James Arthur (mathematician)
Encyclopedia
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.
A pupil of Langlands
, he 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 group
s, 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.
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and former President of the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
. He is currently in the Mathematics Department
of the University of Toronto
University of Toronto
The University of Toronto is a public research university in Toronto, Ontario, Canada, situated on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution of higher learning in Upper Canada...
.
Born in Hamilton, Ontario
Hamilton, Ontario
Hamilton is a port city in the Canadian province of Ontario. Conceived by George Hamilton when he purchased the Durand farm shortly after the War of 1812, Hamilton has become the centre of a densely populated and industrialized region at the west end of Lake Ontario known as the Golden Horseshoe...
, 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
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
in 1970. Arthur taught at Yale from 1970 until 1976. He joined the faculty of Duke University
Duke University
Duke University is a private research university located in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present day town of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco industrialist James B...
in 1976. He has been a professor at the University of Toronto since 1978.
A pupil of Langlands
Robert Langlands
Robert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
, he is known for the Arthur–Selberg trace formula
Arthur–Selberg trace formula
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....
, generalizing the Selberg trace formula
Selberg trace formula
In mathematics, the Selberg trace formula, introduced by , is an expression for the character of the unitary representation of G on the space L2 of square-integrable functions, where G is a Lie group and Γ a cofinite discrete group...
from the rank-one case (due to Selberg himself) to general reductive group
Reductive group
In mathematics, a reductive group is an algebraic group G over an algebraically closed field such that the unipotent radical of G is trivial . Any semisimple algebraic group is reductive, as is any algebraic torus and any general linear group...
s, one of the most important tools for research on the Langlands program
Langlands program
The Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was proposed by ....
. He also introduced the Arthur conjectures
Arthur conjectures
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 , motivated by the Arthur-Selberg trace formula....
.
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
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 2003.
External links
- Works of James Arthur at the Clay institute.