Combinatorics

Abstract

The workshop Combinatorics organised by László Lovász (Redmond) and Hans Jürgen Prömel (Berlin) was held January 1st–January 7th, 2006. This meeting was very well attended with 48 participants from many different countries. The programme consisted of 15 plenary lectures, accompanied by 18 shorter contributions and a vivid problem session led by Vera T. Sós.

The plenary lectures provided a very good overview over the current developments in several areas of combinatorics and discrete mathematics. We were very fortunate that some of the speaker reported on essential progress on longstanding open problems. In particular, Ajtai, Komlós, Simonovits, and Szemerédi solved the Erdős–T. Sós conjecture on trees (for large trees) and Tao and Vu greatly improved the asymptotic upper bound on the probability that a Bernoulli matrix is singular. The shorter contributions ranged over many topics. They were a good platform, especially, for younger researchers to present their results. In the following we include the extended abstracts of all talks in the order they were given.

On behalf of all participants, the organisers would like to thank the staff and the director of the Mathematisches Forschungsinstitut Oberwolfach for providing a stimulating and inspiring atmosphere. The organizers also thank the many participants who traveled on New Year's Eve and New Year's Day to arrive on time for the beginning of the workshop.