#
Monday Lecture and Colloquium

**Monday, January 24, 2011**

Technische Universität Berlin

Fakultät II, Institut für Mathematik

Straße des 17. Juni 136

10623 Berlin

room MA 041

** Lecture - 14:15**

### Frank Lutz -
TU Berlin / BTU Cottbus

### Discretization of Manifolds

*Abstract:*

Triangulations, quadrangulations and more general cell decompositions
of surfaces and higherdimensional manifolds sometimes surprisingly
arise in rather different areas of mathematics. In this lecture,
I will give a survey of combinatorial, topological and geometric
aspects of discretized manifolds.

**Colloquium - 16:00**

###
Dmitry Shabanov - Moskau

### Van der Waerden number and colorings of hypergraphs

*Abstract:*

The van der Waerden number W(n,r) is the smallest integer N such that in any r-coloring of the set {1,2,...,N} there exists a monochromatic arithmetic progression of length n. Famous van der Waerden's theorem states that W(n,r) is finite for all n and r, but does not give any reasonable estimates. This theorem is one of the fundamental results of Ramsey theory. We shall discuss the known bounds for the van der Waerden number. The best upper bounds follow from the density results concerning arithmetic progressions, but the estimating W(n,r) from below finds a very close connection with well-known extremal problems concerning colorings of hypergraphs. We shall present a new asymptotic lower bound for the van der Waerden number obtained by applying the random recoloring method.

Letzte Aktualisierung:
21.01.2011