The 2016 SASTRA Ramanujan prize, for outstanding contributions by young mathematicians to areas influenced by the genius Srinivasa Ramanujan, will be jointly awarded to Kaisa Matomaki of University of Turku, Finland and Maksym Radziwill of McGill University, Canada.

The SASTRA Ramanujan Prize was established in 2005 and is awarded annually for outstanding contributions by young mathematicians to areas influenced by 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 prize will be awarded during December 21-22, 2016, at the International Conference on Number Theory at SASTRA University in Kumbakonam (Ramanujan’s hometown) where the prize has been given annually.

The 2015 SASTRA Ramanujan Prize will be awarded to Dr. Jacob Tsimerman of the University of Toronto, Canada. The SASTRA Ramanujan Prize was established in 2005 and is awarded annually for outstanding contributions by young mathematicians to areas 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 prize will be awarded during December 21-22, 2015 at the International Conference on Number Theory at SASTRA University in Kumbakonam (Ramanujan's hometown) where the prize has been given annually.

The 2014 SASTRA Ramanujan Prize will be awarded to Dr. James Maynard of Oxford University, England, and the University of Montreal, Canada. The SASTRA Ramanujan Prize was established in 2005 and is awarded annually for outstanding contributions by young mathematicians to areas 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 prize will be awarded on Ramanujan's birthday, December 22, 2014 at SASTRA University in Kumbakonam as is the usual practice every year. Maynard will receive the cash award of USD 10,000 along with a citation and will deliver the Ramanujan Birthday Commemorative Lecture.

Dr.Maynard received his PhD from Oxford University two years ago, is currently a post-doc at the University of Montreal, Canada and still holds a position at Oxford. In the last two years he has obtained spectacular results in prime number theory, especially on the small gaps problem. Just within the last few weeks he solved the famous problem of Paul Erdos on large gaps between primes. Thus he has taken the world of number theory by storm. He is only 27 and the SASTRA-Ramanujan Award will be his first major prize to recognize his great work.

The 2014 SASTRA Ramanujan Prize Committee consisted of Professors Krishnaswami Alladi - Chair (University of Florida), Roger Heath-Brown (Oxford University), Winnie Li (The Pennsylvania State University), David Masser (University of Basel), Barry Mazur (Harvard University), Peter Paule (Johannes Kepler University of Linz), and Michael Rapoport (University of Bonn). Previous winners of the Prize are Manjul Bhargava and Kannan Soundararajan in 2005 (two full prizes), Terence Tao in 2006, Ben Green in 2007, Akshay Venkatesh in 2008, Kathrin Bringmann in 2009, Wei Zhang in 2010, Roman Holowinsky in 2011, Zhiwei Yun in 2012, and Peter Scholze in 2013. The award of the 2014 SASTRA Ramanujan Prize to James Maynard is a fitting recognition in the tenth year of this prize and in keeping with the tradition of recognizing path-breaking work by young mathematicians.

The 2013 SASTRA Ramanujan Prize will be awarded to Professor Peter Scholze of the University of Bonn, Germany. This annual prize of $10,000 established in 2005 by SASTRA University is for very young mathematicians for outstanding contributions to areas influenced by 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 2013 prize will be awarded during Dec 21-22 at the International Conference on Number Theory and Galois Representations at SASTRA University in Kumbakonam, Ramanujan's hometown. "Professor Scholze who will turn 26 in December, is the youngest full professor in Germany and the youngest recipient of the SASTRA Ramanujan Prize as well" said Krishnaswami Alladi, Chair of the Prize Committee.

Professor Scholze has made revolutionary contributions to several domains at the interface of Arithmetic Algebraic Geometry and the Theory of Automorphic Forms, and especially in the area of Galois Representations. Already in his Masters Thesis he gave new proofs of the Local Langland Conjecture for p-adic local fields and for general linear groups as well. His approach was strikingly different and much simpler compared to earlier approaches, yet even more efficient. This fundamental work done in 2010 appeared in two papers in the prestigious journal Inventiones Mathematicae in 2013.

While his Masters thesis was groundbreaking, his PhD thesis written under the direction of Professor Michael Rapoport at the University of Bonn was a more marvellous breakthrough and a step up in terms of originality and insight. In his thesis he developed a new p-adic machine called Perfectoid Spaces and used it to prove brilliantly a significant part of the weight monodromy conjecture due to 1978 Fields Medalist Pierre Deligne, thereby breaking an impasse of more than 30 years. He then developed his theory of perfectoid spaces to make advances of other important problems that had resisted solution, such as a problem on spectral sequences that 2010 Abel Prize winner John Tate had raised four decades earlier. Work in his PhD thesis appeared in a massive paper in the publications of the IHES in 2012.

Professor Scholze's most recent work is on Galois representations which in particular has startling implications on the cohomology of locally symmetric spaces. This work again represents the first great progress on certain questions in 40 years.

Peter Scholze was born in Dresden in December 1987 - at the time of the Ramanujan Centennial. Barely over the age of 25 now, he is already one of the most influential mathematicians in the world.
His work has been estimated by the greatest experts to possess the quality of the timeless classics and expected to have a major impact in the progress of mathematics in the coming decades.

The 2013 SASTRA Ramanujan Prize Committee consisted of Professors Krishnaswami Alladi - Chair (University of Florida), Kathrin Bringmann (University of Cologne), Roger Heath-Brown (Oxford University), David Masser (University of Basel), Barry Mazur (Harvard University), Ken Ribet (University of California, Berkeley), and Ole Warnaar (University of Queensland).

The 2012 SASTRA Ramanujan Prize will be awarded to Professor Zhiwei Yun, who has just completed a C. L. E. Moore Instructorship at the Massachusetts Institute of Technology and will be taking up a faculty position at Stanford University in California this fall. The SASTRA Ramanujan Prize was established in 2005 and is awarded annually for outstanding contributions by very young mathematicians to areas 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. Because 2012 is the 125th anniversary of the birth of Srinivasa Ramanujan, the prize will be given in New Delhi (India’s capital) on December 22 (Ramanujan’s birthday), during the concluding ceremony of the International Conference on the Legacy of Ramanujan conducted by the National Board of Higher Mathematics of India and co-sponsored by SASTRA University and Delhi University. Dr. Yun will also be invited to speak at the International Conference during December 14–16 at SASTRA University in Kumbakonam (Ramanujan’s hometown) where the prize has been given annually in previous years.

Dr. Zhiwei Yun has made fundamental contributions to several areas that lie at the interface of representation theory, algebraic geometry and number theory.

Yun’s PhD thesis on global Springer theory at Princeton University, written under the direction of Professor Robert MacPherson of The Institute for Advanced Study, is opening up whole new vistas in the Langlands program, which represents one of the greatest developments in mathematics in the last half-century. Springer theory is the study of Weyl group actions on the cohomology of certain subvarieties of the flag manifold called Springer fibers. Yun’s global Springer theory deals with Hitchin fibers instead of Springer fibers (taking the lead from earlier work on Hitchin fibers by G´erard Laumon and the 2010 Fields Medalist Bao-Chˆau Ngˆo) which he uses to determine the actions of affine Weyl groups on cohomolgy. His work is expected to lead to a geometric and functorial understanding of the Langlands program. Many papers by him on global Springer theory have arisen from his PhD thesis; one has appeared in 2011 in Advances in Mathematics and another will soon appear in Compositio Mathematica.

Bao-Chau Ngˆo was awarded the 2010 Fields Medal for his proof of the Fundamental Lemma in the Langlands Program. Yun has made a major breakthrough in the study of the Fundamental Lemma formulated by Jacquet and Rallis in their program of proving the Gross–Prasad conjecture on relative trace formulas. Yun’s understanding of Hitchin fibrations enabled him to reduce the Jacquet–Rallis fundamental lemma to a cohomological property of the Hitchin fibration. This work, considered a gem of mathematics, appeared in 2011 in the Duke Mathematical Journal.

Yun has collaborated with Ngˆo and Jochen Heinloth on a seminal paper on Klooster- man sheaves for reductive groups which will appear in the Annals of Mathematics. In this wonderful joint paper, Ngˆo, Heinloth and Yun reprove a unicity result of Gross on auto- morphic representations over the rational function field, and use the geometric Langlands theory to the construction of l-adic local systems.

Yun has also done significant work in algebraic geometry. His recent article with Davesh Maulik on the Macdonald formula for curves with planar singularities will appear in The Journal fu¨r die Reine und Angewandte Mathematik. Yun’s most recent work on the uniform construction of motives with exceptional Galois groups is considered to be a fundamental breakthrough. A construction like Yun’s was sought by Fields Medalists Serre and Grothendieck for over 40 years, and Yun’s work is considered one of the most exciting developments in the theory of motives in the last two decades.

Zhiwei Yun was born in Changzhou, China in 1982. He showed his flair for mathemat- ics early by winning the Gold Medal in the 41st Mathematical Olympiad in 2000 in Korea. He joined Peking University in 2000 on a Ming-De Fellowship and obtained a bachelor’s degree there in 2004. He continued his studies at Princeton University, where he received his PhD in 2009. He was Visiting Member at the Institute for Advanced Study in 2009–10, and held the C.L. E. Moore instructorship at MIT during 2010–12. In fall 2012, he will join the mathematics faculty at Stanford University. At the age of 30, he has established himself as one of the young leaders of modern mathematics.

