image: Lennart Carleson, 2006 Abel Prize winner view more
Credit: The Abel Prize/The Norwegian Academy of Science and Letters
King Harald of Norway will present the Abel Prize to Lennart Carleson at an award ceremony in Oslo 23 May.
Carleson's mathematical work: Harmonic analysis and dynamical systems
Harmonic analysis
Harmonic analysis is a vast extension of the mathematics underlying ordinary calculus. It has applications to real world phenomena ranging from the firing of neurons in the brain to quantum computers, and is based on concepts students see in trigonometry. Many phenomena, ranging from the vibrations of violin strings to the propagation of heat through a metal bar, can be viewed as sums of the simple wave patterns called sines and cosines. Such summations are now called Fourier series. One of Carleson's many triumphs was settling a conjecture that had remained unsolved for over 150 years. He showed that every continuous function (one with a connected graph) is equal to the sum of its Fourier series except perhaps at some negligible points. (He actually proved a more general result, that a broader class of functions, called square-integrable, equal the sum of their Fourier series except perhaps at those points.)
Dynamical Systems
Dynamical systems are mathematical models that seek to describe the behavior of large classes of phenomena, such as those observed in weather, financial markets, and many biological systems, from fluctuations in fish populations to epidemiology. Even the simplest dynamical systems can be surprisingly complex. With Michael Benedicks, Carleson studied a dynamical system first proposed in 1976 by the astronomer Michel Hénon, which exhibits the intricacies of weather dynamics and turbulence. This system was generally believed to have a so-called strange attractor, drawn in beautiful detail by computer graphics tools, but poorly understood mathematically. In a great tour de force, Benedicks and Carleson provided the first proof of the existence of this strange attractor in 1991, which has opened the way to a systematic study of this class of dynamical systems.
Biography of Lennart Carleson
Born March 18, 1928 in Stockholm, Carleson received his PhD from Uppsala University in 1950. He was director of the Mittag-Leffler Institute (Stockholm) from 1968 to 1984, building it into one of the prestigious research centers in the world, and was president of the International Mathematical Union (IMU) from 1978 to 1982. During his term as president, he succeeded in getting the People's Republic of China represented in the IMU and was instrumental in the creation of the Nevanlinna Prize, which rewards young computer scientists.
The Abel Prize
The Niels Henrik Abel Memorial Fund, established in 2002, awards the Abel Prize for outstanding scientific work in the field of mathematics. The Norwegian Academy of Science and Letters appoints an international Abel Prize Committee to select a laureate from among the nominees and administers the annual award of nearly 6 million Norwegian Kroner (currently about $910,000). Previous Abel winners are Jean-Pierre Serre (2003), Isadore M. Singer and Sir Michael Atiyah (2004), and Peter Lax (2005). See www.abelprisen.no.
Lennart Carleson
Telephone: + 46 8 512 41588
E-mail: carleson@math.kth.se
Abel Prize Committee Member:
Prof. Ingrid Daubechies
Princeton University
Department of Mathematics
Phone: (609) 258-2262
Email: ingrid@math.princeton.edu
Also:
Prof. James Arthur, President of the American Mathematical Society
University of Toronto
Phone: Home: 416-967-0975, 416-978-4524
Email: arthur@math.toronto.edu
Prof. James Glimm, President-Elect of the American Mathematical Society
SUNY at Stony Brook
Phone: Office: 631-344-8155, or 631-632-8355
Email: glimm@ams.sunysb.edu