Speaker: Tony Feng (MIT)

Title: Derived Chevalley isomorphisms

Abstract: For a reductive group G, the classical Chevalley isomorphism identifies conjugation-invariant functions on G with Weyl-invariant functions on its maximal torus. Berest-Ramadoss-Yeung have conjectured a derived upgrade of this statement, which predicts that the conjugation-invariant functions on the derived commuting variety of G identify with the Weyl-invariant functions on the derived commuting variety of its maximal torus. In joint work with Dennis Gaitsgory we deduce this conjecture for $G = GL_n$ from investigations into derived aspects of the local Langlands correspondence. I’ll explain this story, assuming no background in derived algebraic geometry.