Sums of Weighted Lattice Points of Polytopes

Explore a 53-minute conference talk by Laura Escobar from Washington University in St. Louis on "Sums of weighted lattice points of polytopes" presented at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the long-standing tradition of using polytopes to understand polynomials in algebraic combinatorics, with examples such as Kostka numbers equaling lattice points in Gelfand-Tsetlin polytopes. Examine the connection between polytopes and polynomials, focusing on sums of weighted lattice points and their computation as sums of unweighted lattice points. Discover a computational tool for estimating the maximal weighted lattice point in a polytope, based on joint work with De Loera, Kaplan, and Wang. Recorded on April 18, 2024, this talk provides valuable insights into the intersection of geometry and algebraic combinatorics.