Lauren Nowak (University of Washington)

Padelford Hall (PDL) C401
The establishment of the logconcavity of characteristic polynomials of matroids was a result that took decades to confirm and connected ideas from combinatorics, algebra, and algebraic geometry. In this talk, we will be exploring how this result can be achieved from the perspective of volume theory and polyhedral geometry. In particular, we will explore the conditions under which the mixed volumes of a normal complex  an orthogonal truncation of a polyhedral fan  satisfy the AlexandrovFenchel inequalities. By then specializing to Bergman fans of matroids, we give a new proof of the logconcavity of characteristic polynomials of matroids.