Distinguished Tutte Lecture - Petter Brändén

Title: Lorentzian polynomials

Abstract: Lorentzian polynomials on cones are intimately connected to Hodge theory, matroid theory and the geometry of zeros of polynomials.  We will show how several notorious conjectures on log-concavity in matroid theory, as well as the Alexandrov-Fenchel inequalities for convex bodies follow from the combinatorics and geometry of Lorentzian polynomials. The talk is based on joint work with June Huh and Jonathan Leake.