Title: Reflexive Polytopes and the Reflexive Dimension   

Abstract: Reflexive polytopes were first introduced in the context of theoretical physics and have since played a role in Mirror Symmetry, construction of Calabi-Yau varieties and Gorenstein polytopes.  Applications aside, reflexive polytopes are interesting combinatorial objects.  In this talk we define what it means for a polytope P to be reflexive and characterize P according to its Ehrhart series.  Then we look at the work done by Haase and Melnikov in defining the reflexive dimension of a polytope and producing lower and upper bounds.