James Arthur
University of Toronto
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Primary Section: 11, Mathematics Membership Type:
International Member
(elected 2014)
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Biosketch
James Arthur is a University Professor and Mossman Chair in the Department of Mathematics at the University of Toronto. He works in the general areas of automorphic forms, group representations and number theory. He is known for his work on the Arthur-Selberg trace formula, his introduction of what are now called A-parameters and A-packets for the analysis of automorphic representations, and his recent classification of the automorphic representations of many classical groups. Arthur grew up in Toronto, and graduated from the University of Toronto with a BSc in mathematics and physics in 1966. He obtained his PhD in mathematics at Yale University in 1970, and then taught at Princeton University, Yale University and Duke University before returning to the University of Toronto in 1979. Arthur was awarded the Canada Gold Medal for Science and Engineering in 1999. He served as President of the American Mathematical Society from 2005-2007, and was the academic trustee for mathematics on the Board of Trustees of the Institute for Advanced Study in Princeton. He is a Fellow of the Royal Society of Canada, a Fellow of the Royal Society of London, a Foreign Honorary Member of the American Academy of Arts and Sciences, and a Foreign Associate of the National Academy of Sciences.
Research Interests
James Arthur works in the area of mathematics called automorphic representations. These objects date back to the nineteenth century, but in recent years have come to occupy a central place in mathematics known as the Langlands program. The conjectures of Robert Langlands that define the program are still largely unresolved. Roughly speaking, they assert that concrete spectral data wrapped up in automorphic representations govern fundamental processes from quite different domains of mathematics. One of the primary tools for analyzing automorphic representations has been a complex trace formula that relates this spectral data to various kinds of geometric data. It was introduced in special cases by Selberg in 1956, and was then established for general groups by Arthur over the later period from 1975 to 2000. Arthur has used the trace formula to classify certain automorphic representations and establish some cases of the Langlands conjectures. He is now working on the central premise of the Langlands program known as the principle of functoriality.
