Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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Joint Colloquium/Combinatorics Colloquium: Ehrhart theory and a q-analogue

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
Altgeld 245
Date
Sep 19, 2024   4:00 pm  
Speaker
Victor Reiner (Minnesota)
Contact
Jacob Rasmussen
E-Mail
rasmusj@illinois.edu
Views
41
Originating Calendar
Mathematics Colloquium & Named Lectures

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 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)

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