Rational and integral points on higher-dimensional varieties

December 11-20, 2002

at the

American Institute of Mathematics, Palo Alto, California

organized by

This workshop, sponsored by AIM and the NSF, will be devoted to the study of rational and integral points on algebraic varieties, primarily those of dimension at least two.

We are bringing together researchers in algebraic geometry, diophantine approximation, cohomological methods (e.g. the Brauer-Manin obstruction, universal torsors), analytic methods (e.g. the circle method), and algorithmic arithmetic geometry. We hope especially to facilitate communication between researchers studying theoretical aspects and those with a more computational bent.

The main questions to be addressed concern

existence of points,
distribution of points in various topologies, and
distribution with respect to heights.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These should be specific problems on which there is hope of making some progress during the workshop itself. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and there will be ample time between talks for discussions and for work to be done.

Participants include C.L. Basile, F. Bogomolov, T. Browning, L. Caporaso, A. Chambert-Loir, J.-L. Colliot-Thélène, P. Corn, C. David, J. Ellenberg, D. Harari, B. Hassett, R. Heath-Brown, J. Johnson (tentative), A. Kresch, K. Lauter, Y. Manin (tentative), G. Matthews, B. Mazur, W. McCallum, E. Peyre, G. Rémond, F. Rodriguez-Villegas, V. Rotger, P. Salberger, P. Sarnak, A. Shlapentokh, A. Skorobogatov, W. Stein, M. Stoll, P. Swinnerton-Dyer, R. Takloo-Bighash, R. van Luijk, A. Venkatesh, P. Vojta, J. F. Voloch, O. Wittenberg, T. Wooley, and N. Yui.

The application deadline for participation in this workshop has passed.

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