Daniel Quillen

Daniel Gray Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.

From 1984 to 2006, he was the

In 1978, Quillen received a Fields Medal at the International Congress of Mathematicians held in Helsinki.^[3]

From 1984 to 2006, he was the

Quillen retired at the end of 2006. He died from complications of Alzheimer's disease on April 30, 2011, aged 70, in Florida.^[4]

Mathematical contributions

Quillen's best known contribution (mentioned specifically in his Fields medal citation) was his formulation of higher algebraic K-theory in 1972. This new tool, formulated in terms of homotopy theory, proved to be successful in formulating and solving problems in algebra, particularly in ring theory and module theory. More generally, Quillen developed tools (especially his theory of model categories) that allowed algebro-topological tools to be applied in other contexts.

Before his work in defining higher algebraic K-theory, Quillen worked on the

In related work, he also supplied a proof of Serre's conjecture about the triviality of algebraic vector bundles on affine space, which led to the Bass–Quillen conjecture. He was also an architect (along with Dennis Sullivan) of rational homotopy theory.^[6]

He introduced the Quillen determinant line bundle and the Mathai–Quillen formalism.

See also

• Friedhelm Waldhausen

Selected publications

Scholia has a profile for Daniel Quillen (Q369658).

• Quillen, Daniel G. "Homology of commutative rings". unpublished notes. Archived from the original on 2015-04-20.
• Quillen, Daniel G. (1967). Homotopical Algebra. Lecture Notes in Mathematics. Vol. 43. Berlin, New York:
  MR 0223432
  .
• Quillen, Daniel (1969). "On the formal group laws of unoriented and complex cobordism theory".
  MR 0253350
  .
• Quillen, D. (1969). "Rational homotopy theory". Annals of Mathematics. 90 (2): 205–295.
  MR 0258031
  .
• Quillen, Daniel (1971). "The Adams conjecture".
  MR 0279804
  .
• Quillen, Daniel (1971). "The spectrum of an equivariant cohomology ring. I".
  MR 0298694
  .
• Quillen, Daniel (1971). "The spectrum of an equivariant cohomology ring. II".
  MR 0298694
  .
• Quillen, Daniel (1973). "Higher algebraic K-theory. I". Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972). Lecture Notes in Math. Vol. 341. Berlin, New York:
  MR 0338129
  .
• Quillen, Daniel (1975). "Higher algebraic K-theory". Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974), Vol. 1. Montreal, Quebec: Canad. Math. Congress. pp. 171–176.
  Quillen's Q-construction
  )
• Quillen, Daniel (1974). "Higher K-theory for categories with exact sequences". New developments in topology (Proc. Sympos. Algebraic Topology, Oxford, 1972). London Math. Soc. Lecture Note Ser. Vol. 11.
  MR 0335604
  .
• Quillen, Daniel (1976). "Projective modules over polynomial rings".
  S2CID 119678534
  .
• Quillen, Daniel (1985). "Superconnections and the Chern character".
  MR 0790678
  .