The international panel of experts who formed the 2012 Prize Committee were: Krish- naswami Alladi (chair), University of Florida; Frits Beukers, University of Utrecht; Kathrin Bringmann, University of Cologne; Benedict Gross, Harvard University; Kenneth Ribet, University of California, Berkeley; Robert Vaughan, The Pennsylvania State University; Ole Warnaar, University of Melbourne.

Previous winners of the SASTRA Ramanujan Prize include Manjul Bhargava and Kannan Soundararajan in 2005 (two full prizes), Terence Tao in 2006, Ben Green in 2007, Akshay Venkatesh in 2008, Kathrin Bringmann in 2009, Wei Zhang in 2010 and Roman Holowinsky in 2011. Thus Zhiwei Yun joins an impressive list of brilliant mathematicians who have made monumental contributions at a very young age.

The 2011 SASTRA Ramanujan Prize was awarded to Roman Holowinsky, who is now an Assistant Professor at the Department of Mathematics, Ohio State University, Columbus, Ohio, USA. This annual prize which was established in 2005, is for outstanding contributions by very young mathematicians to areas 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, Ergodic Theory and Dynamics at SASTRA University in Kumbakonam, India (Ramanujan's hometown) on December 22, Ramanujan's birthday.

Dr. Roman Holowinsky has made very significant contributions to areas which are at the interface of analytic number theory and the theory of modular forms. Along with Professor Kannan Soundararajan of Stanford University (winner of the SASTRA Ramanujan Prize in 2005), Dr. Holowinsky solved an important case of the famous Quantum Unique Ergodicity (QUE) Conjecture in 2008. This is a spectacular achievement.

In 1991, Zeev Rudnick and Peter Sarnak formulated the QUE Conjecture which in its general form concerns the correspondence principle for quantizations of chaotic systems. One aspect of the problem is to understand how waves are influenced by the geometry of their enclosure. Rudnick and Sarnak conjectured that for sufficiently chaotic systems, if the surface has negative curvature, then the high frequency quantum wave functions are uniformly distributed within the domain. The modular domain in number theory is one of the most important examples, and for this case, Holowinsky and Soundararajan solved the holomorphic QUE conjecture.

The manner in which this solution came about is amazing. Since 1991, many mathematicians had attacked this problem and made major advances. Luo and Sarnak reduced the problem to obtaining good estimates for certain shifted convolution sums. Elon Lindenstrauss proved the QUE conjecture for Maass forms, but the problem for holomorphic domains remained open. By a study of Hecke eigen values and an ingenious application of the sieve, Dr. Holowinsky obtained critical estimates for shifted convolution sums and this almost settled the QUE conjecture except in certain cases where the corresponding $L$-functions behave abnormally. Simultaneously, Soundararajan who approached the problem from an entirely different direction, and was able to confirm the conjecture in several cases, noticed that the exceptional cases not fitting Holowinsky's approach, were covered by his techniques. Thus by combining the approaches of Holowinsky and Soundararajan, the holomorphic QUE Conjecture was fully resolved in the modular case. The joint work of Holowinsky and Soundararajan appeared in the Annals of Mathematics (2010), and the two papers of Holowinsky on "A sieve method for shifted convolution sums" and "Sieving for mass equidistribution" appeared in the Duke Mathematical Journal (2009), and Annals of Mathematics (2010), respectively.

The QUE Conjecture and its resolution in the modular case is a fine example great mathematical work inspired by a problem in physics. The QUE Conjecture has connections with several important areas within mathematics - the Generalized Riemann Hypothesis, Poincare series, Maass forms, cusp forms, the Sato-Tate conjecture - to name a few. Dr. Holowinsky has been pursuing some of these connections in depth. In another paper that appeared in Inventiones Mathematicae (2010), Holowinsky with Valentin Blomer obtain bounds for sup norms of Maass cusp forms of large level.

Roman Holowinsky was born on July 26, 1979. He obtained a Bachelors in Science Degree from Rutgers University in 2001. He continued at Rutgers to do his doctorate and received his PhD in 2006 under the direction of Professor Henryk Iwaniec. Already in his PhD thesis entitled "Shifted convolution sums and Quantum Unique Ergodicity" he made major advances towards the QUE Conjecture. He held post-doctoral visiting positions at the Institute for Advanced Study, Princeton (2006-07), and (2009-10), the Fields Institute, Toronto (2008), the University of Toronto (2007-09), and before joining the permanent faculty at Ohio State University. At the young age of 32, Dr. Holowinsky is a major figure in the fields of analytic number theory and the theory of modular forms. His resolution of the QUE Conjecture in the modular case with Soundararajan, and his own work on shifted convolution sums is a spectacular achievement of lasting value. In recognition of this, he was awarded the prestigious Alfred P. Sloan Foundation Fellowship in 2011.

