Curtis McMullen(1958 — ?)
Curtis T. McMullen
États-Unis
5 min read
Curtis McMullen is an American mathematician born in 1958, a professor at Harvard University. A specialist in dynamical systems, hyperbolic geometry, and complex analysis, he was awarded the Fields Medal in 1998.
Frequently asked questions
Key Facts
- Born on May 21, 1958, in Berkeley, California
- Awarded the Fields Medal in 1998 for his work in holomorphic dynamics and geometry
- Professor of mathematics at Harvard University since 1998
- Major work on dynamical systems, Riemann surfaces, and three-dimensional hyperbolic geometry
Works & Achievements
Foundational work carried out under the supervision of Dennis Sullivan, laying the groundwork for his research in holomorphic dynamics and hyperbolic geometry.
A major work connecting the renormalization of quadratic maps, the geometry of the Mandelbrot set, and 3-dimensional hyperbolic manifolds.
A book developing a deep parallel between the renormalization of dynamical systems and the geometry of hyperbolic manifolds that fiber over the circle.
An honor recognizing his contributions to the theory of dynamical systems, hyperbolic geometry, and complex analysis.
A series of investigations connecting the dynamics of polygonal billiards to geometry and number theory, opening up new fields of study.
Anecdotes
In 1998, Curtis McMullen received the Fields Medal at the International Congress of Mathematicians in Berlin. This honor, awarded every four years to researchers under the age of 40, is often nicknamed the “Nobel Prize of mathematics,” even though no actual Nobel Prize exists for this discipline.
McMullen long used computers to explore the fractal figures known as Julia sets. By tracing these images of infinite complexity, he connected the visual art of fractals to rigorous mathematical proofs about the chaotic behavior of functions.
Before teaching at Harvard, McMullen was a professor at the University of California, Berkeley, and studied at Williams College and then at Harvard. His thesis advisor was Dennis Sullivan, himself a renowned mathematician in the field of dynamical systems.
Part of his work focuses on “Kleinian groups” and hyperbolic geometry, objects that describe curved spaces impossible to draw on a flat sheet of paper. McMullen helped prove conjectures that had remained open for decades, such as those related to the density of these groups.
McMullen is also interested in mathematical billiards: imagining a perfect ball bouncing endlessly around a polygonal table. The study of these trajectories reveals surprising links between geometry, dynamics, and number theory.
Primary Sources
McMullen has made important contributions to various branches of the theory of dynamical systems, such as the algorithmic study of polynomial equations, the study of the distribution of the points of a lattice, hyperbolic geometry and holomorphic dynamics.
This book gives a self-contained account of the renormalization theory of quadratic-like maps and its connections with the geometry of the Mandelbrot set and with hyperbolic three-manifolds.
We develop a parallel between the renormalization of dynamical systems and the geometry of hyperbolic 3-manifolds that fiber over the circle.
Key Places
University where McMullen earned his PhD and then became a professor of mathematics from 1998 onward. It is where he carries out most of his research and supervises doctoral theses.
Institution where McMullen completed his undergraduate studies and earned his B.A. in 1980. It was the starting point of his mathematical training.
University where McMullen was a professor in the 1990s, before joining Harvard. A major center of American mathematical research.
Institution where McMullen also taught in the early 1990s, alongside the Institute for Advanced Study, a hub of research in pure mathematics.
Place where, in 1998, McMullen received the Fields Medal before the worldwide mathematical community, which gathers every four years.
