Departmental Colloquium

Date: April 11, 2025

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Victor Reiner, University of Minnesota

Title: Ehrhart theory and a q-analogue

Abstract: Classical Ehrhart theory begins with this fact: for a convex polytope P whose vertices lie in the integer lattice Z^n, the number of lattice points in the integer dilates mP grow as a polynomial function of m. We will review some highlights of the classical theory, and explain a new "q-analogue": it replaces the number of lattice points in mP by a polynomial in q that specializes to the lattice point count at q=1. There are q-analogues for several classical Ehrhart theory results, some proven, others conjectural. In particular, a certain new commutative algebra, and the theory of Macaulay's inverse systems, play a prominent role. (Based on arXiv:2407.06511, with Brendon Rhoades)