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Definability and decidability problems in number theory

September 9 to September 13, 2013

at the

American Institute of Mathematics, Palo Alto, California

organized by

Thomas Scanlon, Alexandra Shlapentokh, Xavier Vidaux, and Carlos Videla

This workshop, sponsored by AIM and the NSF, will be devoted to studying definability and decidability questions in number theory, more specifically over rational numbers and their algebraic extensions, as well as over rings of functions of natural interest.

The main topics for the workshop are:

  1. (Un)Definability of integers over rational numbers and number fields, Hilbert's Tenth Problem, its stronger and weaker versions (e.g. Buchi's Problem) over rational numbers, number fields and subrings of number fields
  2. (Un)Decidability of theories of various rings of functions, including rational function fields over complex numbers and function fields of positive characteristic
  3. Definability and Decidability in infinite extensions of rational numbers

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.

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