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American Institute of Mathematics, Palo Alto, California

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This workshop, sponsored by AIM and the NSF, will focus on four inter-related themes:

- Long arithmetic progressions and the Szemeredi regularity lemma
- The Erdos-Szemeredi sum-product conjecture, the Erdos distance set problem, and Szemeredi-Trotter type problems in various dimensions and fields.
- Freiman's inverse theorem and sum-sets
- The Kakeya conjecture in finite fields, and related problems from harmonic analysis.

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 working sessions.

Invited participants include J. Beck, J. Bourgain, J. Bueti, M. Chang, F. Chung, E. Croot, M. Csornyei, G. Freiman, J. Garibaldi, T. Gowers, R. Graham, A. Granville, B. Green, A. Iosevich, N. Katz, I. Laba, V. Lev, G. Mockenhaupt, M. Nathanson, A. Sarkozy, J. Solymosi, V. Sos, B. Sudakov, E. Szemeredi, T. Tao, G. Tardos, V. Vu, T. Wooley, and L. Wu.

The deadline to apply for support to participate in this workshop has passed.

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