This is the third in a series of three courses on discrete geometry. This advanced course will concentrate on the theory of polytopes all of whose vertices have integral coordinates, known as integer polytopes or as lattice polytopes — a particularly nice part of Discrete Geometry, but also of fundamental importance to other fields such as the Geometry of Numbers and Combinatorial Optimization.
As a goal for the course, we will try to reach (and prove) a nice recent result by Christos Athanasiadis about unimodality of generating functions for semi-magic squares:
• C. Athanasiadis, Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley, J. reine angew. Math. 583 (2005), 163-174
see > Resources >> References
There is a "Handapparat" in the library in the making.
The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
Voraussetzungen: Preferably Discrete Geometry I and II.