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by Krishnaswami Alladi Chair - 2005 SASTRA Ramanujan Prize Committee On 20 December 2005, the First SASTRA Ramanujan Prizes were awarded at Kumbakonam, India, Ramanujan's home town, to Professors Manjul Bhargava (Princeton) and Kannan Soundararajan (Michigan). Here I describe the goals of the prize, the events leading up to and including the prize ceremony, and the accomplishments of the winners. It was one of the most thrilling moments of my life to be in Kumbakonam, the hometown of the Indian mathematical genius Srinivasa Ramanujan, and participate in a function when the First SASTRA Ramanujan Prizes were awarded to two of the most brilliant young mathematicians for outstanding contributions to areas of mathematics influenced by Ramanujan. In the preface to the first issue of the Ramanujan Journal I said "the very mention of Ramanujan's name reminds us of the thrill of mathematical discovery". Ramanujan is an inspiration for mathematical aspirants and researchers the world over and a role model and idol for all in India where he is a household name. There can be no better way to commemorate Ramanujan than to award these prizes for exceptional mathematical creativity at a very young age. SASTRA University under the leadership of Vice Chancellor Prof. R. Sethuraman has made laudable efforts in fostering the legacy of Ramanujan and supporting mathematical research by first purchasing Ramanujan's home in 2003 and maintaining it as a museum, by conducting annual international conferences in areas of mathematics influenced by Ramanujan and by launching the Ramanujan Commemoration Lectures, which are talks of wide appeal delivered by very eminent mathematicians annually on December 22, Ramanujan's birthday. Their latest step is the creation of the SASTRA Ramanujan Prize which is one of the finest ways to recognise path breaking contributions to mathematics, and SASTRA has to be congratulated for this. The age limit for the prize was set at thirty two in order to recognise doctoral and post-doctoral research, and also because Ramanujan achieved so much in his brief life of thirty two years. This age limit might appear to be too severe a restriction, but it is not so, because in mathematics, more so than in other fields, path breaking work is often done by very young researchers. If one looks at the lives of outstanding mathematicians, one notices in a vast majority of cases, that their very best work was done in their youth. This is not to say that they did not continue to do influential work in later years. Mathematics is as much an art as it is a science, and it is a subject in which one explores the structures, the symmetries and the inter relationships for their intrinsic beauty. Youthful minds are capable of taking fantastic leaps of imagination. The decision to create the prize was made during a discussion I had with the Vice-Chancellor during the International Conference on Fourier Analysis and Number Theory at SASTRA University, Kumbakonam, in December 2004, which I had the pleasure of inaugurating. The Vice-Chancellor announced that this annual prize of $10,000 will be first awarded at the International Conference on Number Theory and Mathematical Physics at SASTRA's Srinivasa Ramanujan Centre in Kumbakonam in December 2005. I was invited by SASTRA to form and head the 2005 Prize Committee. In forming the committee the desire was to assemble a group of very eminent and experienced mathematicians from different countries to reflect a truly international character, and whose research expertise would broadly span several areas of mathematics influenced by Ramanujan. The 2005 SASTRA Ramanujan Prize Committee consisted of Krishnaswami Alladi, Chair (University of Florida), Mahindra Agarwal (IIT, Kanpur), George Andrews (Pennsylvania State University), Jean-Marc Deshouillers (University of Bordeaux), Tom Koornwinder (University of Amsterdam), James Lepowsky (Rutgers University) and Don Zagier (Max Planck Institute, Bonn, and College de France). The Committee was pleased to receive several excellent nominations of brilliant young mathematicians from around the world supported by leaders in the field. It turned out that two candidates of Indian origin emerged as the best in this international competition - Manjul Bhargava of Princeton University and Kannan Soundararajan of the University of Michigan. The decision was to award prizes to both Bhargava and Soundararajan whose areas of research are algebraic number theory and analytic number theory, respectively. Thus the prizes recognized seminal research in two of the main branches of number theory. The SASTRA Ramanujan Prizes of $10,000 each were awarded to Bhargava and Soundararajan on 20 December, 2005 during the inauguration of the International Conference on Number Theory and Mathematical Physics at Kumbakonam by Dr.Aurobindo Mitra, Executive Director of the Indo-US Forum for Science and Technology, which provided significant support for the conference. In handing out the prizes, Dr. Mitra described many new research programs supported by the Indo-US Forum. The opening lecture of the conference was a talk by Soundararajan on "Large character sums: the Polya-Vinogradov theorem". The conference concluded with the Ramanujan Commemoration Lecture by Bhargava in which he announced his most recent spectacular result (joint with Jonathan Hanke), namely, the complete determination of all universal quadratic forms, thereby solving a problem which has its origins in Ramanujan's work. It was fitting that Bhargava announced this on Ramanujan's birthday (December 22) in Ramanujan's hometown! I interviewed Bhargava and wrote a report of his lecture which appeared in The Hindu, India's National Newspaper, the next day: http://www.hindu.com/2005/12/23/stories/2005122306251400.htm I will now describe briefly the career highlights and research accomplishments of Bhargava and Soundararajan. Manjul