TERENCE TAO TO RECEIVE
2006 SASTRA RAMANUJAN PRIZE
The 2006 SASTRA Ramanujan Prize will be awarded to
Professor Terence Tao of the University of California
at Los Angeles (UCLA). This annual prize, which was
launched in 2005, is for outstanding contributions to
areas of mathematics influenced by the genius Srinivasa
Ramanujan. The age limit for the prize has been set at 32
because Ramanujan achieved so much in his brief life of 32
years. The $10,000 prize will be awarded at the International
Conference on Number Theory and Combinatorics, Dec 1922,
at SASTRA University in Kumbakonam, India, Ramanujan's hometown.
Professor Tao has made pathbreaking contributions in number theory,
harmonic analysis, representation theory, and partial differential
equations. His work has had major impact in combinatorics and
ergodic theory as well. In the course of making significant progress
on fundamental longstanding problems in these different areas,
Tao has collaborated with a wide range of mathematicians.
One of Tao's most notable contributions is to the famous Kakeya
Problem in higher dimensions, which has major applications in
Fourier analysis and partial differential equations. One important
aspect of the problem is to determine the fractal dimension of
the set generated by rotating a needle in ndimensional space.
In joint work with Nets Katz, Izabella Laba and others, Tao
significantly improved all previously known estimates for the
fractal dimension using new and surprisingly simple combinatorial
ideas in an ingenious way.
Another of Tao's outstanding contributions is his joint work with
Ben Green on long arithmetic progressions of prime numbers. One of
the deepest results in this area is a theorem of the Hungarian
mathematician Szemeredi which asserts that any set of positive
integers which has positive density will have arbitrarily long
arithmetic progressions. Another proof of Szemeredi's theorem
using very different ideas was given by 1998 Fields Medallist
Timothy Gowers. Szemeredi's theorem does not apply to the primes
which, due to their spareseness, have density zero. Nevertheless
it was conjectured that there are arbitrarily long arithmetic
progressions of prime numbers and this was proved by Tao and Green
by combining methods of ergodic theory with the ideas of Gowers.
Yet another fundamental contribution of Tao concerns the sumproduct
problem which is due to the late Paul Erdos, one of the greatest
mathematicians of the twentieth century, and his brilliant protege
Szemeredi. Roughly speaking, this problem of Erdos and Szemeredi
states that either the sumset or the product set of any set of
N numbers must be large. Tao was the first to recognize the significance
of this problem in combinatorial number theory and harmonic analysis.
In collaboration with 1994 Fields Medallist Jean Bourgain and
Nets Katz, Tao made important generalizations and refinements of
the original ErdosSzemeredi problem. This "sumproduct theory" has
become one of the key ingredients in many recent breakthroughs in harmonic
analysis and number theory.
Tao's work has also provided a fresh look at on the properties of wave maps
which occur naturally in Einstein's theory of general relativity.
In other contributions that have major impact in physics, Tao and
collaborators have provided new insights in the theory of Schroedinger
equations, which for example, are used to describe the behaviour of
light in an optical cable. Finally, in collaboration with Allen
Knutson, Tao solved the wellknown saturation conjecture in
representation theory. Thus, at this very young age of 31, Tao is
one of the most versatile mathematicians of our generation.
Tao was born in Adelaide, Australia in 1975 and lived there until
1992. He did his BSc (Honours) and MSc at Flinders University of
South Australia. He then went to Princeton University in 1992 for his PhD,
which he completed in 1996 under the direction of Professor Elias
Stein. He received a Sloan Dissertation Fellowship for the final year
of his PhD work. He is currently professor at the University of
California in Los Angeles.
Honours have come in a steady stream to Tao in the past few years.
For his fundamental work in analysis, he was the recipient of the
Salem Prize in 2000. He also received the Bocher Prize of the
American Mathematical Society (AMS) in 2002, and the AMS Conant Prize
in 2005. And in August 2006, at the International Congress of
Mathematicians in Madrid, Tao was awarded the prestigious Fields
Medal. Following that, Tao was awarded the MacArthur Fellowship.
Tao emerged as the top choice for the SASTRA Prize from a pool of
brilliant young mathematicians from around the world. The international
panel of experts who formed 2006 SASTRA Ramanujan Prize Committee are:
Chair  Krishnaswami Alladi (University of Florida), George Andrews
(The Pennsylvania State University), Manjul Bhargava (Princeton University),
James Lepowsky (Rutgers University), Tom Koornwinder (University of
Amsterdam), Kannan Soundararajan (University of Michigan and
Stanford University), and Michel Waldschmidt (University of Paris).
By awarding the first SASTRA Ramanujan Prizes to Manjul Bhargava
and Kannan Soundararajan in 2005, an exceptionally high standard
was set. This is now continued with the award of the 2006 SASTRA
Prize to Terence Tao.
Krishnaswami Alladi
Chair, 2006 SASTRA Ramanujan Prize Committee
OTHER LINKS

Alladi's article
in The Hindu, India's National
Newspaper, on Tao's SASTRA Prize Lecture.

Photos
of the 2006 SASTRA Prize Ceremony at
the
Int'l Conf on Number Theory and Combinatorics
in Kumbakonam, Ramanujan's hometown.
University of Florida *
Mathematics
