Harish-Chandra

from Wikipedia, the free encyclopedia
Harish-Chandra

Harish-Chandra (born October 11, 1923 in Kanpur , India , † October 16, 1983 in Princeton , USA ) was an Indian mathematician who mainly worked in the field of infinite-dimensional representations of Lie groups .

Live and act

Because his father traveled a lot as a hydraulic engineer , he grew up in his wealthy grandfather's house in Kanpur . After an upbringing by private tutors, he started 7th grade at 9 and went to the University of Allahabad at 16 . He studied theoretical physics until his diploma in 1943 and was then assistant to Bhabha , a student of Paul Dirac , in Bangalore . In 1945 he went to Cambridge to do his doctorate under Paul Dirac . In Cambridge he also met Wolfgang Pauli , whom he pointed out to a mistake. He became increasingly interested in mathematics and studied with John Edensor Littlewood . In his doctoral thesis on "Infinite irreducible representations of the Lorentzgroup" in 1947, in which he built on Eugene Wigner , he found the topic for his future research work, the theory of infinite-dimensional representations (i.e. those in functional spaces) of non-compact Lie groups (like the Lorentz group ), which was much more complex than that of the compact Lie groups.

In 1947/48 he accompanied Dirac as his assistant to Princeton, where the meeting with Hermann Weyl , Emil Artin and Claude Chevalley finally made him switch to mathematics. In his opinion he lacked the intuition necessary for theoretical physics, on the other hand he was dissatisfied with the lax handling of mathematical theories among physicists (which also concerned his doctoral thesis). 1949/1950 he was at Harvard with Oscar Zariski . From 1950 to 1963 he was at Columbia University in New York, but spent a long time in visiting professorships, for example at the Tata Institute of Fundamental Research in Bombay in 1952/53 , where he also married. The marriage resulted in two daughters. In 1955/56 he was in Princeton at the Institute for Advanced Study and 1957/58 as a Guggenheim fellow in Paris, where he worked with André Weil . From 1961 to 1963 he was again a Sloan Research Fellow at the Institute for Advanced Study, and then a permanent member. In 1969 and 1970 he had his first two heart attacks and in 1970 went to IHES for a sabbatical year . In 1982 he had another heart attack due to overwork, from which he did not fully recover.

Harish-Chandra developed the theory of the representations of reductive Lie groups and algebraic groups, and the associated "harmonic analysis" (the theory of the functions defined on the group). He defined characters for infinite-dimensional representations and proved the analogues to Weyl's character formula. He also determined the "Discrete Series" of representations and determined the Plancherel measures for semi-simple Lie groups. He also examined applications in the theory of automorphic forms (Eisenstein series, etc.) and number theory (i.e., e.g. p-adic representations). His work is fundamental to the Langlands program . In 1958 he was shortlisted for the Fields Medal .

In 1954 he won the Cole Prize in Algebra. In 1974 he received the Indian Ramanujan Medal. In 1966 he gave a plenary lecture at the International Congress of Mathematicians in Moscow (Harmonic analysis on semi-simple Lie groups) and also in Amsterdam in 1954 (Representations of semisimple Lie groups). He was a Fellow of the Royal Society , the National Academy of Sciences (1981), the Indian National Science Academy and the Indian Academy of Sciences. In 1980 he became a US citizen. In 1981 he received an honorary doctorate from Yale University .

The asteroid (24944) Harish-Chandra was named after him.

His friend and student VS Varadarajan published his collected works.

Harish-Chandra Research Institute

In 1966, the Harish-Chandra Research Institute named after Harish-Chandra was opened in Allahabad . It is dedicated to research in mathematics and theoretical physics.

literature

  • Harish-Chandra Collected papers , 4 volumes, Springer Verlag 1998 (publisher VS Varadarajan)
  • Rebecca Herb Harish-Chandra and his work , Bulletin of the American Mathematical Society, 25, 1991, 1-17, online
  • Armand Borel et al. a. The mathematical legacy of Harish-Chandra , AMS 2000 (Baltimore Conference 1998)
  • VS Varadarajan Harish-Chandra , Mathematical Intelligencer 1984, volume 3
  • Harish-Chandra, JGM Mars (editor) Automorphic forms on semisimple Lie groups , Lecture Notes in Mathematics 62, Springer-Verlag, 1968
  • Harish-Chandra, G. van Dijk (editor): Harmonic analysis on reductive p-adic groups , Lecture Notes in Mathematics 162, Springer Verlag 1970

Web links

Individual evidence

  1. ↑ Michael Barany, The Fields Medal should return to its roots , Nature, Volume 553, 2018, pp. 271-273
personal data
SURNAME Harish-Chandra
BRIEF DESCRIPTION Indian mathematician
DATE OF BIRTH October 11, 1923
PLACE OF BIRTH Kanpur
DATE OF DEATH October 16, 1983
Place of death Princeton