Title: Unimodality Questions in Ehrhart Theory

Abstract: An interesting open problem in Ehrhart theory is to classify the lattice polytopes having a unimodal h*-vector. Although various sufficient conditions have been found, necessary conditions remain a challenge. Some highly-structured polytopes, such as the polytope of real doubly-stochastic matrices, have been proven to possess unimodal h*-vectors, but the same is unknown even for small variations of it. In this talk, we will mainly examine the h*-vectors for two particular classes of polytopes, with special attention given to methods for proving unimodality.