for this workshop

## Graph Ramsey theory

at the

American Institute of Mathematics, San Jose, California

organized by

David Conlon, Jacob Fox, and Dhruv Mubayi

This workshop, sponsored by AIM and the NSF, will be devoted to graph Ramsey theory. The Ramsey number of a graph $H$, denoted $r(H)$, is the smallest $n$ such that any two-coloring of the edges of the complete graph on $n$ vertices is guaranteed to contain a monochromatic copy of $H$. That these numbers exist was first proved by Ramsey in 1930. Since the 1970s, a coherent theory has grown around estimating these numbers and their many variants. In this workshop, we intend to study some topics which have proved particularly fruitful in recent years.

The main topics for the workshop are:

- Hypergraph Ramsey numbers
- Generalized Ramsey numbers
- Geometric Ramsey theorems

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.

For more information email *workshops@aimath.org*