Mariel Supina: The equivariant Ehrhart theory of the permutahedron

Abstract

Ehrhart theory is a topic in geometric combinatorics which involves counting the lattice points inside of lattice polytopes. 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 discuss joint work with Ardila and Vindas-Meléndez (2019) on answering one of Stapledon's open questions: determining the equivariant Ehrhart theory for the permutahedron, and verifying his Effectiveness Conjecture in this special case.