Joint Mathematics Colloquium 

University of Idaho

Washington State University

Spring 2014

Thursday,  April 3, 3:30-4:20 pm, room TLC 149

Refreshments in Brink 305 at 3:00 pm

Intersection-theoretic characteristic polynomial formulas


Graham Denham

Department of Mathematics

University of Western Ontario


The characteristic polynomial of a matroid is an invariant that generalizes the chromatic polynomial of a graph.
The theory of hyperplane arrangements provides it with numerous topological and algebraic interpretations.

I will describe another such interpretation, a characteristic polynomial formula obtained by a fundamental geometric construction involving critical points of products of polynomial functions. In this story, the theory of Chern-Schwartz-MacPherson classes comes up as the perfect tool from the point of view of combinatorics. In joint work with June Huh, we observe the characteristic polynomial as the bidegree of a biprojective variety in a new way that provides, in particular, some new inequalities that the coefficients of the characteristic polynomial of a complex hyperplane arrangement must satisfy.