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Lecture by Matthias Beck (San Francisco State University): Boundary h*-polynomials of rational polytopes

Jun 13, 2022 | 02:15 PM

If P is a lattice polytope (i.e., P is the convex hull of finitely many integer points in R^d), Ehrhart's famous theorem asserts that the integer-point counting function |mP∩Z^d| is a polynomial in the integer variable m. Equivalently, the generating function \sum_{m \ge 0} |mP∩Z^d| t^m is a rational function of the form h*(t)/(1-t)^{d+1}; we call h*(t) the Ehrhart h*-polynomial of P. We know several necessary conditions for h*-polynomials, including results by Hibi, Stanley, and Stapledon, who used an interplay of arithmetic (integer-point structure) and topological (local h-vectors of triangulations) data of a given polytope. We introduce an alternative ansatz to understand Ehrhart theory through the h*-polynomial of the boundary of a polytope, recovering all of the above results and their extensions for rational polytopes in a unifying manner.

This is joint work with Esme Bajo (UC Berkeley).

Time & Location

Jun 13, 2022 | 02:15 PM

Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
Room MA 041 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)