Felix-Klein Colloquium: Günter M. Ziegler (Berlin)
Semi-algebraic sets of integer points.
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 …
The examples that motivated our study come
from polytope theory: Many question of the type
“What is 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 Sjöberg.)