Location: The International Centre for Mathematical Sciences, Edinburgh, UK
Jointly funded by: the Clay Mathematics Institute
and the Heilbronn Institute for Mathematical Research
Organisers
Alex Bartel (University of Glasgow)
Rachel Newton (King’s College London)
Topic description
Questions about rational points on varieties are among the oldest in mathematics, but also are at the centre of vibrant areas of modern research. Two of the remaining six Clay 1 Million Dollar problems concern points on varieties. In recent years, seemingly entirely unrelated problems, such as counting number fields, have been reformulated as problems about points on geometric objects. Moreover, several widely used cryptographic schemes are based on arithmetic properties of varieties.
The summer school will offer research students a rapid entry into the area by exposing them to some of the major fruitful research directions in arithmetic geometry. A mixture of lectures and exercise sessions will ensure that students develop intuition for and familiarity with the technical tools that they will be learning. In addition, there will be several guest lectures on topics of current interest that are not covered by the courses.
The summer school will consist of the following four courses, with one lecturer each:
Course 1: Brauer–Manin and/or other obstructions (Damián Gvirtz, University of Glasgow)
Course 2: The modular method (Samir Siksek, University of Warwick)
Course 3: Galois image on torsion, Mazur’s Programme B (Andrew Sutherland, MIT)
Course 4: Hyperelliptic curves and cluster pictures (Céline Maistret, University of Bristol)
Guest speakers
Tim Browning (IST Austria)
Jennifer Balakrishnan (Boston University)
How to apply
Registration is expected to open in November 2026. Please check back at a later date for details on how to apply.
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