Algebraic Geometry Seminar

A version of the excursion algebra was first introduced by V. Lafforgue in his work on the Langlands decomposition for cusp forms. This is a commutative algebra whose action on the space of automorphic functions refines the action of the Hecke algebra. Later work of D. Arinkin, D. Gaitsgory, D. Kazhdan, S. Raskin, N. Rozenblyum, and Y. Varshavsky reinterpreted this action in terms of the ring of global functions on the moduli space of local systems. It turns out that this ring admits a simple and explicit description. These results are joint with D. Gaitsgory and W. Reeves.