Ehrhart theory and a q-analogue, Victor Reiner (University of Minnesota) -- September 19th, 2024, 4:00pm in Altgeld 245

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 positive integer dilates mP grows 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 many 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)

The seminar co-organizers are Ian Cavey, Andrew Hardt, David Keating, and Alexander Yong.