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Dennis Sullivan

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Collection: 1941 Births, 20Th-Century American Mathematicians, 21St-Century American Mathematicians, City University of New York Faculty, Cuny Graduate Center Faculty, Fellows of the American Mathematical Society, Homotopy Theory, Isi Highly Cited Researchers, Living People, Members of the United States National Academy of Sciences, National Medal of Science Laureates, Princeton University Alumni, Recipients of the Great Cross of the National Order of Scientific Merit (Brazil), Rice University Alumni, State University of New York at Stony Brook Faculty, Topologists
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Dennis Sullivan

Dennis Parnell Sullivan
Born (1941-02-12) February 12, 1941
Port Huron, Michigan
Nationality American
Fields Mathematics
Institutions City University of New York
Stony Brook University
Alma mater Princeton University
Rice University
Doctoral advisor William Browder
Doctoral students Harold Abelson
Curtis T. McMullen
Elmar Winkelnkemper
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[1]) 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.

Contents

  • Work in topology 1
  • Work in dynamics 2
  • Awards and honors 3
  • Selected publications 4
  • References 5
  • External links 6

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

In 1985, he proved the No wandering domain theorem. The Parry–Sullivan invariant is named after him and the English mathematician Bill Parry.

In 1987, he proved Thurston's conjecture about the approximation of the Riemann map by circle packings together with Burton Rodin.

Awards and honors

Selected publications

  • Sullivan, Dennis (1977), "Infinitesimal computations in topology", Publ. I.H.E.S. 47: 269–331,  

References

  1. ^ Phillips, Anthony (2005), "Dennis Sullivan", in Takhtadzhi͡a︡n, Leon Armenovich, Graphs and patterns in mathematics and theoretical physics, Providence: AMS Bookstore, p. xiii,  .
  2. ^ Winners of Prestigious Wolf Prize Announced
  3. ^ List of Fellows of the American Mathematical Society, retrieved 2013-08-05.
  4. ^ "Sullivan awarded Balzan Prize" Notices of the AMS

External links

  • .  
  • Dennis Sullivan at the Mathematics Genealogy Project
  • Sullivan's homepage at CUNY
  • Sullivan's homepage at SUNY Stony Brook
  • Dennis Sullivan International Balzan Prize Foundation
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