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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 Cominatorics, Dec 19-22, at SASTRA University in
Kumbakonam, India, Ramanujan's hometown.
Professor Tao has made
path-breaking contributions in number theory,
harmonic analysis, representation theory, and partial differental
equations. His work has had major impact in combinatorics and
ergodic theory as well. In the course of making significant progress
on fundamental long-standing 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 n-dimensional 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 sum-product
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 Erdos-Szemeredi
problem. This "sum-product 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
well-known saturation conjecture in
representation theory. Thus, at
this very young age, 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, regarded as the "NOBLE
PRIZE" for Mathematics. Following that,
Tao was awarded the MacArthur
Fellowship.
"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" said
Professor Krishnaswami Alladi, Chair
of the Prize Committee.
The 2006 SASTRA Prize
Committee consisted of 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).
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