Yuhan Jiang (Harvard University)
Title: Ehrhart series of positroid and alcoved polytopes.
Abstract: Alcoved polytopes are convex polytopes that are the closure of a union of alcoves in an affine Coxeter arrangement. A positroid is a matroid realized by a matrix such that all maximal minors are non-negative. Positroid polytopes are the matroid polytopes of positroids, which are precisely those matroid polytopes that are alcoved. We give a combinatorial formula for the Ehrhart h-polynomial of any positroid polytope. With Elisabeth Bullock, we give a formula for the Ehrhart series of any alcoved polytope for any Lie type. We also show a bijection between Early’s formula for the h-polynomial of the hypersimplex counted by decorated ordered set partitions and our formula.
Venue: PK-4323, 201 ave du Président-Kennedy, UQAM et via Zoom