Rational curves on algebraic varieties

May 7 to May 11, 2007

at the

American Institute of Mathematics, Palo Alto, California

organized by

Brendan Hassett and Sandor Kovacs

This workshop, sponsored by AIM and the NSF, will be devoted to rationally-connected varieties. The original impetus for studying these varieties came from classification theory, and many central problems in this area remain open: Are all rationally-connected varieties unirational? Is there a rational surface passing through the generic point on a rationally connected variety? If not, what positivity hypotheses might guarantee the existence of such surfaces?

At the same time, techniques developed for studying rationally-connected varieties have found wide application in algebraic and arithmetic geometry. The workshop will focus on the following tools:

One main goal will be to present and discuss state-of-the-art techniques in each of these areas. We expect that a better grasp of these methods should yield new insights into classification questions and a deeper understanding of Diophantine properties of rationally-connected varieties over local and function fields.

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

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