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## Definability and decidability problems in number theory

May 6 to May 10, 2019

at the

American Institute of Mathematics, San Jose, California

organized by

Kirsten Eisentraeger, Valentina Harizanov, Jennifer Park, and Alexandra Shlapentokh

This workshop, sponsored by AIM and the NSF, will be devoted to definability and decidability problems in number theory.

The main topics for the workshop are

• H10 and existential definability of $\mathbb{Z}$ for $\mathbb{Q}$ and big subrings of $\mathbb{Q}$.
• Decidability of the first-order and the existential theory in finite and infinite algebraic extensions of $\mathbb{Q}$. The workshop will bring together mathematicians working in algebraic geometry, number theory, model theory and computability theory to work on problems in decidability/computability and definability in number theory.
• Definability of valuation rings over infinite algebraic extensions of $\mathbb{Q}$ and over 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.

Space and funding is available for a few more participants. If you would like to participate, please apply by filling out the on-line form no later than November 15, 2018. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to apply.

Before submitting an application, please read the description of the AIM style of workshop.