American Institute of Mathematics, Palo Alto, California
Dhruv Mubayi, Oleg Pikhurko, and Benny Sudakov
This workshop, sponsored by AIM and the NSF, will be devoted to the study of the hypergraph Turán 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 Turán 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 Turán-type questions for hypergraphs.
Two notable old problems that may be approachable by modern methods include the Tetrahedron Conjecture of Turán from 1941 and the (6,3)-problem of Ruzsa and Szemerédi from 1978.
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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