Daniel Quillen

From Wikipedia, the free encyclopedia

Daniel Grey ("Dan") Quillen (born June 21, 1940) is an American mathematician, a Fields Medallist, and the current Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He is renowned for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Fields Medal in 1978.

[edit] Biography

Quillen was born in Orange, New Jersey. He entered Harvard University, where he earned both his BA (1961) and his PhD (1964), the latter of which was completed under the supervision of Raoul Bott with a thesis in partial differential equations.

Quillen obtained a position at the Massachusetts Institute of Technology after completing his doctorate. However, he also spent a number of years at several other universities. This experience would prove to be important in influencing the direction of his research. He visited France twice: first as a Sloan Fellow in Paris, during the academic year 1968–69, where he was greatly influenced by Grothendieck, and then, during 1973–74, as a Guggenheim Fellow. In 1969–70, he was a visiting member of the Institute for Advanced Study at Princeton, where he came under the influence of Michael Atiyah.

Before his ground-breaking work in defining higher algebraic K-theory, Quillen worked on the Adams conjecture, formulated by Frank Adams in homotopy theory. His proof of the conjecture used techniques from the modular representation theory of groups, which he later applied to work on cohomology of groups and algebraic K-theory.

In 1978, Quillen received a Fields Medal at the International Congress of Mathematicians held in Helsinki. He received the award for successfully formulating higher algebraic K-theory in 1972, a problem that had baffled mathematicians since algebraic K-theory was first formulated. This new tool, formulated in terms of homotopy theory, proved to be successful in formulating and solving major problems in algebra, particularly in ring theory and module theory. Amongst his collaborating mathematicians is his former PhD student Mathai Varghese.

In related work, he also supplied a proof of Serre's conjecture about the trivality of algebraic vector bundles on affine space.

Quillen has announced his retirement as of 2006