James Arthur: The Langlands program: arithmetic, geometry and analysis

Abstract: As the Abel Prize citation points out, the Langlands program represents a grand unified theory of mathematics. We shall try to explain in elementary terms what this means. We shall describe an age old question concerning the arithmetic prime numbers, together with a profound generalization of the problem that lies at the heart of algebraic geometry. We shall then discuss the tenets of the Langlands program that resolve these questions in terms of harmonic analysis. Finally, we shall say something of Langlands' many fundamental contributions to the program, with the understanding that there is still much to be done. James Arthur is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor at the University of Toronto Department of Mathematics. This lecture was held at The University of Oslo, May 23, 2018 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2018 1. "On the Geometric Theory" by Abel Laureate Robert P. Langlands, Institute for Advanced Study, Princeton University 2. "The Langlands Program: Arithmetic, Geometry and Analysis" by Professor James Arthur, University of Toronto 3. "Langlands Program and Unification" by Professor Edward Frenkel, UC Berkley