Roman Holowinsky was the unanimous choice of the SASTRA Ramanujan Prize Committee to receive the award this year. The international panel of experts who formed the 2011 Committee were: Chair - Krishnaswami Alladi (University of Florida), Frits Beukers (University of Utrecht), Benedict Gross (Harvard University), Christian Krattenthaler (University of Vienna), Ken Ono (Emory University), Robert Vaughan (The Pennsylvania State University), and Akshay Venkatesh (Stanford University).

Krishnaswami Alladi

Chair, 2011 SASTRA Ramanujan Prize Committee

The 2010 SASTRA Ramanujan Prize will be awarded to Wei Zhang, who is now a Benjamin Pierce Instructor at the Department of Mathematics, Harvard University, USA. This annual prize which was established in 2005, is for outstanding contributions by very young mathematicians to areas 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 id="mce_marker"0,000 prize will be awarded at the International Conference on Number Theory and Automorphic Forms at SASTRA University in Kumbakonam, India (Ramanujan's hometown) on December 22, Ramanujan's birthday.

Dr. Wei Zhang has made far reaching contributions by himself and in collaboration with others to a broad range of areas in mathematics including number theory, automorphic forms, L-functions, trace formulas, representation theory and algebraic geometry. We highlight some of his path-breaking contributions: In 1997, Steve Kudla constructed a family of cycles on Shimura varieties and conjectured that their generating functions are actually Siegel modular forms. The proof of this conjecture for Kudla cycles of codimension 1 is a major theorem of the Fields Medalist Borcherds. In his PhD thesis, written under the direction of Professor Shou Wu Zhang at Columbia University, New York, Wei Zhang established conditionally, among other things, a generalization of the results of Borcherds to higher dimensions, and in that process essentially settled the Kudla conjecture. His thesis, written when he was just a second year graduate student, also extended earlier fundamental work of Hirzebruch-Zagier and of Gross-Kohnen-Zagier. The thesis opened up major lines of research and led to significant collaboration with Xinyi Yuan and his PhD advisor Shouwu Zhang. In the first of a series of joint papers (published in Compositio in 2009), the results of Wei Zhang's important thesis are generalized to totally real fields.

In a paper on heights of CM points in Shimura varieties, Wei Zhang along with Shou Wu Zhang and Xinyi Yuan establish an arithmetic analogue of a theorem of Waldspurger that connects integral periods to special values of L-functions. This paper which goes well beyond all earlier work on formulas of Gross-Zagier type will appear in the book series Annals of Mathematical Studies, Princeton.

Yet another outstanding contribution of Wei Zhang is conveyed in his two recent preprints - one on relative trace formulas and the Gross--Prasad conjecture and another on arithmetic fundamental lemmas. In these works he has made decisive progress on certain general conjectures related to the arithmetic intersection of Shimura varieties; in that process he has successfully transposed major techniques due to Jacquet and Rallis into an arithmetic intersection theory setting. With these two preprints and his seminal earlier work, Dr. Wei Zhang has emerged as a worldwide leader in his field.

Wei Zhang who hails from the People's Republic of China, was born on July 18, 1981. After obtaining a Bachelor's degree from Beijing University in 2004, he joined Columbia University to do his PhD. Even as a first year graduate student, while attending the NSF Focused Group Workshop at the University of Maryland in 2005, when he heard about the Kudla Conjecture, he started pursuing it. In just one year, he not only understood the conjecture, but also found an ingenious proof. Thus he shot to prominence very rapidly. After completing his PhD in 2009 at Columbia University under the supervision of Professor Shou Wu Zhang, he went to Harvard University where he was a Post-Doctoral Fellow in 2009-10, and currently holds the prestigious Benjamin Pierce Lectureship. At this very young age of 29, Dr. Zhang has made a profound influence in a wide range of areas in mathematics.

Wei Zhang was the unanimous choice of the SASTRA Ramanujan Prize Committee to receive the award this year. The international panel of experts who formed the 2010 Committee were: Chair - Krishnaswami Alladi (University of Florida), Dorian Goldfeld (Columbia University), Christian Krattenthaler (University of Vienna), Ken Ono (Emory University), Wolfgang Schmidt (University of Colorado), Jeffrey Vaaler (University of Texas, Austin), and Akshay Venkatesh (Stanford University).

