Abstract:In a recent groundbreaking work, V. Lafforgue introduced the excursion operators on the space of cusp forms for a connected reductive group G over a global field of positive characteristic. These operators are defined via the geometry of the moduli space of G-chtoucas with r paws. Using this together with other innovations, he deduced the automorphic to Galois direction of the global Langlands conjecture over function fields. In this talk, or a reading report in disguise, I will try to give a very brief introduction to this circle of ideas.
