Hypergraph Turan problem

March 21 to March 25, 2011

at the

American Institute of Mathematics, Palo Alto, California

organized by

Dhruv Mubayi, Oleg Pikhurko, and Benny Sudakov

Original Announcement

This workshop will be devoted to the study of the hypergraph Turan function ex(n,F), the maximum size of an F-free k-hypergraph on n vertices. Although this fundamental problem of extremal combinatorics was introduced by Paul Turan in 1941, it is still wide open in general. A number of powerful methods and techniques were developed or sharpened in recent years in order to attack various combinatorial problems (such as hypergraph regularity, flag algebras, or hypergraph stability). The purpose of the workshop is to focus this machinery on solving some imporant Turan-type questions for hypergraphs.

Two notable old problems that may be approachable by modern methods include the Tetrahedron Conjecture of Turan from 1941 and the (6,3)-problem of Ruzsa and Szemeredi from 1978.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:
Linear trees in uniform hypergraphs
Choosability with separation of complete multipartite graphs and hypergraphs
Asymptotic improvements to the lower bound of certian bipartite Tur\'an numbers
On possible Tur\'an densities
A problem of Erd\H{o}s on the minimum number of $k$-cliques
Two extensions of Ramsey's theorem
On independent sets in hypergraphs
Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube