MA 715, Polytope Theory.

This course is an introduction to the combinatorial aspects of polytope theory. Starting mostly from scratch, we will be able to reach some striking results, many with quite beautiful proofs. In the process we will encounter techniques from geometry, combinatorics, topology, linear algebra, graph theory, and abstract algebra. Possible Topics: Polyhedra, polytopes, faces, etc.; Graphs of polytopes; Steinitz' Theorem for 3-polytopes; Duality, Gale diagrams, and applications; Shellability and face-vectors, and flag-vectors; Triangulations and subdivisions.

Text: Lectures on Polytopes, Gunter Ziegler.

Prerequisites: While taking MA515 is highly recommended, it is not absolutely essential. You should be comfortable with the notation and basic results of linear algebra.