Daniel Quillen

Daniel Gray Quillen ( born June 22, 1940 in Orange, New Jersey, † April 30, 2011 in Florida) was an American mathematician who worked on algebra and topology.

Life

Quillen was the son of a physics teacher. He studied at Harvard University ( BA 1961), where he received his doctorate in 1964 at Raoul Bott (Formal Properties of Over - deterministic mined system of linear partial differential equations ). As a post-doc, he was at the Massachusetts Institute of Technology (MIT) as a Moore Instructor (1964 ), in 1968/69 as a Sloan Fellow in Paris with Alexander Grothendieck, 1969/70 in Michael Francis Atiyah at the Institute for Advanced Study, and again in 1973 / 74 as a Guggenheim Fellow in Paris. He was from 1984 Waynflete Professor of Mathematics at Magdalen College at the University of Oxford. In 2006 he retired.

1975 Quillen was awarded the Cole Prize for Algebra. He received 1978 Fields Medal for his significant role in the development of algebraic K-theory (1972) and for confirmation ( together with Andrei Suslin, but independently ) of the conjecture of Serre that any algebraic vector bundle is trivial over an affine space ( set of Quillen - Suslin ). The algebraic K-theory went back to ideas of Grothendieck in algebraic geometry, which had been taken up by Atiyah and Friedrich Hirzebruch in the topological K- theory. Had Quillen in the definition of higher algebraic K- groups but entirely new territory, where he transferred techniques from homotopy theory.

In the 1960s he proved a conjecture of John Frank Adams in homotopy theory, in which he applied methods of modular representation theory of groups. He also worked on Gruppenkohomologie, where he proved a structure theorem for the cohomology mod p of finite groups.

In 1974 he gave a plenary lecture at the International Congress of Mathematicians (ICM ) in Vancouver ( Higher algebraic K -theory ) and in 1970 he was invited speaker at the ICM in Nice ( Cohomology of groups).

He was married to a violinist and had five children. He died on 30 April 2011 in a Haven Hospice in northern Florida of complications from Alzheimer 's disease.

Writings

  • Homotopical algebra. Springer, Berlin, Heidelberg, New York 1967. ( Lecture notes in mathematics 43. )
  • Higher algebraic K -theory I, in Hyman Bass (Editor) Higher K- theories, Lecture Notes in Mathematics 341, Springer Verlag, 1973, pp. 85-139 ( Proc. Conf. Battelle Memorial Institute, Seattle, Washington, 1972)
  • On the formal group laws of unoriented and complex cobordism theory, Bulletin of the AMS, Volume 75, 1969, pp. 1293-1298
  • Rational homotopy theory, Annals of Mathematics, Volume 90, 1969, pp. 205-295
  • The Adams conjecture, Topology, Volume 10, 1971, p 67-80
  • The spectrum of an equivariant cohomology ring, part 1.2, Annals of Mathematics, Volume 98, 1971, p 549-571, 573-602
  • Higher K- theory for categories with exact sequences, in: New Developments in topology, Proc. Sympos. Algebraic Topology, Oxford, 1972, London Math Soc. Lecture Note Ser. 11, 1974, Cambridge University Press, pp. 95-103
  • Projective modules over polynomial rings, Inventiones Mathematicae, Volume 36, 1976, p 167-171
  • Super Connections and the Chern character, Topology, Volume 24, 1985, p 89-95
Orange (New Jersey) C.L.E. Moore instructor Serre's modularity conjecture Group cohomology Jesse Douglas Laurent Schwartz Atle Selberg Kunihiko Kodaira Jean-Pierre Serre Klaus Roth Paul Cohen (mathematician) Stephen Smale Alan Baker (mathematician) Heisuke Hironaka Sergei Novikov (mathematician) David Mumford Charles Fefferman Alain Connes Simon Donaldson Gerd Faltings Michael Freedman Vaughan Jones Edward Witten Jean Bourgain Pierre-Louis Lions Jean-Christophe Yoccoz Curtis T. McMullen Laurent Lafforgue Andrei Okounkov Terence Tao Wendelin Werner Elon Lindenstrauss Integrated Authority File
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