16:30-16:50 Uhr Lehrprobe zum Thema The Theorem of Carathéodory (auf Englisch)

ca. 17:00-17:40 Uhr Fachvortrag:

The flatness constant and its relatives

The lattice width of a convex body is a parameter measuring how thin the body is in lattice directions. In each fixed dimension, the flatness constant is the supremum of the widths of a special class of convex bodies, those which are hollow. In this talk we will explore certain generalizations and restrictions of the flatness constant obtained by changing the class of convex bodies whose width we study: hollow lattice polytopes, for example, or those convex bodies which do not contain a certain polytope. We will see how these modified flatness constants have connections and motivations in different fields, like integer linear programming, lattice polytopes, and symplectic geometry.