Mathematics Department Colloquium: Semi-algebraic sets of integer points

Colloquium | August 24 | 4:10-5 p.m. | 60 Evans Hall

 Günter M. Ziegler, Freie Universität Berlin

 Department of Mathematics

We look at sets of integer points in the plane, and discuss possible definitions of when such a set is "complicated"—this might be the case if it is not the set of integer solutions to some system of polynomial equations and inequalities. Let’s together work out lots of examples, and on the way let’s try to develop criteria and proof techniques$\ldots$.

The examples that motivated our study come from polytope theory: Many question of the type "What are the possible pairs of (number of vertices, number of edges) for 5-dimensional polytopes?'' have been asked, many of them with simple and complete answers, but in other cases the answer looks complicated. Our main result says: In some cases it IS complicated! (Joint work with Hannah Sj\"oberg.)