Zhiwei Yun

Abstract: I will explain how ideas from the (geometric) Langlands
program help solve the following purely algebraic problem: describe
the ring of conjugation-invariant functions on the scheme of commuting
pairs in a complex reductive group. The answer was known up to
nilpotents, and we show that this ring is indeed reduced. We also
describe the ring of invariant functions on the derived version of the
commuting scheme. The proof brings in seemingly unrelated objects such
as the Hecke category and character sheaves (of the Langlands dual
group). This is joint work with Penghui Li and David Nadler.