochastic motion of cellular cycles inside CW complexes. This serves as a generalization of random walks on graphs, and a discretization of stochastic flows on smooth manifolds. We will define a notion of stochastic current, connect it to classical electric current, and show it satisfies a quantization result. Along the way, we will define the main combinatorial objects of study, namely spanning trees and spanning co-trees in higher dimensions. We will relate these to stochastic current, as well as discrete Hodge theory.

Seminar URL: https://research.math.osu.edu/tgda/tgda-seminar.html