Krishnaswami Alladi

Chair, 2010 SASTRA Ramanujan Prize Committee

The 2009 SASTRA Ramanujan Prize will be awarded to Professor KATHRIN BRINGMANN of the University of Cologne, Germany and the University of Minnesota, USA. This annual prize, which was established in 2005, is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan (1887-1920). 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 on Dec 22, 2009, during an International Conference on Number Theory at SASTRA University in Kumbakonam, India, Ramanujan's hometown.

Professor Bringmann has done revolutionary work in the areas of modular forms and mock theta functions by herself and in collaboration with several mathematicians. Mock theta functions were discovered by Ramanujan shortly before he died and he communicated his findings in his last letter to G. H. Hardy of Cambridge University. These are now considered to be among Ramanujan's deepest contributions. Mock theta functions are like theta functions in the sense that their coefficients can be evaluated very accurately like those of the theta functions. Ramanujan found transformation formulas for certain classes of mock theta functions. Yet, the exact connections between mock theta functions and theta functions has remained a mystery all these years until recently. Indeed the great physicist and mathematician Freeman Dyson of the Institute for Advanced Study said that the mock theta functions provide tantalizing hints of a grand synthesis still to be discovered and that this is a challenge for the future. The first breakthrough came in the 2003 PhD thesis of Sander Zwegers written under the direction of Professor Don Zagier in Bonn, in which Zwegers used certain identities of George Andrews to rewrite mock theta functions in terms of Lambert series and indefinite theta series. Zwegers showed how the mock theta functions of Ramanujan fit into the theory of real analytic modular forms. From here, Kathrin Bringmann in collaboration with Ken Ono and others obtained far reaching results. In Bringmann's papers these connections with modular forms are made explicit, further questions concerning asymptotics and congruences are addressed, and a comprehensive theory relating holomorphic cusp forms to Maass forms is developed. We now highlight a few of her fundamental contributions.

Kathrin Bringmann's PhD thesis of 2004, written under the direction of Professor Winfried Kohnen at the University of Heidelberg, contains important results on two difficult problems: (i) The Ramanujan-Petersson Conjecture for the coefficients of Siegel cusp forms whose weight is the dimension of the genus group plus one, and (ii) generalizations of the work of Gross, Kohnen and Zagier on the existence of lifting maps between spaces of Jacobi forms and elliptic modular functions. The results in her thesis appeared in Mathematische Zeitschrift (2006) and the Journal of the London Mathematical Society (2006).

After completing her PhD, Bringmann began work on several major projects with Ken Ono at the University of Wisconsin, and others. In a pathbreaking paper in the Annals of Mathematics, Bringmann and Ono, inspired by work of Zwegers and Zagier, show that Ramanujan's 22 mock theta functions are special cases of infinite families of weak Maass forms of weight 1/2. This paper is a major step in resolving Dyson's challenge and also explains many infinite families of congruences for the partition function. In another seminal paper in Inventiones Mathematicae (2006), Bringmann and Ono use Maass forms of weight 1/2 to obtain exact formulas for the coefficients of one of Ramanujan's third order mock theta functions, and as a consequence obtain exact formulas for the number of partitions with even and odd ranks. This settles the 40 year old Andrews-Dragonnette Conjecture. In yet another landmark paper that appeared in the Proceedings of the National Academy of Sciences (2007), Bringmann and Ono define maps that lift homorphic cusp forms of half integral weight to harmonic weak Maass forms, and this theory includes the weight 3/2 Maass forms which contains all of Ramanujan's mock theta functions; in this project, Bringmann also had a significant collaboration with Jeremy Lovejoy. One of her joint papers with Lovejoy that appeared in the International Mathematics Research Notices (2007) concerns connections between Dyson's rank for partitions, overpartitions, and weak Maass forms.

In the 1980s George Andrews and Frank Garvan showed that the Mock Theta Conjectures are equivalent to certain identities which involve linear combination of Eulerian series; these identities were proved by Hickerson (1988). In a paper in the Journal of the American Mathematical Society (2008), Bringmann, Ono and Robert Rhoades have explained these identities and other similar ones by utlizing ideas in the Bringmann-Ono Annals of Mathematics and Inventiones Mathematicae papers. Some other significant papers of Bringmann include her work with Frank Garvan and Karl Mahlburg on partition statistics and quasi-harmonic Maass forms that appeared in International Mathematics Research Notices (2008), her work with Amanda Folsom and Ken Ono on q-series and 3/2 weight Maass forms in Compositio Mathematica (2009), and her recent work with Sander Zwegers on rank-crank type partial differential equations and non-holomorphic Jacobi forms in Mathematics Research Letters.

Kathrin Bringmann was born on May 8, 1977 in Muenster, Germany. She passed the State Examinations in Mathematics and Theology at the University of Wuerzburg, Germany, in 2002, and obtained a Diploma in Mathematics with top honors at Wuerzburg in 2003. She then joined the University of Heidelberg where she received her PhD in 2004. During 2004-07, she was Van Vleck Assistant Professor at the University of Wisconsin where she began her great collaboration with Professor Ken Ono. After briefly serving as an Assistant Professor at the University of Minnesota, she has now joined the University of Cologne, Germany, as Professor. Earlier this year, she was awarded the prestigious Krupp Prize - a 1 million Euro research grant for a five year period awarded to young professors. The SASTRA Ramanujan Prize comes on the heels of the Krupp Prize.

Bringmann emerged as the top choice from a pool of brilliant young mathematicians from around the world. The international panel of experts who formed the 2009 SASTRA Ramanujan Prize Committee are: Chair - Krishnaswami Alladi (University of Florida), Bruce Berndt (University of Illinois at Urbana-Champaign), Jonathan Borwein (Dalhousie University, Canada and University of Newcastle, Australia), Dorian Goldfeld (Columbia University), Stephen Milne (Ohio State University), Wolfgang Schmidt (University of Colorado), and Jeffrey Vaaler (University of Texas).

Krishnaswami Alladi

Chair, 2009 SASTRA Ramanujan Prize Committee

The 2008 SASTRA Ramanujan Prize will be awarded to Akshay Venkatesh, who is now Professor of Mathematics at Stanford University, USA. This annual prize, which was established 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 Modular Forms, Dec 20-22, 2008 at SASTRA University in Kumbakonam, India, Ramanujan's hometown.

Professor Venkatesh has made far reaching contributions to a wide variety of areas in mathematics including number theory, automorphic forms, representation theory, locally symmetric spaces and ergodic theory, by himself and in collaboration with several mathematicians. We highlight a few of his path-breaking works: His paper with H. Helfgott (Journal of the American Mathematical Society 2006), containing a number of very striking and original ideas, gives the first non-trivial upper bound for the 3-torsion in class groups of quadratic fields. His work with Jordan Ellenberg (Inventiones Mathematicae 2007) on representing integral quadratic forms by quadratic forms is spectacular and has its roots in the work of Ramanujan. In collaboration with Ellenberg, Venkatesh has provided a striking application of Ratner's classification of measures invariant under unipotent flows to a central problem on quadratic forms studied by Siegel, the scalar case of which was of interest to Ramanujan. The problem is that of representing integral quadratic forms in m variables by one in n variables; Ellenberg and Venkatesh obtain a local to global principle that provides much sharper results than what was known previously by analytic methods.

An important and difficult topic in number theory is the problem of asymptotically counting number fields of a given degree according to their discriminants. This is a generalization of the classical problem of determining the relation between the number of rational or integral solutions of a polynomial equation in several variables and the coordinates of the solutions - in modern language, the problem of counting integral or rational points on an algebraic variety in terms of the height. In the case of degree up to 5, the problem was solved by Manjul Bhargava (who won the 2005 SASTRA Prize among other awards). In another paper, Ellenberg and Venkatesh (Annals of Mathematics 2006) consider bounding the number of number fields of a given degree with bounded discriminants, and provide the first major improvements (when the degree is large) over earlier bounds of Wolfgang Schmidt, thereby breaking an impasse of several years. Also of great importance is Venkatesh's paper with E. Lindenstrauss (GAFA 2007) in which the conjecture of Peter Sarnak that Weyl's law holds for the cuspidal spectrum of a congruence quotient of a locally symmetric space, is proved. In addition, with Lior Silberman, Venkatesh established partial results towards the "quantum unique ergodicity" conjecture of Rudnick and Sarnak for higher rank arithmetic locally symmetric spaces. One of his most spectacular achievements is his own individual work on subconvexity of automorphic L-functions. The problem of sub-convex bounds at the center of the critical strip for L-functions is very important. Venkatesh provides a very novel and more direct way of establishing sub-convexity in numerous cases thereby going beyond the foundational work of Hardy-Littlewood-Weyl, Burgess, and Duke-Friendlander-Iwaniec that dealt with important special cases. This work of Venkatesh is destined to be a classic in the analytic theory of automorphic forms. Finally, Venkatesh's recent work with Manfred Einseidler, Elon Lindenstrauss and Philippe Michel on Duke's theorem for cubic fields is very striking.

