1. Outline & Descriptions

In this course I will discuss recent progress on Langlands duality for symmetric varieties. I will review the structure theory for symmetric varieties X=G/K for a complex connected reductive group G, and explain combinatorial constructions of dual groups H_X of symmetric varieties. Then I discuss relative geometric Satake equivalence which provides a geometric construction H_X using perverse sheaves on the loop space of X. Finally, I will discuss the derived version of the story and its connections to Coulomb branches and geometric Langlands for real groups.

2. Registration

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