Special Year 2020-21: Geometric and Modular Representation Theory

Continuation of the previous talk.

The talk introduces the Kazhdan-Lusztig equivalence between the Kazhdan-Lusztig category of representations of affine algebra and category of modules over the quantum group.

I will report on a joint work in progress with K. Coulembier and V. Ostrik. We show that a symmetric tensor category in characteristic $p > 0$ admits a fiber functor to the Verlinde category (semisimplification of $Rep(Z/p)$) if and only if it has...

I'll discuss joint work with Zhiwei Yun constructing a natural functor from the automorphic category of a nodal curve to the automorphic category of a smoothing. The results depend on the microlocal geometry of sheaves with nilpotent singular...

Continuation from last time.

I will report on a project joint with Roman Bezrukavnikov (and partly with Laura Rider) aiming at constructing a variant for positive-characteristic coefficients of the equivalence constructed by Bezrukavnikov in "On two geometric realizations of an...