Groupoids, which generalise fibrations of groups over manifolds, have become central tools to host singular structures. After some prerequisites on groupoids, this course presents three instances in which groupoids arise in different forms and for different purposes. We shall first discuss van Erp and Yuncken's groupoid approach to pseudodifferential operators by means of the tangent groupoid. We shall then define and study direct connections on groupoids and their jet prolongations, which play a role in Hairer's regularity structures. If time allows, we shall finally discuss principal bundles groupoids, which when viewed as groupoids in the category of principal bundles, can be seen as building blocks for higher gauge theories.
The lectures start on 25.04.2022 and run until 25.07.2022
Mondays 12:15 -13:45 Room 2.09.1.10 Prof. Dr. Paycha
The exercise sessions start on 27.04.2022 and run until 27.07.2022
Wednesdays 12:15- 13:45 Room 2.25.D1.02 Dr. Reiss
- Kursleiter*in: Prof. Dr. Sylvie Paycha