Colloquium: Monday, November 6, 4 pm. Speaker: John Klein (Wayne State Univ.). Title: “Variations on a duet of Kirchhoff and Boltzmann”.
The Kirchhoff and Boltzmann distributions date back to the nineteenth century, dealing respectively with the flow of electrical current in a circuit and with the distribution of particles in a gas. I will show how both can be derived as a solution to a pair of dual combinatorial Hodge theory problems, where the solution involves the spanning trees and vertices in graph. I will explain how algebraic topology comes in generalizing these distributions to higher dimensions. Time permitting, I will explain how the latter connects with Reidemeister torsion.