- Manjul Bhargava
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Manjul Bhargava Born August 8, 1974
Hamilton, OntarioNationality Canadian American Fields Mathematics Institutions Princeton University Alma mater Harvard University
Princeton UniversityDoctoral advisor Andrew Wiles Doctoral students Wei Ho
Arul Shankar
Michael Volpato
Melanie WoodKnown for Gauss composition laws Notable awards Cole Prize (2008)
Clay Research Award (2005)
SASTRA Ramanujan Prize (2005)
Hasse Prize (2003)
Morgan Prize (1996)Manjul Bhargava (मञ्जुल भार्गव) (born August 8, 1974[1]) 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 research contributions to algebraic number theory and representation theory.
Contents
Biography
Bhargava's mother, Mira Bhargava, is a mathematician at Hofstra University and his father is a chemist. Bhargava grew up in Long Island, NY. [2] Manjul Bhargava completed all of his high school math and computer courses by age 14.[3] He attended Plainedge High School, graduating in 1992 as the class valedictorian. He obtained his B.A. from Harvard University in 1996 and received his doctorate from Princeton in 2001, working under Andrew Wiles. 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. [4] He is still the youngest standing tenured full professor at Princeton.[citation needed]
Bhargava is also an accomplished tabla player, having studied under gurus such as Zakir Hussain. [5]. He has also studied Sanskrit. His grandfather Dr. Purushottam Lal Bhargava is a well-known scholar of Sanskrit and ancient Indian history.
Contributions
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, and to the study of ideal class groups of algebraic number fields.[6] 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 of the 290 theorem.
- A novel generalization of the factorial function, resolving a decades-old conjecture by George Pólya.
In July 2010 Manjul Bhargava and Arul Shankar proved that the limit superior of the average rank of all elliptic curves is bounded, and is in fact less than 1.17. As a consequence of their methods, they established that the Birch and Swinnerton-Dyer conjecture is true for a positive proportion of elliptic curves.[7]
Awards and Honors
Bhargava is the second youngest full professor in Princeton University's history, after Charles Fefferman (professor at Princeton at age 24). [8]
Bhargava has won several awards for his research, including the Morgan Prize[9] in 1996, the Merten M. Hasse Prize from the MAA in 2003,[10] a Clay Research Fellowship, 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.
Peter Sarnak of Princeton University has said of Bhargava[11]:
“ 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 recently won the American Mathematical Society's Cole Prize and 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.
In 2008, Bhargava was awarded the Cole Prize.[12] The citation reads:
“ 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 ” Selected Publications
- Bhargava, Manjul (2000). "The Factorial Function and Generalizations". The American Mathematical Monthly 107 (9): 783–799. doi:10.2307/2695734. http://mathdl.maa.org/images/upload_library/22/Hasse/00029890.di021346.02p0064l.pdf.
- 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. http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n1-p03.pdf.
- 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. http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n2-p09.pdf.
- 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. http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n3-p08.pdf.
- 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. http://annals.math.princeton.edu/wp-content/uploads/annals-v162-n2-p10.pdf.
- 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. http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n1-p02.pdf.
- 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. http://annals.math.princeton.edu/wp-content/uploads/annals-v162-n2-p10.pdf.
- 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.
References
- ^ Gallian, Joseph A. (2009). Contemporary Abstract Algebra. Belmont, CA: Cengage Learning. p. 571. ISBN 9780547165097. http://books.google.com/?id=CnH3mlOKpsMC&lpg=PP1&dq=Contemporary%20Abstract%20Algebra&pg=PA571#v=onepage&q&f=false.
- ^ Fareed Zakaria is India Abroad Person of the Year - Rediff.com India News
- ^ [1]
- ^ Vakil, Ravi (2008). A Mathematical Mosaic. Burlington, ON: Brendan Kelly Publishing. p. 159. ISBN 9781895997040. http://books.google.com/books/about/A_mathematical_mosaic.html?id=GvTHNPSkoN4C.
- ^ http://www.princeton.edu/pr/pwb/03/1208/1b.shtml
- ^ Clay Mathematics Institute
- ^ Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0
- ^ http://www.math.princeton.edu/graduate/generals/bhargava_manjul
- ^ 1996 AMS-MAA-SIAM Morgan Prize
- ^ About the MAA
- ^ Bhargava GS '98 awarded Clay Research prize
- ^ 2008 Cole Prize in Number Theory
External links
Categories:- Living people
- Canadian people of Indian descent
- Canadian mathematicians
- Number theorists
- Harvard University alumni
- Princeton University alumni
- Princeton University faculty
- 21st-century mathematicians
- 1974 births
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