The National Science Foundation (NSF) is proud to announce that 32-year-old Terence Tao, a professor of mathematics at the University of California at Los Angeles, will receive its 2008 Alan T. Waterman Award. Called a "supreme problem-solver," and named one of "the Brilliant 10" scientists by Popular Science (October 2006), Tao's extraordinary work, much of which has been funded by NSF through the years, has had a tremendous impact across several mathematical areas. He will receive the award at a black tie dinner program at the U.S. Department of State on May 6. The annual Waterman award recognizes an outstanding young researcher in any field of science or engineering supported by NSF. Candidates may not be more than 35 years old, or seven years beyond receiving a doctorate, and must stand out for their individual achievements. In addition to a medal, the awardee receives a grant of $500,000 over a 3-year period for scientific research or advanced study in their field. Terence Tao was born in Adelaide, Australia, in 1975. His genius at mathematics began early in life. He started to learn calculus when he was 7 years old, at which age he began high school; by the age of 9 he was already very good at university-level calculus. By the age of 11, he was thriving in international mathematics competitions. Tao was 20 when he earned his doctorate from Princeton University, and he joined UCLA's faculty that year. UCLA promoted him to full professor at age 24. Tao now holds UCLA's James and Carol Collins Chair in the College of Letters and Science. He is also a fellow of the Royal Society and the Australian Academy of Sciences (corresponding member). Nicknamed "the Mozart of Math," Tao's areas of research include partial differential equations (PDE), combinatorics, number theory and harmonic analysis. Harmonic analysis is an advanced form of calculus that uses equations from physics. Some of this work involves, in a colleague's words, "geometrical constructions that almost no one understands." Tao also works in a related field, nonlinear partial differential equations, and in the entirely distinct fields of algebraic geometry, number theory and combinatorics, which involves counting. In addition to the prestigious Waterman award, Tao has received a number of other awards, including the Salem Prize in 2000; the Bochner Prize in 2002; the Fields Medal, often touted as the "Nobel Prize for Mathematics" and SASTRA Ramanujan Prize in 2006; and the MacArthur Fellowship and Ostrowski Prize in 2007. Through the years, Tao's research has often been funded by other NSF grants. His current research is funded by NSF Award #0649473, "Global Behaviour of Critical Nonlinear PDE."

Project Report

WATERMAN AWARD TERENCE TAO The research supported by the Waterman award covers a wide array of subjects in both pure and applied mathematics, which are too nu- merous to describe here in full. Nevertheless, one can point out some common themes in these research topics, such as studying the role of randomness in affecting the outcome of various tasks. For instance, the Netix problem asks to try to predict the movie preferences of a large number of consumers, given a partial database of previous movies rated by these customers; this is an example of a more general math- ematical question known as the matrix completion problem . From a deterministic viewpoint, this problem seems hopeless to solve; there are just too many unknowns and not enough data. But, remarkably, just by fitting a model to from a relatively small random sampling of the data, one can obtain a surprisingly good prediction for the remainder of the preference matrix; one of my research outcomes was to provide an explanation for this phenomenon in terms of the theory of random matrices (and the tting algorithm proposed in this research, known as nuclear norm minimisation , has in fact been used in practice, in particular as part of the winning algorithm for the Netix prize). This theory is in turn connected to a number of other basic questions in pure mathematics, such as those involving random walks . A typical ques- tion here is: if one takes a deck of cards and shuffes it a small number of times, how likely is it that one will return back to the original or- dering of the cards? Intuitively, one expects after a suffcient number of shuffes that the ordering should become completely random, but some shuffing methods are more rapidly "mixing" than others. I have devoted a number of research papers to studying mixing properties of various types of operations, which involves a number of branches of mathematics including ergodic theory, group theory , and the theory of new insight as to the mixing properties of the prime numbers, leading for instance into a quite precise description of the prevalence of certain types of patterns (such as arithmetic progressions) inside the prime numbers. Another theme in my research is the nature of universality . It is a remarkable phenomenon of nature that many completely unrelated, and quite complicated, processes, end up being governed by the same universal mathematical law. One example of this is the central limit theorem, which informally speaking asserts that a single distribution (popularly known as the bell curve ) governs any statistic that is in- uenced by a large number of small but independent random factors; this law governs statistics as diverse as the height distribution of adult males and the number of car crashes nationally in a given day. A dif- ferent type of universal law (known as the Dyson sine process ) appears to govern a large number of spectral distributions, ranging from the en- ergy levels of atomic nuclei to the arrival times of buses to the zeroes of a number-theoretic object called the Riemann zeta function . The pre- cise explanation for this universality phenomenon is not yet understood in general, but I have been part of recent (and still ongoing) research developments that have rigorously established and clari ed the reason for this universality for at least one type of mathematical model, which are called the Wigner random matrix models . One of the emerging explanations for universality appears to be that random-like behaviour is ubiquitious in large systems; unless one's initial con guration is in an exceptionally structured state to begin with, it will naturally tend to a universal (and randomly distributed) limiting state if one evolves it in a suffciently "mixing" fashion. This phenomenon is still poorly understood in general, but my research has managed to describe it in at least some model cases. expander graphs. One of the outcomes of this line of research was some

National Science Foundation (NSF)
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Bruce P. Palka
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University of California Los Angeles
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