Yujie Xu (Columbia University): On Hecke algebras for p-adic groups and applications to the local Langlands correspondence

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. Last but not least, I will talk about a categorical local Langlands correspondence featuring certain coherent Springer sheaves on moduli spaces of Langlands parameters, and prove a fully faithful functor from the automorphic side to the spectral side.
Parts of the talk are based on recent joint work with David Helm and Maarten Solleveld.

Zoom (635 7328 0984, Kenncode: kleinste sechsstellige Primzahl)