July 4-10, 2010

Rational Points 3

Abstracts of Invited Talks

Background

This workshop continues the series started with the workshops

Rational Points on Curves - Explicit Methods and Rational Points on Curves and Higher-Dimensional Varieties: Theory and Explicit Methods held in 2005 and 2007 in Bremen.

Similarly to the earlier events, this workshop aims at bringing together the leading experts in the field, ranging from the more theoretically-oriented over the explicit to the algorithmic. The fundamental problem motivating the workshop asks for a description of the set of rational points X(Q) for a given algebraic variety X defined over Q. When X is a curve, the structure of this set is known, and the most interesting question is how to determine it explicitly for a given curve. When X is higher-dimensional, much less is known about the structure of X(Q), even when X is a surface. So here the open questions are much more basic for our understanding of the situation, and on the algorithmic side, the focus is on trying to decide if a given variety goes have any rational point at all.

Aim

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.

Format

This is a small workshop with about 30 to 35 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 (9:30-10:30 and 11:15-12:15); the afternoons will be available for shorter invited talks, discussions, informal talks and collaboration.

Invited Speakers

Nils Bruin (Simon Fraser Universtiy, Vancouver)
Tom Fisher (University of Cambridge)
David Harari (Université Paris-Sud)
Bjorn Poonen (Massachusetts Institute of Technology)
Samir Siksek (University of Warwick)
Alexei Skorobogatov (Imperial College, London)
Andreas Stein (Universität Oldenburg)
Jakob Stix (Universität Heidelberg)
Tony Várilly-Alvarado (Rice University)
Bianca Viray (UC Berkeley)

Further Participants

Ingrid Bauer-Catanese (Universität Bayreuth)
Martin Bright (University of Warwick)
Brendan Creutz (Universität Bayreuth)
Cyril Demarche (Université Paris-Sud)
Ulrich Derenthal (LMU München)
Andreas-Stephan Elsenhans (Universität Bayreuth)
Victor Flynn (University of Oxford)
Yonatan Harpaz (Hebrew University, Jerusalem)
David Holmes (University of Warwick)
Evis Ieronymou (EPF Lausanne)
Andrew Kresch (Universität Zürich)
Kamal Makdisi (American University of Beirut)
Tzanko Matev (Universität Bayreuth)
Robert Miller (University of Washington, Seattle)
Jan Steffen Müller (Universität Bayreuth)
Cecília Salgado (Universiteit Leiden)
Tomer Schlank (Hebrew University, Jerusalem)
Sandra Schlotmann (Universität Oldenburg)
Peter Swinnerton-Dyer (University of Cambridge)
Szabolcs Tengely (Debreceni Egyetem)
Damiano Testa (University of Oxford)

Travel and Accomodation

Sunday, July 4, is arrival day; Saturday, July 10, is departure day. Accomodation is provided in Schloss Thurnau and in the town of Thurnau.

Thurnau no longer sports a railway station. The best places to go by railway are Kulmbach and Bayreuth. Kulmbach is closer and reasonably well reachable if you come from west or north (e.g. Frankfurt airport), whereas Bayreuth is usually more convenient when you come from Nuremberg or Munich. I will try to organize a pick-up service; otherwise you can take a taxi. For railway connections, see the Deutsche Bahn website.

Attention: The trains going from Nuremberg to Bayreuth usually have several parts that get separated somewhere on the way. Only one of them goes to Bayreuth. So be careful when boarding the train to enter the right part!