Combinatorics Seminar: Matroids arising from electrical networks

Seminar | October 21 | 12:10-1 p.m. | 939 Evans Hall

 Bob Lutz, MSRI

 Department of Mathematics

In this talk I will introduce Dirichlet matroids, a generalization of graphic matroids defined by electrical networks. First, I will describe an interaction between duals of Dirichlet matroids and duals of circular electrical networks. Second, I will characterize the Bergman fans of Dirichlet matroids as explicit subcomplexes of graphic Bergman fans. For "complete" networks, we obtain a description in terms of phylogenetic trees. And third, time permitting, I will discuss a connection between electrical response matrices and the half-plane property of matroids. No prior knowledge of electrical networks is necessary!