for this workshop

## Noncommutative surfaces and Artin's conjecture

at the

American Institute of Mathematics, San Jose, California

organized by

Jason Bell, Colin Ingalls, and Matthew Satriano

This workshop, sponsored by AIM and the NSF, is devoted to the working on the birational classification of noncommutative surfaces and related problems. The goal is that these related results would deal with important cases in Artin's conjectured classification and make progress towards an ultimate classification.

The main topics are

- Reduction to characteristic p: Smoktunowicz has shown under general conditions that division algebras of transcendence degree 2 over finite fields are finite over their centers. Can we obtain consequences of this result in characteristic zero by using reduction to characteristic p?
- Cohen Structure Theorem: If we assume a division algebra of transcendence degree two has a valuation, can we use noncommutative analogues of Cohen's structure theorem to classify division rings with a non-trivial valuation?
- Can we show that a division algebra of transcendence degree two has a non-trivial rank one discrete valuation?

This event will be run as an AIM-style workshop. 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*