Prof. James C. Arthur from the University of Toronto in Canada won the 2015 Wolf Prize in the mathematics category

The prize was awarded to him for his monumental work on the Aikba formula and his fundamental contributions to the theory of automorphic representations of reductive sets

Prof. James C. Arthur from the University of Toronto in Canada won the 2015 Wolf Prize in the mathematics category. The prize was awarded to him for his monumental work on the Aiqaba formula and his fundamental contributions to the theory of automorphic representations of reductive sets.

The jury elaborates: "The development of the Aiqaba formula for reductive groups by Arthur is a monumental mathematical achievement. He generalizes Selberg's trace formula to the bundle SL(2) from 1956. In his work, Arthur introduced many central tools in non-commutative harmonic analysis on general reductive bundles. Drawing on the work of Langlands, Shelstedt, Kutwitz, Waldsporja and others, Arthur obtained the Aiqaba formula in its stable form. Using the elementary lemma, proved by Ngo, Arthur's work qualified for the climax in describing, as predicted by Langlands, the structure of the automorphic representations of the classical bundles (symplectic bundles and special orthogonal bundles, bifurcating). Among the highlights are the punctoriality suitable for the standard presentation, the multiplicity formulas in the discrete spectrum, the sorting of all predicted counterexamples to the Ramanujan hypothesis and the description of the local L-packs and the global A-packs.

"Arthur's work has had a huge impact. For example, it served as a central tool in Laporg's proof of Langland's matching to function fields. Recently, Clausel, Harris, Taylor and others used it in the construction, by p-eddy methods, of Galois representations corresponding to automorphic patterns. Arthur's ideas, his achievements and the techniques he introduced will have many more important uses in the theory of automorphic representations and in the study of locally symmetric spaces. Arthur's work is a milestone in mathematics, which will inspire generations of mathematicians in the future."