Venkatesh, who is of South Indian descent (a Tamilian like Ramanujan), was born in New Delhi in 1981 but was raised in Perth, Australia. He showed his brilliance in mathematics very early and was awarded the Woods Memorial Prize in 1997 at the University of Western Australia when he finished his undergraduate degree.

Venkatesh's entry into research began as a PhD student at Princeton in 1998 under Professor Peter Sarnak, one the most versatile and influential mathematicians of our time. In his PhD thesis Venkatesh realized the first step of a program proposed by Langlands of counting automorphic forms by analytic methods. After completing his PhD in 2002, he was C. L. E. Moore Instructor at MIT for two years before being selected as Clay Research Fellow in 2004. He was then appointed as Associate Professor at the Courant Institute of Mathematical Sciences at NYU. In 2007 he was recognized with the Salem Prize and the Packard Fellowship. And now, just as he is turning 27, he has just been elevated to rank of Full Professor at Stanford University.

Venkatesh emerged as the top choice from a pool of brilliant young mathematicians from around the world. The international panel of experts who formed the 2008 SASTRA Ramanujan Prize Committee are: Chair - Krishnaswami Alladi (University of Florida), Manjul Bhargava (Princeton University), Bruce Berndt (University of Illinois at Urbana-Champaign), Jonathan Borwein (Dalhousie University, Canada and University of Newcastle, Australia), Stephen Milne (Ohio State University), Kannan Soundararajan (Stanford University), and Michel Waldschmidt (University of Paris).

Krishnaswami Alladi

Chair, 2008 SASTRA Ramanujan Prize Committee

The 2007 SASTRA Ramanujan Prize will be awarded to Ben Green, who is Hershel Smith Professor of Mathematics at Cambridge University, England. This annual prize, which was established 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, Mathematical Physics, and Special Functions, Dec 20-22, at SASTRA University in Kumbakonam, India, Ramanujan's hometown.

Professor Green has made phenomenal contributions to several important problems in combinatorial additive number theory, by himself and in collaboration with Fields Medalist Terence Tao of UCLA, who won the 2006 SASTRA Prize. This stunning progress has been achieved by ingenious new methods involving an interplay of combinatorial ideas, number theoretic methods and analytic techniques. Green's PhD thesis of 2002, written under the direction of Fields Medalist Tim Gowers of Cambridge University, is a collection of several outstanding papers. In one of them that appeared in the Bulletin of the London Mathematical Society in 2004, he solved the Cameron-Erdos conjecture which is a bound for the number of sum free subsets among the positive integers up to a given number N. Over the years several top mathematicians had worked on this problem which was finally solved by Green.

Green's most spectacular contribution is to the study of long arithmetic progressions of primes, starting with his seminal paper of 2005 in the Annals of Mathematics. This paper contained very fundamental ideas which he and Terence Tao could greatly develop and build on to settle the long standing conjecture that the primes contain arbitrarily long arithmetic progressions. A fundamental result in Combinatorial Additive Number Theory is a 1953 theorem of K. F. Roth which asserts that any set of positive integers with positive density contains arithmetic progressions of length 3. This paved the way for the Hungarian mathematician Szemeredi to obtain a substantially deeper and stronger result, namely, that any set of positive integers which has positive density contains arbitrarily long arithmetic progressions. Tim Gowers, who revolutionized Combinatorial Additive Number Theory with the powerful new idea called higher uniformity, provided among other things an entirely new proof of Szemeredi's theorem. Szemeredi's theorem does not apply to the primes, which have density zero. Nevertheless, it had long been conjectured that the primes do contain arbitrarily long arithmetic progressions. The first significant advance in this direction was provided by Green in his Annals of Mathematics paper of 2005 where he established a Roth type theorem for the primes, namely that any set of primes with relative positive density contains arithmetic progressions of length 3. Green's combinatorial proof of this result makes significant improvements on the techniques of Gowers and contained the basic ideas that led to far reaching extensions. Green's work attracted Tao, whose expertise complemented that of Green. Together they first extended Green's result to arithmetic progressions of length 4 within sets of primes of relative positive density, and soon thereafter proved that there are arbitrarily long arithmetic progressions among sets of primes with relative positive density. In this process, Green and Tao have significantly extended the Circle Method by linking it with Gowers' ideas as well as with ergodic theory. The Circle Method, originally due to Hardy and Ramanujan for estimating the number of partitions of an integer, was later developed by Hardy and Littlewood into a versatile tool in Additive Number Theory. This work of Green and Tao which is soon to appear in the Annals of Mathematics, is having an impact on analytic number theory, of a magnitude that has not been witnessed in a very long time.

