Tensor Categories
Collections of sets, vector spaces, topological spaces, group modules, and probably also collections of your favorite mathematical objects form intriguing structures called categories. For example, given any two vector spaces V and W of dimension m and n, respectively, we can construct their direct sum V⊕W of dimension m+n and their tensor product V⊗W of dimension mn, and there is a "distributive law" for the two constructions. Welcome to the world of tensor categories!
I will try to convince you that tensor categories are everywhere in modern mathematics, and that recognizing and dealing with them is a math superpower. We will be using complicated-sounding words such as
- functors,
- additive and abelian categories,
- monoidal and braided categories
- Grothendieck groups and rings
- Hopf algebras and supergroups
- fiber functors and reconstruction theorems,
and see many examples of (tensor) categories in action to get familiar with the area and eventually understand some deep results. This is a 6 credit point course designed for Master students or interested advanced Bachelor students. Registration is via RWTHonline, the course will be organized via RWTHmoodle. Our main reference will be the book Tensor Categories by Etingof, Gelaki, Nikshych, and Ostrik.
Looking forward to seeing you in the spring!
Johannes