Günter M. Ziegler - TU Berlin

Topological Methods: Kneser and Tverberg

• The Kneser conjecture was proved by Lovász using the Borsuk-Ulam theorem, and for 25 years no combinatorial proof was known. But is the topology needed? How much intuition is in the combinatorial proofs?

• The ''topological Tverberg theorem'' was established by topological methods in the prime power case, but obstruction theory shows that the topological methods beyond that. Does that mean that there are counter-examples? Or do we have to use more of the geometry of the problem?

Colloquium - 16:00

Felix Breuer - FU Berlin

Characterization of Closed Curves in the Plane

Abstract:
With every closed curve in the plane that has finitely many double points and no other multi points we can associate a chord diagram. There are several criteria that characterize the chord diagrams of crossing curves. Generalizing the approach of de Fraysseix and Ossona de Mendez, we will give two characterizations of chord diagrams of curves that can have both touching and crossing double points.

Bruno Benedetti - Genoa

Bankruptcy Rules - Compositions vs. Convex Combinations

Abstract:
Bankruptcy theory (dev. 1982) searches mathematical solutions to the question: “how to divide the estate of a firm that went bankrupt among his creditors?” We'll exploit a recent “physical” approach (due to M.Kaminski) to overview the known results, and to introduce a new operator which “combines” two rules together.