Oberwolfach Reports
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Combinatorics
Organized by: Laszlo Lovasz (1) and Hans Jürgen Prömel (2)
(1) Theory Group, Microsoft Research, One Microsoft Way, WA 98052, REDMOND, UNITED STATES(2) Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099, BERLIN, GERMANY
The workshop \emph{Combinatorics} organised by L\'aszl\'o Lov\'asz (Redmond)
and Hans J\"{u}rgen Pr\"{o}mel (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.~S\'os.
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, Koml\'os, Simonovits, and Szemer\'edi solved the
Erd\H os--T. S\'os 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 \emph{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.
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