Dear all, You all are cordially invited. Location: 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. |