Lectures and Colloquia during the semester

**Monday, October 23, 2006**

Technische Universität Berlin

Straße des 17. Juni 136

10623 Berlin

Math building - Room MA 041

** Lecture - 14:15**

### Günter M. Ziegler - TU Berlin

###

### Topological Methods: Kneser and Tverberg

*Abstract:*

We discuss two classical applications of topological
methods in combinatorics and discrete geometry:
- 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.