[Facets-of-complexity] Invitation to Monday's Lecture & Colloquium June 13.

[Ita Brunke <i.brunke@fu-berlin.de>]

Dear all,

next Monday's Lecture and Colloquium will take place on June 13 in attendance at 14:15 & 16:00 at TU Berlin.

You all are cordially invited.

Location:

Room MA 041 - Ground Floor
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin

Time: Monday, June 13 - 14:15

Lecture: Matthias Beck (San Francisco State University)

Title: Boundary h*-polynomials of rational polytopes

Abstract:

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 \cap Z^d| is a polynomial in the integer variable m. Equivalently, the generating function \sum_{m \ge 0} |mP \cap 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).

Coffee & Tea Break :

Room MA 316 - Third Floor


Time: Monday, June 13 - 16:00 s.t.

Colloquium: Andrei Comăneci (Technische Universität Berlin)

Title: Tropical Medians by Transportation

Abstract:

The Fermat-Weber problem seeks a point that minimizes the average distance from a given sample. The problem was studied by Lin and Yoshida (2018) using the standard tropical metric with the purpose of analyzing phylogenetic data. In this talk, we argue that using a related asymmetric distance we have better geometric and algorithmic properties. The new formulation is strongly related to tropical convexity and is equivalent to a transportation problem. This gives a geometric perspective to the transportation problem, which was exploited by Tokuyama and Nakano (1995) to obtain efficient algorithms. At the end, we will see an application to computational biology: a new method for computing consensus trees. The talk is based on joint work with Michael Joswig.