This retreat-style workshop will be held between 14th and 18th of December 2026 at Dryburgh Abbey in the Scottish Borders, just south of Edinburgh. It will be structured around fewer, 1.5h-long talks and time for discussions. Participation is by invitation only.
The goal is to provide an opportunity for cross-pollination between international experts from several communities and disciplines which touch upon rational points on higher-dimensional varieties in Kodaira dimension 0 and beyond. In particular, we hope that the conversations at the workshop will kickstart new research directions and questions. In recent years, varieties in non-negative Kodaira dimension have been studied from different overlapping points of view:
through cohomological obstructions to rational points, especially those coming from Brauer groups. It is conjectured that for K3 surfaces over number fields the Brauer-Manin obstruction is the only one, but the situation in positive Kodaira dimension is much more unclear and also deserving of exploration.
through (non-)abundance properties like density and thinness of rational points. The philosophy of Campana strongly ties this to aspects of a variety's hyperbolicity and makes precise predictions. In the case of the Hilbert Property and its variants, an interesting interplay is found in covers of a base variety by varieties of higher arithmetic and geometric complexity.
through degree d points on curves. These can usually be expressed in terms of rational points on certain higher-dimensional varieties, which are typically of zero or positive Kodaira dimension. While this might only produce special cases, by leveraging the geometry and arithmetic of curves, it is often possible to get (nearly) complete descriptions of these rational points.
Organisers: Damián Gvirtz-Chen and James Rawson
Funding provided by: UKRI grant no. UKRI094