Department of Mathematics,
University of California San Diego
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Math 269: Combinatorics Seminar
Ethan Partida
Brown University
Graded Ehrhart theory of unimodular zonotopes
Abstract:
Graded Ehrhart theory is a new q-analogue of Ehrhart theory introduced by Reiner and Rhoades. Roughly, it is the study of how a canonical, graded lattice point count of a polytope behaves under dilations. The grading in this count is constructed via the orbit harmonics method. In this talk, I will discuss the graded Ehrhart theory of unimodular zonotopes and its connections to matroid theory. In particular, I will explain why graded lattice point counts of unimodular zonotopes are q-integer evaluations of Tutte polynomials and how arrangement Schubert varieties can be used to study the harmonic algebras of unimodular zonotopes. This talk is based on joint work with Colin Crowley.
Host: Brendon Rhoades
April 21, 2026
2:00 PM
Research Areas
Combinatorics****************************
