Combinatorics Seminar: Electrical networks and hyperplane arrangements

Seminar | November 19 | 12:10-1 p.m. | 939 Evans Hall

 Bob Lutz, University of Michigan

 Department of Mathematics

This talk defines Dirichlet arrangements, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. After establishing some basic properties we characterize Dirichlet arrangements whose Orlik-Solomon algebras are Koszul and show that the underlying matroids satisfy the half-plane property. We also discuss the role of Dirichlet arrangements and harmonic functions on electrical networks in problems coming from mathematical physics.