Ehrhart Positivity of Certain Polytopes

The Ehrhary Polynomial of an Integral Polytope P counts the number of lattice points inside the integer dilations of P. There are several families of polytopes for which the Ehrhart Polynomial has been extensively studied. In this sense, it is a very hard problem to understand what the coefficients of this polynomial represent. In fact, a relevant issue is to determine if they are positive or not. We will discuss some of the known results and conjectures on this topic.