Daniel Gray Quillen

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Daniel Gray Quillen (born June 22 or June 27, 1940 in Orange , New Jersey , † April 30, 2011 in Florida ) was an American mathematician who studied algebra and topology .

Life

Quillen was the son of a physics teacher. He studied at Harvard University (Bachelor's degree in 1961), where he received his doctorate from Raoul Bott in 1964 ( Formal Properties of over-determined systems 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 Research Fellow in Paris with Alexander Grothendieck , in 1969/70 with Michael Francis Atiyah at the Institute for Advanced Study and again in 1973 / 74 as a Guggenheim Fellow in Paris. From 1984 he was Waynflete Professor of Mathematics at Magdalen College at the University of Oxford . In 2006 he retired.

In 1975 Quillen was awarded the Cole Prize for Algebra. He received the Fields Medal in 1978 for his instrumental role in the development of the algebraic K-theory (1972) and for confirming (simultaneously with Andrei Suslin , but independently) Serre's conjecture that any algebraic vector bundle over an affine space is trivial ( Quillen-Suslin theorem ). The algebraic K-theory was based on ideas of Grothendieck in algebraic geometry, which had also been taken up by Atiyah and Friedrich Hirzebruch in the topological K-theory. Quillen had to go completely new ways in the definition of the higher algebraic K-groups, using techniques from the homotopy theory.

In the 1960s he proved a conjecture by John Frank Adams in homotopy theory , using methods of modular representation theory of groups. He also worked on group cohomology, where he proved a structure theorem for the cohomology ring 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 ). In 1978 Quillen was elected to the National Academy of Sciences .

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

Fonts

  • 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. Batelle Memorial Inst., Seattle, Washington, 1972)
  • On the formal group laws of unoriented and complex cobordism theory , Bulletin AMS, Volume 75, 1969, pp. 1293-1298
  • Rational homotopy theory , Annals of Mathematics, Vol. 90, 1969, pp. 205-295
  • The Adams conjecture , Topology, Vol. 10, 1971, pp. 67-80
  • The spectrum of an equivariant cohomology ring , part 1,2, Annals of Mathematics, Volume 98, 1971, pp. 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, pp. 167-171
  • Superconnections and the Chern character , Topology, Vol. 24, 1985, pp. 89-95
  • Robert Penner (Ed.): Topology and K-Theory. Lectures by Daniel Quillen , Springer, Lecture notes in mathematics, 2262, 2020 (lectures at MIT 1979/80)

Web links

Individual evidence

  1. ↑ according to the obituary in the Guardian by Graeme Segal , June 23, 2011, online
  2. ↑ Encyclopedia Britannica, Article Quillen
  3. ↑ Daniel Quillen :: commalg.org :: the commutative algebra community , accessed on May 16, 2011 (English)
  4. ↑ Haven Hospice of Florida Overview ( Memento from April 2, 2009 in the Internet Archive ), accessed on May 16, 2011 (English)
personal data
SURNAME Quillen, Daniel Gray
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 22, 1940 or June 27, 1940
PLACE OF BIRTH Orange , New Jersey
DATE OF DEATH April 30, 2011
Place of death Florida