TAGG seminar

Abstract: The Hodge-Riemann relations are signature conditions on certain multiplication maps in the cohomology ring of a smooth Kaehler manifold. In 2018, Adiprasito, Katz and Huh used analogues of these relations to settle some long standing conjectures in combinatorics related to log concavity. I will discuss an algebraic framework in which to study analogues of the Hodge-Riemann relations and log concavity, inspired by the theory of Lorentzian polynomials introduced by Branden and Huh. I will also discuss some recent work with Pedro Macias Marques and Alexandra Seceleanu that connects the Hodge-Riemann relations in codimension two with a notion of total nonnegativity that generalizes log concavity.