[Facets-of-complexity] Invitation to EXCEPTIONAL THURSDAY Lecture - July 5th

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

You are cordially invited to our next Lecture on Thursday, July 5th, at 14:15 h at FU Berlin.

Speaker: Akihiro Higashitani (Kyoto Sangyo University)

Title: Finding a new universal condition in Ehrhart theory

Time: THURSDAY, July 5th - 14:15 h

Location:

Seminar Room
Freie Universität Berlin
Institut für Mathematik
Arnimallee 2
14195 Berlin

Abstract:
Recently, Balletti and I proved that for the h^*-polynomial h_0^*+h_1^*t+... of a lattice polytope, if we assume h_3^*=0, then (h_1^*, h_2^*) satisfies (i) h_2^*=0; or (ii) h_1^* \leq 3h_2^* + 3; or (iii) (h_1^*,h_2^*)=(7,1). These conditions derive from Scott's theorem (1976), who characterized the possible h^*-polynomials of 2-dimensional lattice polytopes, and Scott's theorem is also essentially valid for lattice polytopes with degree at most 2 (Treutlein (2010)). On the other hand, we proved that it also holds under the assumption h_3^*=0. Since the assumption h_3^*=0 is independent of both dimension and degree of polytopes, we call the conditions (i), (ii), (iii) universal. In this talk, towards finding a new universal condition, we investigate the possibility for the polynomial h_0^*+h_1^*t+... to be the h^*-polynomial of some lattice polytope under the assumption that some of h_i^*'s vanish.

Exceptionally, this talk will be on Thursday.

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Graduiertenkolleg 'Facets of Complexity' www.facetsofcomplexity.de/monday