August 8, 1974 |
|Alma mater||Harvard University
|Doctoral advisor||Andrew Wiles|
|Doctoral students||Michael Volpato
|Known for||Gauss composition laws
15 and 290 theorems
ranks of elliptic curves
|Notable awards||Infosys Prize (2012)
Fermat Prize (2011)
Cole Prize (2008)
Clay Research Award (2005)
SASTRA Ramanujan Prize (2005)
Hasse Prize (2003)
Morgan Prize (1996)
Hoopes Prize (1996)
Manjul Bhargava (मञ्जुल भार्गव) (born August 8, 1974) is a Canadian-American mathematician of Indian origin. He is the R. Brandon Fradd Professor of Mathematics at Princeton University. He is known primarily for his contributions to number theory.
Bhargava's mother, Mira Bhargava, is a mathematician at Hofstra University and his father a chemist. Bhargava grew up in Long Island, New York. Manjul Bhargava completed all of his high school math and computer courses by age 14. He attended Plainedge High School, graduating in 1992 as the class valedictorian. He obtained his B.A. from Harvard University in 1996. For his research as an undergraduate, he was awarded the 1996 Morgan Prize. Bhargava went on to receive his doctorate from Princeton in 2001, supervised by Andrew Wiles. He was a visiting scholar at the Institute for Advanced Study in 2001-02. Princeton hired him at the rank of tenured full professor within only two years of finishing graduate school, which is considered a record in the Ivy League.
Bhargava is also an accomplished tabla player, having studied under gurus such as Zakir Hussain. He has also studied Sanskrit. His grandfather Purushottam Lal Bhargava is a well-known scholar of Sanskrit and ancient Indian history.
His Ph.D. thesis generalized the classical Gauss composition law for quadratic forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study of asymptotic behavior of arithmetic properties of these orders and fields.
His research also includes fundamental contributions to the representation theory of quadratic forms, to interpolation problems and p-adic analysis, to the study of ideal class groups of algebraic number fields, and to the arithmetic theory of elliptic curves. A short list of his specific mathematical contributions are:
- 14 new Gauss-style composition laws.
- Determination of the asymptotic density of discriminants of quartic and quintic number fields.
- Proofs of the first known cases of the Cohen-Lenstra-Martinet heuristics for class groups.
- Proof of the 15 theorem, including an extension of the theorem to other number sets such as the odd numbers and the prime numbers.
- Proof (with Jonathan Hanke) of the 290 theorem.
- A novel generalization of the factorial function, resolving a decades-old conjecture by George Pólya.
- Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded.
Awards and Honors 
Bhargava has won several awards for his research, including the Morgan Prize in 1996, a Clay 5-year Research Fellowship, the Merten M. Hasse Prize from the MAA in 2003, the Clay Research Award in 2005, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005.
|“||At mathematics he's at the very top end. For a guy so young I can't remember anybody so decorated at his age. He certainly started out with a bang and has not let it get to his head, which is unusual. Of course he couldn't do what he does if he wasn't brilliant. It's his exceptional talent that's so striking||”|
He was named one of Popular Science Magazine’s “Brilliant 10” in November 2002. He won the $10,000 SASTRA Ramanujan Prize, shared with Kannan Soundararajan, awarded by SASTRA in 2005 at Tanjavur, India, for his outstanding contributions to number theory.
|“||Bhargava’s original and surprising contribution is the discovery of laws of composition on forms of higher degree. His techniques and insights into this question are dazzling; even in the case considered by Gauss, they lead to a new and clearer presentation of that theory||”|
In 2011, Bhargava was awarded the Fermat Prize for "various generalizations of the Davenport-Heilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves".
Bhargava is also a sought-after speaker, having given numerous public lectures around the world. In 2011, he delivered the prestigious Hedrick lectures of the MAA in Lexington, Kentucky. He was also the 2011 Simons Lecturer at MIT.
Bhargava was also awarded the 2012 Infosys Prize in mathematics for his “extraordinarily original work in algebraic number theory”, which has revolutionized the way in which number fields and elliptic curves are counted.
Selected Publications 
- Bhargava, Manjul (2000). "The Factorial Function and Generalizations". The American Mathematical Monthly 107 (9): 783–799. doi:10.2307/2695734.
- Bhargava, Manjul (2004). "Higher Composition Laws I: A New View on Gauss Composition, and Quadratic Generalizations". The Annals of Mathematics 159: 217–250. doi:10.4007/annals.2004.159.217.
- Bhargava, Manjul (2004). "Higher Composition Laws II: On Cubic Analogues of Gauss Composition". The Annals of Mathematics 159 (2): 865–886. doi:10.4007/annals.2004.159.865.
- Bhargava, Manjul (2004). "Higher Composition Laws III: The Parametrization of Quartic Rings". The Annals of Mathematics 159 (3): 1329–1360. doi:10.4007/annals.2004.159.1329.
- Bhargava, Manjul (2005). "The density of discriminants of quartic rings and fields". The Annals of Mathematics 162: 1031–1063. doi:10.4007/annals.2005.162.1031.
- Bhargava, Manjul (2008). "Higher composition laws IV: The parametrization of quintic rings". The Annals of Mathematics 167: 53–94. doi:10.4007/annals.2008.167.53.
- Bhargava, Manjul (2010). "The density of discriminants of quintic rings and fields". The Annals of Mathematics 172: 1559–1591. doi:10.4007/annals.2010.172.1559.
- Bhargava, Manjul; Shankar, Arul (2010). Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves. arXiv:1006.1002.
- Bhargava, Manjul; Shankar, Arul (2010). Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0. arXiv:1007.0052.
- Bhargava, Manjul; Satriano, Matthew (2010). On a notion of "Galois closure" for extensions of rings. arXiv:1006.2562v1.
- Gallian, Joseph A. (2009). Contemporary Abstract Algebra. Belmont, CA: Cengage Learning. p. 571. ISBN 978-0-547-16509-7.
- Manjul Bhargava Receives Hasse Prize at MathFest
- Fareed Zakaria is India Abroad Person of the Year - Rediff.com India News
- India Abroad - Archives 2003-2008
- Institute for Advanced Study: A Community of Scholars
- Vakil, Ravi (2008). A Mathematical Mosaic. Burlington, ON: Brendan Kelly Publishing. p. 159. ISBN 978-1-895997-04-0.
- Princeton - Weekly Bulletin 12/08/03 - Bhargava strikes balance among many interests
- Clay Mathematics Institute
- Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
- Manjul's Princeton generals
- 1996 AMS-MAA-SIAM Morgan Prize
- About the MAA
- Bhargava GS '98 awarded Clay Research prize
- 2008 Cole Prize in Number Theory
- Fermat Prize 2011
- Earle Raymond Hedrick Lecturers
- MIT Mathematics | Simons
- Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced
- List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
- "Subrahmanyam, Chaudhuri get Infosys Prize". The Hindu (Bangalore). November 24, 2012. Retrieved November 24, 2012.
- Manjul Bhargava at Princeton
- Manjul Bhargava at CMI
- Manjul Bhargava at NPR
- Manjul Bhargava at ICTS
- Article in The Hindu on Bhargava winning the SASTRA prize
- Princeton University article by Steven Schultz
- Princeton University article by Viola Huang
- Manjul Bhargava at the Mathematics Genealogy Project