Rational curves and A^1-homotopy theory

October 5 to October 9, 2009

at the

American Institute of Mathematics, Palo Alto, California

organized by

Aravind Asok, Fabien Morel, and Jason Starr

This workshop, sponsored by AIM and the NSF, will be devoted to studying recent interactions between rational connectivity and the newly developing theory of Aš-algebraic topology.

A smooth proper variety over an algebraically closed field k having characteristic 0 is rationally connected if any pair of k-points is contained in a rational curve. Rationally connected varieties have highly non-trivial arithmetic structure. More recently, rationally connected varieties have been shown to have interesting homotopic structure as well: they are connected (in an appropriate sense) from the standpoint of Aš-homotopy theory. One expects that techniques of homotopy theory can be applied to study arithmetic and geometry of rationally connected varieties and, conversely, geometric properties of specific rationally connected varieties can provide insights about Aš-homotopy theory. The goal of this program is to introduce participants studying arithmetic of rationally connected varieties to the techniques of homotopy theory and vice versa.

During the workshop, we will focus on the following problems.

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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