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.

The program will bring together specialists from diverse areas of the theory of Diophantine equations and provide an excellent opportunity for interactions between them. Moreover we intend to publish a proceedings volume of the workshop, which we hope will serve as an introduction to the modern theory of Diophantine equations.

The four month trimester program will culminate in a week long research conference, from the 23rd until the 29th of April.

## HIM Trimester Program on

# Diophantine Equations

## January - April 2009

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