at the

American Institute of Mathematics, San Jose, California

organized by

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

The main topics for the workshop are:

- (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
- (Un)Decidability of theories of various rings of functions, including rational function fields over complex numbers and function fields of positive characteristic
- Definability and Decidability in infinite extensions of rational numbers

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

A computable functor from graphs to fields

by Russell Miller, Bjorn Poonen, Hans Schoutens, and Alexandra Shlapentokh, *J. Symb. Log. 83 (2018), no. 1, 326–348 * MR3796287

Fields on the bottom

by Moshe Jarden and Carlos Videla, *J. Théor. Nombres Bordeaux 28 (2016), no. 1, 213-219 * MR3464618