Algebra and Combinatorics Seminar

Date: April 25, 2025

Time: 2:00PM - 2:50PM

Location: BLOC 306

Speaker: Shixuan Zhang, TAMU

Title: Finite generation of integer points in convex cones

Abstract: We study the question whether the affine semigroup of integer points in a convex cone can be finitely generated up to symmetries of the cone. We first establish general properties of such finite generation and construct examples and non-examples, such as Fermat cones. Then we concentrate on irrational polyhedral cones. In particular, we classify such finitely generated affine semigroups in dimension 2 and those in pointed polyhedral cones in dimension 3.