Special Colloquium
Peter Keevash
Caltech
The hypergraph Turan problem
Abstract: A central problem of extremal combinatorics is to determine the
Turan number of a given r-uniform hypergraph F, i.e. the maximum number of
edges in an r-uniform hypergraph on n vertices that does not contain a
copy of F. Since the problem was introduced over sixty years ago, it has
only been solved for relatively few hypergraphs F. Many of these results
were found very recently by means of the stability method, which has
brought new life to research in a challenging area. However, this method
only has the potential to solve the problem when the extremal
configuration is unique, so in other cases we need new techniques. In this
talk we will discuss the history of Tur\'an problems for graphs and
hypergraphs, the methods that have been successfully used by various
authors, and challenges for future research in the area.
Monday December 11, 2006 at 3:00 PM in SEO 636