# Akihiro Higashitani: Characterizing h^*-polynomials of lattice simplices with small volumes

**Time: **
Fri 2023-06-02 10.15 - 11.15

**Location: **
KTH 3418

**Participating: **
Akihiro Higashitani (Osaka University)

Abstract: One of the most important invariants of lattice polytopes is the Ehrhart polynomials, or equivalently, the \(h^*\)-polynomials. The problem of which polynomials can be \(h^*\)-polynomials of lattice polytopes have been studied by many people, including the speaker. In this talk, we discuss the characterization of the \(h^*\)-polynomials of lattice polytopes with small normalized volumes. We mainly treat them for lattice simplices. Moreover, we also discuss (almost) shifted-symmetric \(h^*\)-polynomials of lattice simplices with small normalized volumes and give some results obtained in the on-going project.