at the

American Institute of Mathematics, Palo Alto, California

organized by

Bjorn Poonen, Alexandra Shlapentokh, Xavier Vidaux, and Karim Zahidi

This workshop, sponsored by AIM and the NSF, will be devoted to extensions of Hilbert's Tenth Problem and related questions in Number Theory and Geometry. The main topics for the workshop are

- HTP over rings and fields of algebraic numbers (in particular HTP over rational numbers, Mazur's Conjectures, elliptic curve methods)
- HTP over functions fields of arbitrary characteristic, elementary equivalence versus isomorphism problem for function fields.
- HTP for rings and fields of meromorphic functions (both complex and p-adic)

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 G. Cornelissen, M. Davis, K. Eisentraeger, G. Everest, M. Jarden, L. Lipshitz, A. Macintyre, Y. Matiyasevich, L. Moret-Bailly, T. Pheidas, B. Poonen, F. Pop, K. Rubin, T. Scanlon, A. Shlapentokh, A. Silverberg, M. VanDieren, X. Vidaux, and K. Zahidi.

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

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