July 2128, 2007Rational Points on Curves and HigherDimensional Varieties:

One of the fundamental problems in Arithmetic Geometry is to determine or describe the set of rational points X(Q) for a given algebraic variety X defined over Q.
If X is a curve, then the structure of X(Q) is known (a oneparameter family, a finitely generated abelian group, a nonempty finite set, or empty) and has a finite description in each case. Here the main question is whether it is possible to find this finite description algorithmically. There has been some progress recently, at least in understanding what the situation could be, which we want to review. By integrating various aspects, we hope to lay the basis for future success.
If X is higherdimensional, much less is known about the structure of X(Q), even when X is a surface. For example, it is an open question whether there is a finite description of X(Q) when X is a K3 Surface (say). Experiments carried out by algorithmic methods may help here; they can suggest what the general patterns might be. By bringing together people working on the “explicit” or experimental side with people working more on the theoretical side, we hope to create a situation that leads to a fruitful exchange.
By bringing together the leading experts and giving them the opportunity to present their latest results and their view on the field in general, we hope to provide a fertile basis for animated discussions. As a result, we hope to achieve a better understanding of the current state of the art and, more importantly, to identify and explore the most promising directions for future work.
This is a small workshop with about 30 participants. Every participant is expected to contribute actively to the success of the event, by giving talks and/or by taking part in the discussions. There will be two invited talks every morning (9:3010:30 and 11:1512:15); the afternoons will be available for discussions, informal talks and collaboration.
Anna ArnthJensen (Oxford), Carlos Barros (Warwick), Nils Bruin (Vancouver), Brendan Creutz (Jacobs University), JeanLouis ColliotThélène (Orsay), Ulrich Derenthal (Zürich), Belgacem Draouil (Bizerte), Noam Elkies (Harvard), Tom Fisher (Cambridge), Victor Flynn (Oxford), David Harari (Orsay), Florian Hess (TU Berlin), Mostafa Ibrahim (Warwick), Kamal KhuriMakdisi (Beirut), Andrew Kresch (U Zürich), Remke Kloosterman (Hannover), Abhinav Kumar (MIT), Thomas Ludsteck (Stuttgart), Ronald van Luijk (Vancouver), Tzanko Matev (Jacobs University), Stephen Meagher (Groningen), Jan Steffen Müller (Jacobs University), Bjorn Poonen (Berkeley), Anna Posingies (HU Berlin), Samir Siksek (Warwick), Denis Simon (Caen), Michael Stoll (Jacobs University), Damiano Testa (Jacobs University), Thotsaphon Thongjunthug (Warwick), Yuri Tschinkel (Göttingen), Tony Varilly (Berkeley), Bianca Viray (Berkeley), Mark Watkins (Bristol), Olivier Wittenberg.
Saturday, July 21, is arrival day; Saturday, July 28, is departure day.
Accomodation is provided in one of the residential colleges on
the Jacobs University campus. See here
for information on how to get to the Jacobs University campus.
Michael Stoll (Jacobs University Bremen^{*})
Jacobs University Bremen^{*}; Deutsche Forschungsgemeinschaft; Number Theory Foundation