James Greig Arthur (born May 18, 1944) is a Canadian mathematician working on

automorphic forms In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G o ...

, and former President of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. He is a Mossman Chair and University Professor at the

University of Toronto Department of Mathematics The University of Toronto Department of Mathematics is an academic department within the Faculty of Arts and Science at the University of Toronto. It is located at the university's main campus at the Bahen Centre for Information Technology. The ...

Education and career

Born in

Hamilton, Ontario Hamilton is a port city in the Canadian Provinces and territories of Canada, province of Ontario. Hamilton has a Canada 2016 Census, population of 569,353, and its Census Metropolitan Area, census metropolitan area, which includes Burlington, ...

, Arthur graduated from Upper Canada College in 1962, 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 Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...

in 1970. He was a student of

Robert Langlands Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study o ...

; his dissertation was ''Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One''. 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 The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

between 1976 and 2002.

Contributions

Arthur is known for the

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 (mathematician), James Arthur in a long series of pape ...

, generalizing the

Selberg trace formula In mathematics, the Selberg trace formula, introduced by , is an expression for the character of the unitary representation of a Lie group on the space of square-integrable functions, where is a cofinite discrete group. The character is given b ...

from the rank-one case (due to Selberg himself) to general

reductive group In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group ''G'' over a perfect field is reductive if it has a representation with finite kernel which is a direct ...

s, one of the most important tools for research on the

Langlands program In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic num ...

. He also introduced the Arthur conjectures.

Recognition

Arthur was elected a

Fellow of the Royal Society of Canada Fellowship of the Royal Society of Canada (FRSC) is an award granted to individuals that the Royal Society of Canada judges to have "made remarkable contributions in the arts, the humanities and the sciences, as well as in Canadian public lif ...

in 1981 and a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemat ...

in 1992. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He was elected a Foreign Honorary Member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, a ...

in 2003. In 2012 he became a fellow of the

. He was elected as a fellow of the Canadian Mathematical Society in 2019.

References

External links

*
Works of James Arthur
at the

Clay institute The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. Formerly based in Peterborough, New Hampshire, the corporate address is now in Denver, Colorado. CMI's scie ...

Archive of Collected Works of James Arthur
at the

Wolf Prizes 2015

Author profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastruct ...

{{DEFAULTSORT:Arthur, James Living people 1944 births 20th-century Canadian mathematicians Companions of the Order of Canada Duke University faculty Fellows of the American Academy of Arts and Sciences Fellows of the American Mathematical Society Fellows of the Canadian Mathematical Society Canadian Fellows of the Royal Society Fellows of the Royal Society of Canada Foreign associates of the National Academy of Sciences Institute for Advanced Study visiting scholars People from Hamilton, Ontario Presidents of the American Mathematical Society University of Toronto alumni University of Toronto faculty Yale Graduate School of Arts and Sciences alumni Yale University faculty 21st-century Canadian mathematicians

Education and career

Contributions

Recognition

References

Further reading

External links