Dennis P. Sullivan

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

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

• 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 of the American Mathematical Society
• 2014 Balzan Prize in Mathematics (pure or applied)
• 2022 Abel Prize