Groupes, algèbres et représentations

The exact content varies over the years but alternates between the following subjects:

• Deligne’s approach to Tannaka-Krein duality: Deligne proved that an algebraic group (in particular, a finite group) is can be reconstructed from it’s finite dimensional representations. We will study this theorem and introduce all the ingredients to reach this goal, such as algebraic groups and the tensor product of representations. (this was the content in 2020-21)
• Descent theory: Descent theory is a technique which can be applied in various subfield of algebra and geometry. Given a morphism f:X\to Y (e.g. a field extension or a continuous map between topological spaces), the aim of descent theory is to provide a description of structures over Y (e.g. vector spaces or sheaves) induced by structures over X along this morphism f. (this will be the content in 2021-22)

Aim: To deepen the understanding and intuition in the fabric of algebraic structures and to reach a higher level of abstraction by studying profoundly a specific topic in realm of modern algebra. This topic can depend of the interests of the students.

Required and Corequired knowledge and skills

Basic notions in algebra and geometry as treated in the bachelor courses.

Ex-cathedra theory courses

References, bibliography, and recommended reading

Lecture notes are available on UV.

Course notes

• Syllabus
• Université virtuelle

Contacts

Joost Vercruysse, Campus Plaine, bureau 2.O8.104. Email: joost.vercruysse@ulb.be

Campus

Plaine

Method(s) of evaluation

• Other

Other

Written exam with oral defense and discussions.

Mark calculation method (including weighting of intermediary marks)

Note on 20 for the final exam.

Language(s) of evaluation

• french
• (if applicable english )