The work of Robert Langlands

James G. Arthur

Published 2023-07-05Version 1

This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have tried to communicate the remarkable continuity that runs throughout all of his work, with its roots in several fundamental areas of mathematics. What is now known as the Langlands Program represents a unification of some of the deepest parts of these areas. We hope that at least some parts of the report will be accessible to a broader mathematical audience. Other parts will inevitably be more difficult. However, we can also hope that the report is presented in such a way as to lead to a better understanding of all sides of Langlands' work.