June 28 – July 5, 2015

Rational Points 2015

Workshop at Franken-Akademie Schloss Schney


List of Open Problems


This workshop is the fifth in a series that started with the workshops

Rational Points on Curves - Explicit Methods
Rational Points on Curves and Higher-Dimensional Varieties: Theory and Explicit Methods
held in 2005 and 2007 in Bremen, followed by the workshops
Rational Points 3 and Rational Points 2013
in Thurnau in 2010 and 2013.

In the tradition of the earlier events, this workshop aims at bringing together the leading experts in the field, covering a broad spectrum reaching from the more theoretically-oriented over the explicit to the algorithmic aspects. 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 does have any rational point at all.


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 50 participants. Participation is by invitation. 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. Wednesday afternoon is free. See the (tentative) schedule of talks.


Travel and Accomodation

Sunday, June 28, is arrival day; Sunday, July 5, is departure day. Accomodation is provided at the Franken-Akademie Schloss Schney. Here is a plan of the various buildings. The local costs (room and board) will be covered for all participants.

Schney has a station, which is a short walk (uphill to the castle) from the Franken-Akademie. The station of Lichtenfels is a short taxi ride (or a longer walk) away and offers a variety of regional and long-distance train connections. There are connections from Frankfurt or Munich Airport that take 3-4 hours or from Nuremberg Airport in about 1:30 hours, see the Deutsche Bahn website. Here is a list of connections from Frankfurt Airport to Lichtenfels and here are connections from Lichtenfels to Schney, both on June 28.

Most connections from Frankfurt Airport involve some 40 minutes waiting time at Lichtenfels if you want to take a train to Schney. Alternatively, you can take a taxi from Lichtenfels to the Franken-Akademie. There should be taxis available at the station, but just in case, here is a list of phone numbers of local taxi companies. The taxi ride should cost about EUR 10 (plus perhaps a small amount for waiting time, plus EUR 0.50 per piece of luggage, plus tip).

Participants are expected to cover travel expenses from their own sources.


Michael Stoll (Universität Bayreuth)

Supported by


Link to Workshop 2005
Link to Workshop 2007
Link to Workshop 2010
Link to Workshop 2013

Last modified: 2015-06-30
Michael Stoll