Jun 30th 15:15

Matthias Beck (San Francisco State University)

Title: f^*- and h^*-vectorsAbstract: If P is a lattice polytope (i.e., P is the convex hull of finitely many integer points in R^d), Ehrhart's theorem asserts that the integer-point counting function L_P(m) = #(mP \\cap Z^d) is a polynomial in the integer variable m. Our goal is to study structural properties of Ehrhart polynomials - essentially asking variants of the (way too hard) question which polynomials are Ehrhart polynomials? Similar to the situations with other combinatorial polynomials, it is useful to express L_P(m) in different bases. E.g., a theorem of Stanley (1976) says that L_P(m), expressed in the polynomial basis \\binom(m,d), \\binom(m+1,d), …, \\binom(m+d,d), has nonnegative coefficients; these coefficients form the h^*-vector of P. More recent work of Breuer (2012) suggests that one ought to also study L_P(m) as expressed in the polynomial basis \\binom(m-1,0), \\binom(m-1,1), \\binom(m-1,2), …; the coefficients in this basis form the f^*-vector of P. We will survey some old and new results (the latter joint work with Danai Deligeorgaki, Max Hlavaczek, and Jéronimo Valencia) about f^*- and h^*-vectors, including analogues and dissimilarities with f- and h-vectors of polytopes and polyhedral complexes.

Jul 7th 15:15

Anna Hartkopf and Erin Henning (FU Berlin)

Jul 14th 15:15

Volkmar Welker (Philipps-Universität Marburg)

Jul 21st 15:15

Anton Dochtermann (Texas State University)