James Arthur | |
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Born | Hamilton, Ontario, Canada | May 18, 1944
Alma mater | University of Toronto (BSc, MSc) Yale University (PhD) |
Known for | Arthur–Selberg trace formula Arthur conjectures |
Awards | John L. Synge Award (1987) Jeffery–Williams Prize (1993) CRM-Fields-PIMS prize (1997) Henry Marshall Tory Medal (1997) Gerhard Herzberg Canada Gold Medal for Science and Engineering (1999) Wolf Prize (2015) Leroy P. Steele Prize for Lifetime Achievement (2017) |
Scientific career | |
Fields | Mathematics |
Institutions | Yale University Duke University University of Toronto |
Thesis | Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One (1970) |
Doctoral advisor | Robert Langlands |
Doctoral students | Cristina Ballantine |
James Greig Arthur CC FRSC FRS (born May 18, 1944) [1] is a Canadian mathematician working on automorphic forms, and former President of the American Mathematical Society. He is a Mossman Chair and University Professor Emeritus at the University of Toronto Department of Mathematics. [2]
Born in Hamilton, Ontario, Arthur graduated from Upper Canada College in 1962, [3] received a BSc from the University of Toronto in 1966, and a MSc from the same institution in 1967. He received his PhD from Yale University in 1970. He was a student of Robert Langlands; his dissertation was Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One. [4]
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. [1] He was four times a visiting scholar at the Institute for Advanced Study between 1976 and 2002. [5]
Arthur is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case (due to Selberg himself) to general reductive groups, one of the most important tools for research on the Langlands program. He also introduced the Arthur conjectures.
Arthur was elected a Fellow of the Royal Society of Canada in 1981 and a Fellow of the Royal Society in 1992. [6] [7] In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. [8] He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 2003. [9] In 2012 he became a fellow of the American Mathematical Society. [10] He was elected as a fellow of the Canadian Mathematical Society in 2019. [11]
Atle Selberg was a Norwegian mathematician known for his work in analytic number theory and the theory of automorphic forms, and in particular for bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950 and an honorary Abel Prize in 2002.
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In mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group G on the space L2(Γ\G) of square-integrable functions, where Γ is a cofinite discrete group. The character is given by the trace of certain functions on G.
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In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over global fields, developed by James Arthur in a long series of papers from 1974 to 2003. It describes the character of the representation of G(A) on the discrete part L2
0(G(F)\G(A)) of L2(G(F)\G(A)) in terms of geometric data, where G is a reductive algebraic group defined over a global field F and A is the ring of adeles of F.
In mathematics, the Arthur conjectures are some conjectures about automorphic representations of reductive groups over the adeles and unitary representations of reductive groups over local fields made by James Arthur, motivated by the Arthur–Selberg trace formula.
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