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James Greig Arthur is a Canadian mathematician and former President of the American Mathematical Society. He is currently in the Mathematics Department of the University of Toronto.
Born in Hamilton, Ontario, Arthur received a B.Sc. from the University of Toronto in 1966, and a M.Sc. from the same institution in 1967. He received his Ph.D. from Yale University in 1970. Arthur taught at Yale from 1970 until 1976. He joined the faculty of Duke University in 1976. He has been a professor at the University of Toronto since 1978. He was four times a visiting scholar at the Institute for Advanced Study between 1976 and 2002.
A pupil of Langlands, he is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case to general reductive groups, one of the most important tools for research on the Langlands program. He also introduced the Arthur conjectures.
In 1992 he was elected a Fellow of the Royal Society He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 2003. In 2012 he became a fellow of the American Mathematical Society.
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