Joint Mathematics Colloquium


Abstract 

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 ChernSchwartzMacPherson 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.
