组织者：单芃，赵启弦

课程介绍/摘要：
This three-lecture series is an expanded exposition of joint work with Gurbir Dhillon, Zhiwei Yun, and Xinwen Zhu on monodromic (metaplectic) affine Hecke categories. Affine Hecke categories are geometric categorifications of affine Hecke algebras and play a central role in geometric representation theory and the quantum geometric Langlands program. In the metaplectic setting, these categories are twisted by monodromy data arising from central extensions of loop groups.

Building on the ideas presented in the accompanying talk, the lectures will develop the combinatorial and geometric foundations of affine Hecke categories in greater depth. A central theme will be the description of monodromic affine Hecke categories in terms of Soergel bimodules, which enables a direct comparison with ordinary affine Hecke categories associated to smaller, endoscopic groups. This generalizes earlier results of Lusztig and Yun for finite Hecke categories.

The series will conclude with applications and consequences of these equivalences, including categorical endoscopy for affine Hecke categories, the metaplectic derived Satake equivalence, and connections with conjectures of Gaitsgory in quantum geometric Langlands. Throughout the lectures, examples will be used to illustrate the main ideas and mechanisms underlying the results.