ALGAR 2024: Quadratic forms, linear algebraic groups and their invariants

Antwerp Summer School in Algebra and Arithmetic

Description

In 2024, the ALGAR summer school will be dedicated to quadratic forms, linear algebraic groups and their invariants.

Some familiarity with basic quadratic form theory will be assumed. The lectures will be accompanied by exercise sessions and a couple of research talks.

Target group: Bachelors (3rd year), masters, PhD and postdoc.

Program

Quadratic forms are algebraic objects with particularly nice algebraic and geometric properties. The theory of quadratic forms is embedded in the theory of linear algebraic groups.

In this summer school, we want to look at invariants of quadratic forms. An intriguing way to obtain such invariants is by using operations in the Witt-Grothendieck ring of a field. Quadratic forms occur themselves as invariants for other objects, such as for algebras with involutions and linear algebraic groups.

We further want to shed a light on the usage of quadratic form theory in the study of rationality questions for certain varieties.

The summer school will consist of 16-18 lectures, which are complemented by exercise sessions and some research talks.

Remarks

3 ECTS credits are awarded upon successful completion of the programme.