# Extensions of Hilbert's Tenth Problem

March 21 to March 25, 2005

at the

American Institute of Mathematics, Palo Alto, California

organized by

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

## Original Announcement

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

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A description of projects arising from the discussion sessions has been made available by Gunther Cornelissen.

Other useful material:
Hilbert's 10th homepage, maintained by Yuri Matiyasevich.

Jeroen Demeyer's talk Recursively enumerable subsets of $F_q[Z]$.

Gunther Cornelissen's talk Improving Julia Robinson, along with an introduction for a general (mathematical) audience.