Green was born in Bristol, England in 1977. He went to Cambridge University to do his BA (1995-98) and continued there to do his PhD (1999-2002) during which time he was awarded the Smith Prize (2001). He held post-doctoral positions at the Alfred Renyi Institute in Budapest (2003-04) and the Pacific Institute of Mathematics in Vancouver (2005-06), before being quickly elevated to appointment as Professor at the University of Bristol in 2005. His spectacular contributions have had so much impact in such a short span of time that in the last two years recognitions have come to him in a flood. He received the prestigious Fellowship at the Clay Institute in 2005 and was appointed Hershel Smith Professor at Cambridge University in 2006 at the young age of 29. He was also delivered one of the invited lectures at the International Congress of Mathematicians at Madrid in 2006. Green is Fellow of Trinity College, Cambridge, following a great tradition at that College where Hardy, Littlewood and Ramanujan were Fellows.

Green emerged as the top choice from a pool of brilliant young mathematicians from around the world. The international panel of experts who formed the 2007 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 (Stanford University), and Michel Waldschmidt (University of Paris).

Krishnaswami Alladi

Chair, 2007 SASTRA Ramanujan Prize Committee

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 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 differential 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 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

The 2005 SASTRA Ramanujan Prize will be jointly awarded to Professors MANJUL BHARGAVA (Princeton University) and KANNAN SOUNDARARAJAN (University of Michigan). This annual prize, being awarded for the first time, is for outstanding contributions by individuals not exceeding the age of 32 in areas of mathematics influenced by Ramanujan in a broad sense. The age limit was set at 32 because Ramanujan achieved so much in his brief life of 32 years. The $10,000 prize will be awarded annually in December at the Srinivasa Ramanujan Centre of SASTRA University in Ramanujan's hometown, Kumbakonam, South India.

MANJUL BHARGAVA has made phenomenal contributions to number theory, most notably by his discovery of higher order composition laws. This is his PhD thesis, written under the direction of Professor Andrew Wiles of Princeton University and published as a series of papers in the Annals of Mathematics. Gauss, the Prince of Mathematicians, constructed a law of composition for 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 d. The question is trivial for d=1, and Gauss himself solved the case d=2 in 1801. Then in 1971 Davenport and Heilbronn solved the d=3 case. Bhargava has now 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 on 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 very little activity since the time of Gauss. Bhargava is currently a Full Professor at Princeton University, the youngest at that rank in that prestigious academic institution.

KANNAN SOUNDARARAJAN has made brilliant contributions to several areas in 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 families of L-functions. As an undergraduate at the University of Michigan, Soundararajan made two outstanding contributions. First, in joint work with R. Balasubramaniam, he proved a famous conjecture of Ron Graham in combinatorial number theory. Next he obtained some fundamental results on the distribution of zeros of the Riemann zeta function. Subsequently, in his PhD thesis, written under the direction of Professor Peter Sarnak of Princeton University, Soundararajan proved the spectacular result that more than 7/8-ths of quadratic Dirichlet L-functions have no zeros at the critical point s=1/2, thereby providing strong evidence for a conjecture of Chowla. A part of his PhD 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 in Inventiones Mathematicae, he and Ken Ono, assuming the generalized Riemann hypothesis, confirmed a certain conjecture of Ramanujan regarding a ternary quadratic form. Soundararajan is also a leading expert on random matrix theory and its implications in analytic number theory. Here his recent work with Hugh Montgomery shows that prime numbers in short intervals are distributed normally, but with a variance that is surprisingly different from classical heuristics. Soundararajan, considered to be one of the most creative young minds to emerge in the last decade, is currently Full Professor at the University of Michigan, Ann Arbor.

Bhargava and Soundararajan were selected as the top candidates from a pool of brilliant young mathematicians from around the world. The international panel of experts who formed the 2005 SASTRA Ramanujan Prize Committee are: (Chair) Krishnaswami Alladi - University of Florida, Manindra Agarwal - Indian Institute of Technology, Kanpur, George Andrews - The Pennsylvania State University, Jean-Marc Deshouillers - University of Bordeaux, Tom Koornwinder - University of Amsterdam, James Lepowsky - Rutgers University, and Don Zagier - Max Planck Institute for Mathematics, Bonn, and the College de France. This being the first year the award is given, the competition was especially strong and the decision was to give the prize to two equally deserving outstanding candidates.

Bhargava and Soundararajan will be awarded the prize during the International Conference on Number Theory and Mathematical Physics, December 19-22, 2005, at SASTRA University, where both will be invited to give talks on their work.

Krishnaswami Alladi

Chair, 2005 SASTRA Ramanujan Prize Committee