**Dennis Sullivan** is an American mathematician known for his work on topology, both algebraic and geometric, and on dynamical systems.

- At Princeton his thesis advisor was William Browder and Sullivan was awarded a Ph.D. in 1966 for his thesis Triangulating Homotopy Equivalences.
- Dennis' thesis was in this vein and led to his work on the Hauptvermutung (1967).
- It was this work which led to Sullivan receiving the Oswald Veblen Prize in Geometry in 1971 from the American Mathematical Society.
- After the award of his doctorate Sullivan was appointed to a NATO Fellowship at Warwick University in England.
- After holding the fellowship at Warwick, Sullivan held a Miller Fellowship at the University of California at Berkeley working on the Adams conjecture, KKK-theory, and étale homotopy.
- The importance of this work can be clearly seen from the fact that in 2005, thirty-five years after they were written, both the lecture notes and Sullivan's lecture to the Nice Congress were published by Springer-Verlag.
- C T C Wall wrote of the MIT notes, "it is difficult to summarise Sullivan's work so briefly: the full philosophical exposition in (the notes) should be read." The exposition in the notes focuses on epistemological questions - in particular, what is the underlying algebraic nature of a manifold, and how can we know it?
- Sullivan spent the academic year 1973-74 in France visiting the University of Paris-Orsay.
- Recent Fields Medalist Curtis McMullen is a good example of Sullivan's influence: Although McMullen received his Ph.D. from Harvard, he was really Sullivan's student, and it was while visiting the IHÉS that McMullen got the idea for his thesis problem.
- Another example is Gromov: It was Sullivan's invitation that first brought Gromov to the IHÉS as a visitor in 1977, three years after Gromov had gotten out of the Soviet Union.
- In 1996 Sullivan resigned from his professorship in Paris to take up a professorship in mathematics at the State University of New York at Stony Brook, continuing to hold his part-time position at the Graduate Center of the City University of New York.
- In session 1998-99 SUNY promoted Sullivan to Distinguished Professor.
- Sullivan has received other major honours.
- Sullivan has made important contributions to the study of foliations and dynamical systems.
- In 2006 Sullivan received the Leroy P Steele Prize for Lifetime Achievement from the American Mathematical Society.
- Sullivan used it to solve the Adams Conjecture and the Hauptvermutung for combinatorial manifolds.
- Later Sullivan developed and applied rational homotopy theory to problems about closed geodesics, the automorphism group of a finite complex, the topology of Kähler manifolds, and the classification of smooth manifolds.
- These brief remarks do not do justice to the scope of Sullivan's ideas and influence.
- Sullivan and Quillen introduced the rational homotopy type of space.
- Sullivan showed that it can be computed using a minimal model of an associated differential graded algebra.
- Sullivan's ideas have had far-reaching influence and applications in algebraic topology.
- One of Sullivan's most important contributions was to forge the new mathematical techniques needed to rigorously establish the predictions of Feigenbaum's renormalization as an explanation of the phenomenon of universality in dynamical systems.
- Sullivan's "no wandering domains" theorem settled the classification of dynamics for iterated rational maps of the Riemann sphere, solving a sixty-year-old conjecture by Fatou and Julia.
- Sullivan's work has been consistently innovative and inspirational.

Born 12 February 1941, Port Huron, Michigan, USA.

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Origin Usa, Topology, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive