Joint IAS/PU Arithmetic Geometry

Arthur proposed a description of automorphic forms in terms of tempered automorphic forms for centralizers of SL2 homomorphisms. I will explain a point of view on the Arthur parameterization in the setting of function fields coming from relative Langlands duality, emphasizing the role of shearing (the symmetry of the derived category of graded vector spaces which simultaneously shifts weights and cohomological degrees). Shearing helps account for a deficit of Tannakian formalism in the derived context - there are more eigenvalues for tensor actions than one might expect. The talk reports on joint work with Yiannis Sakellaridis and Akshay Venkatesh.