Combinatorics Seminar: The determinant of the Varchenko Matrix for oriented matroids

Seminar | September 10 | 12-1 p.m. | 939 Evans Hall

 Volkmar Welker, MSRI

 Department of Mathematics

We generalize the Varchenko matrix of a hyperplane arrangement to oriented matroids. We show that the celebrated determinant formula for the Varchenko matrix, first proved by Varchenko, generalizes to oriented matroids. It follows that the determinant only depends on the matroid underlying the oriented matroid and analogous formulas hold for cones in oriented matroids. We follow a proof strategy for the original Varchenko formula first suggested by Denham and Hanlon. Besides several technical lemmas this strategy also requires a topological result on supertopes which is of independent interest.