The Norwegian Academy of Science and Letters has decided to award the Able Prize for 2018 to Robert P. Langlands (81) of the Institute for Advanced Study, Princeton, USA, “for his visionary program connecting representation theory to number theory.”
The President of the Norwegian Academy of Science and Letters, Ole M. Sejersted, announced the winner of the 2018 Abel Prize at the Academy in Oslo on 20 March.
The Langlands Program is a project that aims to show deep connections between two very different mathematical fields, that of harmonic analysis, and that of number theory.
Robert P. Langlands program predicts the existence of a tight web of connections between automorphic forms and Galois groups. The great achievement of algebraic number theory in the first third of the 20th century was class field theory. This theory is a vast generalisation of Gauss’ law of quadratic reciprocity. It provides an array of powerful tools for studying problems governed by abelian Galois groups. The non-abelian case turns out to be substantially deeper.
In a famous letter to André Weil in 1967, Robert P. Langlands outlined a far-reaching program that revolutionised the understanding of this problem.
The two fields between which the Langlands Program seeks to establish connections are harmonic analysis and number theory. The former side is one of waves, curves, symmetries and geometry, and on the other side one of numbers, equations and their stubborn idiosyncrasies. Two different worlds, with different mathematical languages and histories.
Since Langlands first suggested the deep connections between these fields in 1967, hundreds of the world’s best mathematicians have made it their lives’ work to prove his conjectures.
The Langlands program is exciting for mathematicians because it bridges apparently unrelated disciplines, revealing a deeper structure underlying all mathematics and providing new ways to solve intractable problems.
Robert P. Langlands was born in New Westminster, British Columbia, in 1936. He graduated from the University of British Columbia with an undergraduate degree in 1957 and a M.Sc. in 1958 and from Yale University with a Ph.D. in 1960. He has held faculty positions at Princeton University and Yale University, and is currently a Professor at the Institute for Advanced Study in Princeton New Jersey. He has won several awards recognizing his outstanding contributions to the theory of automorphic forms.
Robert Langlands will receive the Abel Prize from His Majesty King Harald V at an award ceremony in Oslo on 22 May.