Dennis Sullivan

Dennis Parnell Sullivan (born February 12, 1941) is an American mathematician known for his work in algebraic topology, geometric topology, and dynamical systems. He holds the Albert Einstein Chair at the Graduate Center of the City University of New York and is a distinguished professor at Stony Brook University.

Sullivan was awarded the Wolf Prize in Mathematics in 2010 and the Abel Prize in 2022.

Early life and education Sullivan was born in Port Huron, Michigan, on February 12, 1941.

He entered Rice University to study chemical engineering but switched his major to mathematics in his second year after encountering a particularly motivating mathematical theorem.

He received his Bachelor of Arts degree from Rice University in 1963.

Career Sullivan worked at the University of Warwick on a NATO Fellowship from 1966 to 1967.

Sullivan was an associate professor at Paris-Sud University from 1973 to 1974, and then became a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS) in 1974. In 1981, he became the Albert Einstein Chair in Science (Mathematics) at the Graduate Center of the City University of New York and reduced his duties at the IHÉS to a half-time appointment. and left the IHÉS the following year.

Research Topology Geometric topology Along with Browder and his other students, Sullivan was an early adopter of surgery theory, particularly for classifying high-dimensional manifolds. (or localized), a procedure hitherto applied to the algebraic constructs made from them.

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. Sullivan's conjecture was also first presented in his 1970 notes. It examines "rationalizations" of simply connected topological spaces with homotopy groups and singular homology groups tensored with the rational numbers, ignoring torsion elements and simplifying certain calculations.

Conformal and quasiconformal mappings The Connes–Donaldson–Sullivan–Teleman index theorem is an extension of the Atiyah–Singer index theorem to quasiconformal manifolds due to a joint paper by Simon Donaldson and Sullivan in 1989 and a joint paper by Alain Connes, Sullivan, and Nicolae Teleman in 1994.

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

String topology Sullivan and Moira Chas started the field of string topology, which examines algebraic structures on the homology of free loop spaces. String topology has been used in multiple proposals to construct topological quantum field theories in mathematical physics.

Dynamical systems In 1975, Sullivan and Bill Parry introduced the topological Parry–Sullivan invariant for flows in one-dimensional dynamical systems.

In 1985, Sullivan proved the no-wandering-domain theorem. 1981 Prix Élie Cartan, French Academy of Sciences 1991 Member, American Academy of Arts and Sciences 1994 King Faisal International Prize for Science 2012 Fellow of the American Mathematical Society 2014 Balzan Prize in Mathematics (pure or applied) 2022 Abel Prize

Personal life Sullivan is married to fellow mathematician Moira Chas.