July 23 – 29, 2023

Rational Points 2023

Workshop at Franken-Akademie Schloss Schney


List of problems from the Problem Session


This workshop is the ninth 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 and the workshops
Rational Points 2015, Rational Points 2017, Rational Points 2019 and Rational Points 2022
in Schney.

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 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.

Travel and Accomodation

Sunday, July 23, is arrival day; Saturday, July 29, is departure day. Accommodation 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 railway 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.

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

Code of Conduct



Michael Stoll (Universität Bayreuth)

Scientific Committee

Jennifer Balakrishnan (Boston University), Samir Siksek (University of Warwick), Bianca Viray (University of Washington).

Supported by

Link to Workshop 2005
Link to Workshop 2007
Link to Workshop 2010
Link to Workshop 2013
Link to Workshop 2015
Link to Workshop 2017
Link to Workshop 2019
Link to Workshop 2022

Last modified: 2023-12-21
Michael Stoll