Motives and Automorphic Forms

Following a line of research culminating in the works of Weil, Eichler, Shimura and Taniyama, then further pushed by the emerging of the Langlands program, many deep and fruitful bridges between automorphic forms and algebraic geometry have been explored and led to spectacular results. During the fifty years span from the proof of Ramanujan’s conjecture on the discriminant modular form, using the validity of the Weil conjectures in algebraic geometry over finite fields, to the recent proof of the Sato-Tate conjectures for elliptic curves over CM fields, using automorphic machinery, it has been clearly established that the interaction between these two fields has amazing applications in both directions. Moreover, several guiding principles in this area have been inspired by the philosophy of motives, which has now developed into a mature theory providing not only heuristics, but concrete and sophisticated new tools to attack problems. The aim of the conference is to present the state of the art of the field by gathering leading experts at the crossroads of automorphic forms, arithmetic geometry and representation theory, and celebrating Günter Harder’s influence on these topics.