Number Theory Seminar

I will talk about several results on Hecke algebras attached to Bernstein blocks of arbitrary reductive p-adic groups, and their applications to the local Langlands program. One such application is an explicit understanding of the (classical) arithmetic Local Langlands correspondence with explicit L-packets. Another such application involves various categorical "upgrades", for example, an equivalence between module categories of Hecke algebras arising from both the automorphic and the spectral sides. If time permits, I will talk about a categorical local Langlands correspondence featuring certain coherent Springer sheaves on moduli spaces of Langlands parameters. Moreover, I will try to explain why such results are of interest to number theorists.