8 August 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||Fields Medal (2014)
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 (born 8 August 1974) is a Canadian-American mathematician. He is the R. Brandon Fradd Professor of Mathematics at Princeton University and is known primarily for his contributions to number theory.
Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation, he was awarded the prize "for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves." He has an Erdős number of 2.
Education and career
Bhargava was born in Hamilton, Ontario of parents who had immigrated from Jaipur, Rajasthan, India. He grew up primarily in Long Island, New York. He 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 selected as the first 5-year Clay Research Fellow in 2000. He was a visiting scholar at the Institute for Advanced Study in 2001-02, and at Harvard University in 2002-03. Princeton appointed him to full professor with tenure in 2003.
Bhargava is also an accomplished tabla player, having studied under gurus such as Zakir Hussain. He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a well-known scholar of Sanskrit and ancient Indian history.
His PhD thesis generalized Gauss's classical law for composition of binary 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:
- Fourteen 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, the most prestigious being the Fields Medal, the highest award in the field of mathematics, which he won in 2014.
In addition, he was won 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".
In 2014, Bhargava was awarded the Fields Medal at the International Congress of Mathematicians in Seoul for "developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves".
- 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.
Notes and references
- Gallian, Joseph A. (2009). Contemporary Abstract Algebra. Belmont, CA: Cengage Learning. p. 571. ISBN 978-0-547-16509-7.
- "List of all 2014 awardees with brief citations" (Press release). International Mathematical Union. Retrieved August 12, 2014.
- AMS Collaboration Distance http://www.ams.org/mathscinet/collaborationDistance.html
- "Fareed Zakaria is India Abroad Person of the Year - Rediff.com India News". News.rediff.com. 2009-03-21. Retrieved 2014-08-14.
- "India Abroad - Archives 2003-2008". Indiaabroad-digital.com. 2009-12-30. Retrieved 2014-08-14.
- "Institute for Advanced Study: A Community of Scholars". Ias.edu. Retrieved 2014-08-14.
- "Bhargava strikes balance among many interests". Princeton.edu. 2003-12-08. Retrieved 2014-08-14.
- "Fields Medal Winner Bhargava". Business Insider. Retrieved 2014-08-14.
- "Fellows and Scholars | Clay Mathematics Institute". Claymath.org. Retrieved 2014-08-14.
- "Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0". Arxiv.org. Retrieved 2014-08-14.
- "1996 AMS-MAA-SIAM Morgan Prize" (PDF). Retrieved 2014-08-14.
- "About the MAA". Maa.org. Retrieved 2014-08-14.
- Bhargava GS '98 awarded Clay Research prize[dead link]
- "2008 Cole Prize in Number Theory" (PDF). Retrieved 2014-08-14.
- Fermat Prize 2011[dead link]
- "Earle Raymond Hedrick Lecturers". Maa.org. Retrieved 2014-08-14.
- "MIT Mathematics | Simons". Math.mit.edu. Retrieved 2014-08-14.
- "Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced". Foundationcenter.org. 2012-07-24. Retrieved 2014-08-14.
- 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.
- "Professor Manjul Bhargava Has Been Elected to National Academy of Sciences". Math.princeton.edu. Retrieved 2014-08-14.
- "List of all 2014 awardees with brief citations". mathunion.org. Retrieved 2014-08-24.
- Manjul Bhargava at Princeton
- Manjul Bhargava at NPR
- Manjul Bhargava at ICTS
- Article in The Hindu on Bhargava winning the SASTRA prize
- Princeton University article by Steven Schultz
- Manjul Bhargava at the Mathematics Genealogy Project