Abstract:
This is a follow-up on my last talk on 6-functor formalisms. I will introduce the 2-category of kernels, which is an incredibly powerful tool attached to any 3-functor formalism. We will see how its morphisms can be viewed as Fourier--Mukai functors. Moreover, one can use this 2-category to encode certain geometric notions (e.g., smooth, étale, or proper). The same idea enables us to study some finiteness properties of sheaves (e.g., universally locally acyclic, compact, or invertible) and how they relate to different kinds of duality. If time permits, I will explain some recent applications to the representation theory of locally profinite groups, which arose in joint work with Lucas Mann.
streaming via zoom:
https://uni-paderborn-de.zoom-x.de/j/66180880183?pwd=FoCQiQaFusJRhZ6aKJbDSBz7gpOB1P.1
Meeting ID: 661 8088 0183
Passcode: gradsempb