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Michael Catanzaro : Stochastic dynamics of cellular cycles

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.

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