Arithmetic of Function Fields

A conference on 'Arithmetic of Function Fields' will take place June 26-30, 2017, at the University of Muenster, Germany.

The purpose of this conference is to bring together international experts in a variety of areas of arithmetic geometry, automorphic forms, and function field arithmetic. The emphasis of the conference will be on recent spectacular developments in the theory of Drinfeld moduli spaces, Drinfeld modular forms, and their applications. It is hoped that having at the same place and time a large number of researchers with different viewpoints on function field arithmetic will illuminate previously unnoticed connections within the area, thus facilitating future progress. The organizers of the conference will make a strong effort to ensure an active participation of a large number of junior researchers and underrepresented groups.

Since their emergence in 1970s, Drinfeld moduli spaces had a tremendous impact on the Langlands program leading to a successful resolution of the global and local Langlands conjectures over function fields. Over the last few years, there has been an explosion of activity in function field arithmetic, with many spectacular results on special values of higher derivatives of L-functions of automorphic forms, special values of Carlitz-Goss L-functions, and Drinfeld modular forms. Moreover, new tantalizing connections have been discovered between different topics of function field arithmetic, such as special values of characteristic p zeta functions, deformations of Drinfeld modular forms, and function field analogue of Fontaine's theory. In many of these works, Drinfeld moduli spaces play a prominent role.

These developments, along with possible future directions of research, will be addressed by the invited speakers of this conference with the hope to inspire new generations to take part in this important and very active area of Number Theory.

Conference website: http://wwwmath.uni-muenster.de/sfb878/activities/AFF_announce.html