Sophia Elia:Rational Ehrhart Theory

Abstract: Ehrhart theory is the study of the discrete volume of polytopes; the Ehrhart counting function of a polytope $P$ encodes the number of lattice points in integral dilations of $P$ and agrees with a quasipolynomial when $P$ has rational vertices. Ehrhart quasipolynomials were introduced in the 1960s, satisfy several fundamental structural results and have applications in many areas of mathematics and beyond. We use rational generating functions to extend the Ehrhart counting function to encode lattice point counts for rational and real dilations of rational polytopes, building on work of Linke (2011) and Stapledon (2017). We also define a rational analogue of Gorenstein polytopes and prove that many properties extend from the lattice case. This is joint work with Matthias Beck and Sophie Rehberg.

Zoom meeting ID: 654 5562 3260

Zoom link: https://kth-se.zoom.us/j/65455623260