Dennis Sullivan

2014 Balzan Prize for Mathematics (Pure/Applied)

For his major contributions to topology and the theory of dynamical systems, opening new perspectives for generations to come. For his exceptional results in many fields of mathematics, such as topology, geometry, the theory of Kleinian groups, analysis, and number theory.

Dennis Parnell Sullivan is a US citizen, born in Port Huron, Michigan, on February 12, 1941.
He is the Albert Einstein Professor of Science and Distinguished Professor of Mathematics at the City University of New York Graduate School and University Center (since 1981) and is Professor of Mathematics at Stony Brook University (since 1995).

He was brought up in Houston,Texas, attending school there before entering Rice University to study Physical Chemistry. He gravitated to Mathematics and earned his BA at Rice University in 1963. He then went to Princeton University for graduate studies in Mathematics, and earned his PhD in January 1966.

After his doctorate, Sullivan was awarded a NATO Fellowship at Warwick University in England during 1966, was an Instructor at Princeton (1966-67), a Miller Fellow at the University of California at Berkeley (1967-69) and The Sloan Fellow of Mathematics at the Massachusetts Institute of Technology (1969-73).

He spent the academic year 1973-74 in France as professeur associé at the University of Paris-Orsay and became in 1974 a permanent professor at the Institut des Hautes Études Scientifiques. In 1981 he was appointed to the Einstein Chair at the City University of New York, working jointly with the Institut des Hautes Études Scientifiques until 1996.

After his resignation from the professorship in Paris he became professor of mathematics at the State University of New York at Stony Brook, working jointly with the Graduate Center of the City University of New York. In 1998 the Regents promoted him to Distinguished Professor of the State University of New York.

He was elected member to the US National Academy of Sciences (1983), corresponding member of the Brazilian National Academy of Sciences (1983), member of the New York Academy of Sciences (1984), fellow of the American Academy of Arts and Sciences (1991), corresponding member of the Irish Royal Society (2012) and honorary member of the London Mathematical Society (2013). He also served as Vice-president (1990-93) of the American Mathematical Society.

He received the Oswald Veblen Prize in Geometry 1970 (USA), the Elie Cartan Prize in Geometry 1981 (France), the King Faisal International Prize for Science 1994 (Saudi Arabia), the Gold Medal of the Brasilian Academy of Sciences 1996, the US National Medal of Science 2005, the AMS Steele Prize for Lifetime Achievement 2006 and the Wolf Prize for Mathematics 2010 (Israel).

Among his most important scientific publications:

1970. Geometric Topology: Localisation, Periodicity, and Galois Symmetry. Cambridge, MA: MIT.
1974. Genetics of homotopy theory and the Adams conjecture. Annals of Mathematics: 1-79.
1976. Cycles for the dynamical study of foliated manifolds and complex manifolds. Inventiones mathematicae 36 (1): 225-255.
1977. Infinitesimal computations in topology. Publ. I.H.E.S. 47: 269-331.
1977. Hyperbolic Geometry and Homeomorphisms. Proceedings of Georgia Topology Conference 1977.
1979. The density at infinity of a discrete group of hyperbolic motions. Publications Mathématiques de l’IHÉS 50 (1): 171-202.
1981. On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions. Ann. of Math. Stud. 97: 465-496.
1983. Conformal dynamical systems. Geometric dynamics. Bulletin of the AMS: 725-752.
1985. Quasiconformal Homeomorphisms and Dynamics I: Solution of the Fatou-Julia Problem on Wandering Domains. Annals of Mathematics 122.
1986. Quasiconformal Homeomorphisms and Dynamics II: Structural stability implies hyperbolicity for Kleinian groups. Acta mathematica 155 (1): 243-260.
1991. Bounds, Quadratic Differentials, and Renormalization Conjectures. AMS Publications. Proceedings of the 1988 Centennial Conference.
2005. Geometric Topology: Localization Periodicity and Galois Symmetry: the 1970 MIT Notes. Springer.
2014. 3D incompressible fluids: combinatorial models, eigenspace models, and a conjecture about well-posedness of the 3D zero viscosity limit. J. Differential Geom.97, no. 1: 141-148.

Co-authored works:

-Sullivan DP, Deligne P, Griffiths P, Morgan J. 1975. Real homotopy Theory of Kähler manifolds. Inventiones mathematicae 29 (3): 245-274.
-Sullivan DP, Ruelle D. 1975. Currents, flows and diffeomorphisms. Topology 14 (4): 319-327.
-Sullivan DP, Mané R, Sad P. 1983. On the dynamics of rational maps. Annales scientifiques de l’École Normale Supérieure 16 (2): 193-217.
-Sullivan DP, Donaldson SK. 1989.Quasiconformal 4-manifolds. Acta Mathematica Vol 163.
-Sullivan DP, Rodin B. 1987. The convergence of circle packings to the Riemann mapping. Journal of Differential Geometry 26 (2): 349-360.
-Sullivan DP, Gardiner FP. 1992. Symmetric structures on a closed curve. American Journal of Mathematics (1992): 683-736.
-Sullivan DP, Chas M. 1999. String topology. Arxiv.

(October 2014)

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