Bhargava was an undergraduate at Harvard University from where he graduated with highest honours (summa cum laude) in mathematics in 1996. He was Harvard University Salutatorian and won the Hoopes Prize for excellence in scholarly work and research at Harvard in 1996. He was also awarded the Frank and Brennie Morgan Prize of the American Mathematical Society for undergraduate research in 1996. He then went on to do his Ph.D at Princeton University under the direction of Prof. Andrew Wiles of Fermat's Last Theorem fame. Bhargava wrote a phenomenal Ph.D thesis in Princeton in 2001 in which he described his discovery of higher order composition laws. His thesis was published as a series of four papers in Annals of Mathematics, one of the most exclusive mathematics journals. Gauss, the Prince of Mathematicians, had constructed a composition law from binary quadratic forms. Bhargava introduced entirely new and unexpected ideas that led to his discovery of such composition laws for forms of higher degree. Bhargava then applied these composition laws to solve a new case of one of the fundamental questions of number theory, that of the asymptotic enumeration of number fields of a given degree. The question is the trivial for d = 1, and Gauss himself solved the case d = 2 in 1801. Then in 1971 Davenport and Heilbronn solved the case for d = 3. Bhargava has solved the d = 4 and d = 5 cases which previously had resisted all attempts. Bhargava also applied his work to make significant progress on the problem of finding the average size of ideal class groups and the related conjectures of Cohen and Lenstra. Bhargava's research has created a whole new area of research in a classical topic that has seen a very little activity since the time of Gauss. Naturally, Bhargava received several recognitions for work of such great significance. After his Ph.D, he was appointed Long Term Prize Fellow at the CLAY Mathematics Institute. It is the CLAY Institute which has created the Millennium Prizes of $1 million each for seven of the most outstanding problems in mathematics. For his revolutionary Ph.D work Bhargava was awarded the Blumenthal Prize of the American Mathematical Society in January 2005. In early December 2005 he received the Clay Prize at a ceremony at Oxford University. Bhargava was appointed Full Professor at Princeton University at the age of 28 and is the youngest to hold that high rank in that prestigious institution.
Kannan Soundararajan's first publications were three papers that appeared in 1992 based on work that he did a few years prior to that while he was a student at Padma Seshadri High School in Nungambakkam in Madras. In one of those papers that appeared in the Journal of Number Theory, he improved an inequality on multiplicative functions that I had proved in collaboration with Paul Erdös, one of the legends of twentieth century mathematics, and Jeff Vaaler. Soundararajan joined the University of Michigan, Ann Arbor, in 1991 for undergraduate studies, and graduated with highest honours in 1995. He has made brilliant contributions to several areas of analytic number theory, that include multiplicative number theory, the Riemann zeta function and Dirichlet L-functions, and more recently with the analytic theory of automorphic forms and the Katz-Sarnak theory of symmetric groups associated with automorphic forms. As an undergraduate at the University of Michigan, Soundararajan made two significant contributions. First in joint work with R. Balasubramanian, he proved a famous conjecture of Ron Graham in combinatorial number theory. Next he obtained fundamental results on the distribution of zeros of the Riemann zeta function. For his undergraduate research he was awarded the Morgan Prize of the American Mathematical Society in 1995, the very first year this prize was instituted. Soundararajan then joined Princeton University in 1995 to do his Ph.D under the guidance of Professor Peter Sarnak, one of the foremost number theorists in the world today. In his Ph.D thesis, Soundararajan proved the spectacular result that more than seven-eighths of the quadratic L-functions have zeros at the critical point s = ½. A part of his Ph.D thesis is published in the Annals of Mathematics. More recently, in a paper with Brian Conrey in Inventiones Mathematicae, Soundararajan proved that a positive proportion of Dirichlet L-functions have no zeros on the real axis within the critical strip. In another paper with Ken Ono, also in Inventiones, he proved assuming the generalized Riemann hypothesis, a certain conjecture of Ramanujan on ternary quadratic forms. Soundararajan is also a leading expert on random matrix theory. His recent work with Hugh Montgomery shows that prime numbers are distributed normally but with a variance that is surprisingly different from classical heuristics. Soundararajan has received numerous awards and recognitions starting with the Silver Medal in the 1991 International Mathematics Olympiad. As a graduate student at Princeton, he held a prestigious Sloan Foundation Fellowship. For his outstanding contributions to analytic number theory, he was awarded the Salem Prize in 2003. Shortly after his Ph.D he was awarded a Five Year American Institute of Mathematics (AIM) Fellowship, the very first year the fellowship was launched. Soundararajan is currently a Full Professor at the Mathematics Department, University of Michigan, Ann Arbor. Bhargava and Soundararajan have several things in common. Both received the Morgan Prize of the American Mathematical Society for undergraduate research. Both received their Ph.Ds from Princeton University. And now, both have received the SASTRA Ramanujan Prizes. By awarding this prize to these two brilliant young mathematicians, an exceptionally high standard has been set in the true spirit of Ramanujan.
Department of Mathematics University of Florida Gainesville, FL 32611, USA Dec 25, 2005
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