Mariel Supina: Techniques in Equivariant Ehrhart Theory

Abstract

Ehrhart theory is a topic in geometric combinatorics which involves counting the lattice points inside of lattice polytopes. Alan Stapledon (2010) introduced equivariant Ehrhart theory, which combines discrete geometry, combinatorics, and representation theory to give a generalization of Ehrhart theory that accounts for the symmetries of polytopes. In this talk, I will give an overview of equivariant Ehrhart theory and discuss some recent results in this area. This includes joint work with Federico Ardila and Andrés Vindas-Meléndez (2020) on the equivariant Ehrhart theory of the permutahedron, and recent preprint with Sophia Elia and Donghyun Kim on techniques for computing equivariant H*-series.