The talk will start with a pre-seminar at 11:30am:
Title: Combinatorial Hodge theory
Abstract: Fifty years ago, McMullen stated the g-conjecture: this is a list of inequalities which characterize entirely the number of faces of simplicial polytopes. Stanley discovered how Hodge theory can finish to solve this conjecture: one can associate a variety to a (sufficiently nice) simplicial polytope, and the necessity of the g-conjecture can be translated in terms of Hodge theoretic properties of the cohomology of the variety. For more complicated combinatorial objects, for instance for fans associated to matroids, such a variety does not exist in general, which make combinatorial analogs of properties of Hodge theory harder to prove for these objects. In this talk, after a detailed presentation of this context, I will explain how tropical varieties and tropical Hodge theory can help to establish these properties.