# Johanna Steinmeyer:Lefschetz and unimodality for Lattice Polytopes

**Time: **
Wed 2022-10-05 10.15 - 11.15

**Location: **
3721

Abstract: One of the fundamental questions of Ehrhart theory lies in characterizing the possible $h^*$-polynomials. Given a Gorenstein lattice polytope with the integer decomposition property, Hibi and Ohsugi conjectured that the coefficients of the $h^*$-polynomial are always unimodal. By establishing generic anisotropy and strong Lefschetz properties in the associated semigroup algebra, I will present a proof of this conjecture. As time permits, I will also discuss the boundary of the methods and where the more general conjecture beyond the Gorenstein case may still fail.

No prior knowledge of combinatorial Hodge theory is assumed.

Based on joint work with Adiprasito, Papadakis and Petrotou.