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.
Courses and Lecturers
The summer school will consist of the following four courses, with one lecturer each.
Course 1: Brauer groups and obstructions (Damián Gvirtz-Chen, 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)
Organisers
Alex Bartel (University of Glasgow)
Rachel Newton (King’s College London)
Who should apply
This school is primarily aimed at PhD and Masters students, but we also welcome applications from postdoctoral researchers who would benefit from participating.
Additional Information
This event will take place in-person at the International Centre for Mathematical Sciences, Edinburgh.
Accommodation, lunch and subsistence will be provided; while participants are expected to fund their own travel, limited funds may be available for those unable to secure travel costs from their home institution.
Registration: Please register your interest by completing the application form.
Before completing the form, please ensure that you have one of the following documents available, this should be uploaded to support your application:
- Masters students - your most recent transcript
- PhD students - a letter of support from your surpervisor (up to two paragraphs)
- Postdocs - a motivational letter indicating the relevance of the summer school to your research (up to two paragraphs)
The closing date for registration is Sunday 21st March 2027 (23.59pm UK time). Successful applicants will be notified early April 2027.
Confirmed Speakers
Céline Maistret
Samir Siksek
Damián Gvirtz-Chen
Andrew Sutherland
Tim Browning
