The problem of deciding, given a complex variety X , a point x ∈ X , and a subvariety Z ⊆ X , whether there is an automorphism of X mapping x into Z is proved undecidable. Along the way, we prove the undecidability of a version of Hilbert’s tenth problem for systems of polynomials over Z defining an affine Q-variety whose projective closure is smooth.

Lectures Two types of lectures were programmed into the schedule. First there were a number of introductory lectures which were were meant to introduce non-specialist into the area of Hilbert’s Tenth Problem. Since quite a few of the participants came from different backgrounds this was an ideal way to get a feeling of the problems which come up in this area of mathematics. The second type of l...