# Diophantine Equations

Hausdorff Trimester Program

January - April 2009

**Organizers:** D.R. Heath-Brown, A. MacIntyre, Yu.I. Manin, Yu.V. Matiyasevich, and B.Z. Moroz

The study of Diophantine equations is one of the oldest branches of pure mathematics, and is still flourishing. The 20th century saw great progress: the proof of Siegel’s theorem on integer points of algebraic curves, the negative solution of Hilbert’s 10th problem, the proof of Mordell’s conjecture, and the proof of Fermat’s Last Theorem.

This Hausdorff Trimester Program brought together specialists from different areas of the theory of Diophantine equations and provided an excellent opportunity for interactions between them. A proceedings volume of the workshop was published which is conceived as a survey of the modern theory of Diophantine equations. The four month program culminated in a week long research conference, from the 23rd until the 29th of April.