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|Dennis Parnell Sullivan|
February 12, 1941 |
Port Huron, Michigan
|Institutions||City University of New York
Stony Brook University
|Alma mater||Princeton University
|Doctoral advisor||William Browder|
|Doctoral students||Harold Abelson
Curtis T. McMullen
|Known for||Work in topology, dynamical systems|
|Notable awards||Balzan Prize (2014)
Wolf Prize in Mathematics (2010)
Leroy P. Steele Prize (2006)
National Medal of Science (2004)
Oswald Veblen Prize in Geometry (1971)
Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician. He is known for work in topology, both algebraic and geometric, and on dynamical systems. He holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at Stony Brook University.
Work in topology
He received his B.A. in 1963 from Rice University and his doctorate in 1966 from Princeton University. His Ph.D. thesis, entitled Triangulating homotopy equivalences, was written under the supervision of William Browder, and was a contribution to surgery theory. He was a permanent member of the Institut des Hautes Études Scientifiques from 1974 to 1997.
Sullivan is one of the founders of the surgery method of classifying high-dimensional manifolds, along with Browder, Sergei Novikov and C. T. C. Wall. In homotopy theory, Sullivan put forward the radical concept that spaces could directly be localised, a procedure hitherto applied to the algebraic constructs made from them. He founded (along with Daniel Quillen) rational homotopy theory.
The Sullivan conjecture, proved in its original form by Haynes Miller, states that the classifying space BG of a finite group G is sufficiently different from any finite CW complex X, that it maps to such an X only 'with difficulty'; in a more formal statement, the space of all mappings BG to X, as pointed spaces and given the compact-open topology, is weakly contractible. This area has generated considerable further research. (Both these matters are discussed in his 1970 MIT notes.)
Work in dynamics
Awards and honors
- 1971 Oswald Veblen Prize in Geometry
- 1981 Prix Élie Cartan, French Academy of Sciences
- 1994 King Faisal International Prize for Science
- 2004 National Medal of Science
- 2006 Steele Prize for lifetime achievement
- 2010 Wolf Prize in Mathematics, for "his contributions to algebraic topology and conformal dynamics"
- 2012 Fellow, American Mathematical Society
- 2014 Balzan Prize in Mathematics (pure or applied) 
- Sullivan, Dennis (1977), "Infinitesimal computations in topology", Publ. I.H.E.S. 47: 269–331, MR 0646078
- Phillips, Anthony (2005), "Dennis Sullivan", in Takhtadzhi͡a︡n, Leon Armenovich, Graphs and patterns in mathematics and theoretical physics, Providence: AMS Bookstore, p. xiii, ISBN 0-8218-3666-8.
- Winners of Prestigious Wolf Prize Announced
- List of Fellows of the American Mathematical Society, retrieved 2013-08-05.
- "Sullivan awarded Balzan Prize" Notices of the AMS
- O'Connor, John J.; Robertson, Edmund F., "Dennis Sullivan", MacTutor History of Mathematics archive, University of St Andrews.
- Dennis Sullivan at the Mathematics Genealogy Project
- Sullivan's homepage at CUNY
- Sullivan's homepage at SUNY Stony Brook