# Curtis T. McMullen

Curtis Tracy McMullen ( born May 21, 1958 in Berkeley, California) is Professor of Mathematics at Harvard University. He won the 1998 Fields Medal for his work in particular in the field of differential geometry and complex dynamics, an area that became popular through the Mandelbrot set and Julia set.

## Life

He studied at Williams College, where in 1980 he his bachelor's degree summa cum laude acquired, and then a year at the University of Cambridge ( Emmanuel College), where he cut off the second part of the Tripos examinations for Best. From 1981 he was at Harvard University, where he studied with David Mumford. In 1985 he completed his doctorate there in the topologists Dennis Sullivan, who was not even at Harvard, with whom he but on the advice of Mumford at IHES before ( in 1984, when Sloan Fellow ) worked. There he met Stephen Smale, who gave him his real Promotions topic ( Families of rational maps and iterative root -finding algorithms ), in which he of the existence of ( for each initial value ) of Newton's method for quadratic polynomials analog iterative methods for finding roots with third-degree polynomials proved, but also that for polynomials of higher degree, there is no such algorithm. At the same McMullen worked during the summer months (as well as Mumford ) at the Thomas J. Watson Research Center of IBM in Yorktown Heights, where he worked on combinatorial optimization problems for VLSI design, but also Benoit Mandelbrot in the creation of computer graphics via iteration of complex functions (more precisely, fixed point quantities small shear groups) assisted. As a post-doctoral researcher McMullen was at the Massachusetts Institute of Technology as a Moore Instructor and 1986/86 the Institute for Advanced Study in Princeton. In 1987 he was assistant professor at Princeton University and Professor in 1990, but went in the same year as a professor at the University of California, Berkeley, where he was Professor Miller in 1994. In 1998 he went back to Harvard University, where he is a professor Maria Moors Cabot since 2001. He was from 2001 a regular guest scientist at the Max Planck Institute for Mathematics in Bonn.

He is a Fellow of the American Mathematical Society.

His doctoral include Jeffrey Brock and Maryam Mirzakhani.

## Services

In his work on the dynamics of complex functions ( in iteration, etc.), among other things, he turned Renormierungstechniken from physics ( quantum field theory ) (as before him, the physicist Mitchell Feigenbaum in the iteration of the quadratic mapping of the unit interval). With Renormierungstechniken he gave new evidence of sets of Dennis Sullivan in the complex dynamics and William Thurston on hyperbolic 3-manifolds.

## Honors

McMullen in 1991 received the Salem Prize in 1998 and the Fields Medal (Presentation: Rigidity and inflexibility in conformal dynamics). 1984 and 1988 he was a Sloan Fellow and Presidential Young Investigator 1988-1993. In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( Rational maps and Kleinian groups).

- Renormalization and 3- manifolds did fiber over the circle, Princeton 1996 ( = Annals of Mathematics Studies Vol. 142). Princeton University Press, Princeton, NJ 1996, ISBN 0-691-01153-2.
- Complex dynamics and renormalization ( = Annals of Mathematics Studies Vol. 135). Princeton University Press, Princeton, NJ 1994, ISBN 0-691-02982-2 ).

## Writings (selection )

- Families of rational maps and iterative root -finding algorithms. Ann. of Math ( 2) 125 (1987 ), no 3, 467-493.
- Amenability, Poincaré series and quasiconformal maps. Invent. Math 97 (1989 ), no 1, 95-127.
- Iteration on Teichmüller space. Invent. Math 99 (1990 ), no 2, 425-454.
- Hausdorff dimension and conformal dynamics. I: J. Differential Geom 51 (1999 ), no 3, 471-515; II: Comment. Math Helv 75 (2000 ), no 4, 535-593; III: Amer. J. Math 120 (1998), no.4, 691-721.
- The moduli space of Riemann surfaces is Kähler hyperbolic. Ann. of Math ( 2) 151 (2000 ), no 1, 327-357.
- The Alexander polynomial of a 3 -manifold and the Thurston norm on cohomology. Ann. Sci. École standard. Sup ( 4) 35 (2002 ), no 2, 153-171.
- Billiards and Teichmüller curves on Hilbert modular surfaces. J. Amer. Math Soc. 16 (2003 ), no 4, 857-885
- Dynamics of SL (2, R) over moduli space in genus two. Ann. of Math (2 ) 165 (2007 ), no 2, 397-456.