Towards a tamely ramified local geometric Langlands correspondence for p-adic groups

Abstract: For a reductive $p$-adic group $G$, Kazhdan-Lusztig prove an isomorphism of the the extended affine Hecke algebra and the $G^\vee$-equivariant $K$-group of the Steinberg variety of the Langlands dual group $G^\vee$. It has a profound application of proving an important case of the local Langlands correspondence which is known as the Deligne-Langlands conjecture. For $G$ being a reductive group over an equal-characteristic local field, Bezrukavnikov upgrades Kazhdan-Lusztig's isomorphism to an equivalence of monoidal categories and proves the tamely ramified local geometric Langlands correspondence. In this talk, we discuss an ongoing project with João Lourenço on proving a tamely ramified local geometric Langlands correspondence for reductive $p$-adic groups. Time permitting, I will mention an interesting variant of Bezrukavnikov's equivalence in Ben-Zvi-Sakellaridis-Venkatesh's framework of the relative Langlands program based on a joint work in preparation with Milton Lin and Toan Pham.

number theory

Audience: researchers in the topic

Comments: pre-talk at 1:20pm

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.