American mathematician (1940?2011)
Daniel Quillen
|
---|
Born
| (
1940-06-22
)
June 22, 1940
|
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Died
| April 30, 2011
(2011-04-30)
(aged 70)
|
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Nationality
| American
|
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Known for
| Algebraic
K
-theory
(
Quillen's Q-construction
),
Quillen?Suslin theorem
,
Bass?Quillen conjecture
,
rational homotopy theory
,
Quillen determinant line bundle
,
Mathai?Quillen formalism
,
Quillen's lemma
,
Quillen metric
,
Quillen's theorems A and B
|
---|
Awards
| Fields Medal
(1978)
Cole Prize
(1975)
Putnam Fellow
(1959)
|
---|
Scientific career
|
Fields
| Mathematics
|
---|
Thesis
| Formal Properties of Over-Determined Systems of Linear Partial Differential Equations
(1964)
|
---|
Doctoral advisor
| Raoul Bott
|
---|
Doctoral students
| Kenneth Brown
Varghese Mathai
|
---|
|
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
Waynflete Professor of Pure Mathematics
at
Magdalen College, Oxford
.
Education and career
[
edit
]
Quillen was born in
Orange, New Jersey
, and attended
Newark Academy
. He entered
Harvard University
, where he earned both his
AB
, in 1961, and his
PhD
in 1964; the latter completed under the supervision of
Raoul Bott
, with a thesis in
partial differential equations
. He was a
Putnam Fellow
in 1959.
[2]
Quillen obtained a position at the
Massachusetts Institute of Technology
after completing his doctorate. He also spent a number of years at several other universities. 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
in
Princeton
, where he came under the influence of
Michael Atiyah
.
In 1978, Quillen received a
Fields Medal
at the
International Congress of Mathematicians
held in
Helsinki
.
[3]
From 1984 to 2006, he was the
Waynflete Professor of Pure Mathematics
at
Magdalen College
,
Oxford
.
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
[
edit
]
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
Adams conjecture
, formulated by
Frank Adams
, in
homotopy theory
.
[5]
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. He also worked on
complex cobordism
, showing that its
formal group law
is essentially the universal one.
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
[
edit
]
Selected publications
[
edit
]
- 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:
Springer-Verlag
.
doi
:
10.1007/BFb0097438
.
ISBN
978-3-540-03914-3
.
MR
0223432
.
- Quillen, Daniel
(1969).
"On the formal group laws of unoriented and complex cobordism theory"
.
Bulletin of the American Mathematical Society
.
75
(6): 1293?1298.
doi
:
10.1090/S0002-9904-1969-12401-8
.
MR
0253350
.
- Quillen, D. (1969). "Rational homotopy theory".
Annals of Mathematics
.
90
(2): 205?295.
doi
:
10.2307/1970725
.
JSTOR
1970725
.
MR
0258031
.
- Quillen, Daniel
(1971).
"The Adams conjecture"
.
Topology
.
10
: 67?80.
doi
:
10.1016/0040-9383(71)90018-8
.
ISSN
0040-9383
.
MR
0279804
.
- Quillen, Daniel
(1971). "The spectrum of an equivariant cohomology ring. I".
Annals of Mathematics
. Second Series.
94
(3): 549?572.
doi
:
10.2307/1970770
.
ISSN
0003-486X
.
JSTOR
1970770
.
MR
0298694
.
- Quillen, Daniel
(1971). "The spectrum of an equivariant cohomology ring. II".
Annals of Mathematics
. Second Series.
94
(3): 573?602.
doi
:
10.2307/1970770
.
ISSN
0003-486X
.
JSTOR
1970771
.
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:
Springer-Verlag
. pp. 85?147.
doi
:
10.1007/BFb0067053
.
ISBN
978-3-540-06434-3
.
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.
MR
0422392
.
(
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.
Cambridge University Press
. pp. 95?103.
MR
0335604
.
- Quillen, Daniel
(1976). "Projective modules over polynomial rings".
Inventiones Mathematicae
.
36
: 167?171.
Bibcode
:
1976InMat..36..167Q
.
doi
:
10.1007/BF01390008
.
S2CID
119678534
.
- Quillen, Daniel
(1985).
"Superconnections and the Chern character"
.
Topology
.
24
(1): 89?95.
doi
:
10.1016/0040-9383(85)90047-3
.
ISSN
0040-9383
.
MR
0790678
.
References
[
edit
]
- ^
commalg.org (1 May 2011).
"Daniel Quillen"
.
- ^
"The Mathematical Association of America's William Lowell Putnam Competition"
. Retrieved
2013-03-28
.
- ^
"Home - International Mathematical Union (IMU)"
.
www.mathunion.org
.
- ^
"commalg.org: Daniel Quillen"
. 2011
. Retrieved
5 May
2011
.
- ^
Segal, Graeme (June 23, 2011),
"Daniel Quillen obituary"
,
The Guardian
- ^
Quillen, D. (1969), "Rational homotopy theory",
Annals of Mathematics
,
90
(2): 205?295,
doi
:
10.2307/1970725
,
JSTOR
1970725
,
MR
0258031
External links
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International
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National
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Academics
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Other
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