Quadratic forms are algebraic objects with particularly nice algebraic and geometric properties. Local-global principles for quadratic forms are a classical topic of algebra and number theory. The Hasse-Minkowski Theorem formulates such a local-global principle for the case of a number field or a function field of a curve over a finite field. Quadratic form theory over fields is also a basis for the study of linear algebraic groups. In the summer school we will look at certain problems of current research on algebraic groups over semi-global fields, that is, function fields in one variable over a complete discretely valued field. This will include rationality problems and the norm principle. The summer school will consist of 12-14 lectures, which are complemented by exercise sessions and some research talks.
Target group
The summer school is tailored specifically for master students and PhD students, but also advanced bachelor students and post-docs are welcome to apply.
Participants should have a basic understanding of number theory, algebraic geometry and/or quadratic form theory.
Campus
This summer school takes place at two different locations:
- The introductory programme on 1-3 July 2026: Middelheim Campus (Middelheimlaan 1, 2020 Antwerp) of the University of Antwerp.. This campus can be reached from the city centre by bike or public transport.
- The main programme on 6 - 10 July 2026: Stadscampus of the University of Antwerp. This campus is located in the city centre.
Micro-credential and study credits (ECTS)
Successful completion of the summer school can be awarded with 3 credits according to the European Credit Transfer System (ECTS). Credits will be awarded by the University of Antwerp based on active participation in the entire summer school and submitting an additional assignment.
To include the credits in the curriculum at the home institution, participants need an agreement with the responsible person at their university. Students of the University of Antwerp eligible to include the ECTS credits earned during an Antwerp Summer or Winter University programme as part of their study programme must register via Mobility Online and SisA.
All certificates of completion are issued as a micro-credential. Participants who attend the scheduled course contact hours, but don't complete the tasks will receive a certificate of attendance.
Learning outcomes
- The student acquires insight into a vibrant research area within fundamental mathematics.
- The student learns modern concepts and methods from algebra and algebraic geometry involved in recent results of an area of modern research in alebra and number theory.