# Dennis Sullivan

Wolf Prize Laureate in Mathematics 2010

**Dennis Sullivan**

#### Affiliation at the time of the award:

**Stony Brook University, USA**

**CUNY Graduate School and University Center, ****USA**

#### Award citation:

**“for his innovative contributions to algebraic topology and conformal dynamics”.**

#### Prize share:

**Dennis Sullivan **

**Shing-Tung Yau**

Dennis Sullivan (born in 1941, USA) has made fundamental contributions in many areas, especially in algebraic topology and dynamical systems. His early work helped lay the foundations for the surgery theory approach to the classification of higher dimensional manifolds, most particularly, providing a complete classification of simply connected manifolds within a given homotopy type. He developed the notions of localization and completion in homotopy theory, and used this theory to prove the Adams Conjecture (also proved independently by Quillen). Profs. 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 60 year-old conjecture by Fatou and Julia. His work generated a surge of activity, by introducing quasiconformal methods to the field and establishing an inspiring dictionary between rational maps and Kleinian groups of continuing interest. His rigidity theorem for Kleinian groups has important applications in Teichmuller theory and for Thurston´s geometrization program for 3-manifolds. His recent work on topological field theories and the formalism of string theory can be viewed as a byproduct of his quest for an ultimate understanding of the nature of space, and how it can be encoded in strange algebraic structures.

Sullivan’s work has been consistently innovative and inspirational. Beyond the solution of difficult outstanding problems, his work has generated important and active areas of research, pursued by many mathematicians.