Speaker: Raymond Hemmecke

Joined work with Robert Weismantel

Title: Integer points in semialgebraic cones

Abstract:

This talk deals with the integer points in semialgebraic sets. In particular, we characterize all sets that have a finite integral basis, i.e., a minimal subset of integer points in the given set such that every integer point in the given set is representable as a nonnegative integer combination of the points in the subset. Then we generalize the notion of an integral basis to integral function bases. It is shown how the special case of rational polyhedra can be recovered in this general setting. Various novel finiteness results will be established. The algorithmic relevance of the underlying questions is presented as well.