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

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.