Search

Talk

Spanning Trees, Effective Resistances and Curvature on Graphs

  • Karel Devriendt (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)

Abstract

Kirchhoff's celebrated matrix tree theorem expresses the number of spanning trees of a graph as the maximal minor of the Laplacian matrix of the graph. In modern language, this determinantal counting formula reflects the fact that spanning trees form a regular matroid. In this talk, I will discuss some consequences of this perspective for the study of a related quantity from electrical circuit theory: the effective resistance. I will give a new characterization of effective resistances in terms of a certain polytope and discuss applications to recent work on discrete notions of curvature based on the effective resistance.

Antje Vandenberg

MPI for Mathematics in the Sciences Contact via Mail

Diaaeldin Taha

MPI for Mathematics in the Sciences Contact via Mail