Manjul Bhargava
Manjul Bhargava  

Manjul in 2005
 
Born 
Hamilton, Ontario, Canada

8 August 1974
Nationality 
Canada United States 
Alma mater 
Harvard University Princeton University 
Known for  higher composition laws 15 and 290 theorems factorial function average rank of elliptic curves Bhargava factorial 
Awards 
Fields Medal (2014) Infosys Prize (2012) Fermat Prize (2011) Cole Prize (2008) Clay Research Award (2005) SASTRA Ramanujan Prize (2005) Blumenthal Award (2005) Hasse Prize (2003) Morgan Prize (1996) Hoopes Prize (1996) Hertz Fellowship (1996) 
Scientific career  
Institutions 
Princeton University Leiden University University of Hyderabad 
Doctoral advisor  Andrew Wiles 
Doctoral students 
Alison Miller Melanie Wood 
Manjul Bhargava (born 8 August 1974)^{[1]} is a CanadianAmerican mathematician. He is the R. Brandon Fradd Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory^{[2]} at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He 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".^{[3]}
Contents
Education and career
Bhargava was born in Hamilton, Ontario, Canada but grew up and attended school primarily in Long Island, New York. His mother Mira Bhargava, a mathematician at Hofstra University, was his first mathematics teacher.^{[4]}^{[5]} He completed all of his high school math and computer science courses by age 14.^{[6]} He attended Plainedge High School in North Massapequa, and graduated 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 and funded by a Hertz Fellowship. He was a visiting scholar at the Institute for Advanced Study in 200102,^{[7]} and at Harvard University in 200203. Princeton appointed him as a tenured Full Professor in 2003. He was appointed to the Stieltjes Chair in Leiden University in 2010.
Bhargava is also an accomplished tabla player, having studied under gurus such as Zakir Hussain.^{[8]} He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a wellknown scholar of Sanskrit and ancient Indian history.^{[9]} He is an admirer of Sanskrit poetry.^{[10]}
Contributions
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 padic analysis, to the study of ideal class groups of algebraic number fields, and to the arithmetic theory of elliptic curves.^{[11]} A short list of his specific mathematical contributions are:
 Fourteen new Gaussstyle composition laws.
 Determination of the asymptotic density of discriminants of quartic and quintic number fields.
 Proofs of the first known cases of the CohenLenstraMartinet 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, Bhargava factorial, resolving a decadesold conjecture by George Pólya.
 Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded.
 Proof that most hyperelliptic curves over Q have no rational points.
In 2015 Manjul Bhargava and Arul Shankar proved the Birch and SwinnertonDyer conjecture for a positive proportion of elliptic curves.^{[12]}
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.
Bhargava is the third ^{[13]} youngest full professor in Princeton University's history, after Charles Fefferman and John Pardon.
In addition, he won the Morgan Prize^{[14]} and Hertz Fellowship^{[15]} in 1996, a Clay 5year Research Fellowship, the Merten M. Hasse Prize from the MAA in 2003,^{[16]} 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:^{[17]}
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 Thanjavur, India, for his outstanding contributions to number theory.
In 2008, Bhargava was awarded the American Mathematical Society's Cole Prize.^{[18]} 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
In 2009, he was awarded the Face of the Future award at the India Abroad Person of the Year ceremony in New York City.^{[19]} In 2014, the same publication, the most prestigious and most widely read of the diaspora publications, gave him a second prize, India Abroad Publisher's Prize for Special Excellence.^{[20]}
In 2011, he was awarded the Fermat Prize for "various generalizations of the DavenportHeilbronn estimates and for his startling recent results (with Arul Shankar) on the average rank of elliptic curves".^{[21]}
In 2011, he delivered the Hedrick lectures of the MAA in Lexington, Kentucky.^{[22]} He was also the 2011 Simons Lecturer at MIT.^{[23]}
In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,^{[24]} and became a fellow of the American Mathematical Society in its inaugural class of fellows.^{[25]}
He was 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".^{[26]}
In 2013, he was elected to the National Academy of Sciences.^{[27]}
In 2014, Bhargava was awarded the Fields Medal at the International Congress of Mathematicians in Seoul^{[9]} 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".^{[28]}
In 2015, he was awarded the Padma Bhushan, the third highest civilian award of India.^{[29]}
In 2018 Bhargava was named as the inaugural occupant of The Distinguished Chair for the Public Dissemination of Mathematics at The National Museum of Mathematics (MoMath). This is the first visiting professorship in the United States dedicated exclusively to raising public awareness of mathematics.^{[30]}
Selected publications
 Bhargava, Manjul (2000). "The Factorial Function and Generalizations" (PDF). 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" (PDF). 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" (PDF). 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" (PDF). 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" (PDF). 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" (PDF). 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" (PDF). The Annals of Mathematics. 172: 1559–1591. arXiv:1005.5578. doi:10.4007/annals.2010.172.1559.
 Bhargava, Manjul; Satriano, Matthew (2014). "On a notion of "Galois closure" for extensions of rings". Journal of the European Mathematical Society. 16 (9): 1881–1913. arXiv:1006.2562. doi:10.4171/JEMS/478. MR 3273311.
 Bhargava, Manjul; Shankar, Arul (2015). "Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves". Annals of Mathematics. 181 (1): 191–242. arXiv:1006.1002. doi:10.4007/annals.2015.181.1.3. MR 3272925.
 Bhargava, Manjul; Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0". Annals of Mathematics. 181 (2): 587–621. arXiv:1007.0052. doi:10.4007/annals.2015.181.2.4.
See also
Notes and references
 ^ Gallian, Joseph A. (2009). Contemporary Abstract Algebra(((((Vaishali))))). Belmont, CA: Cengage Learning. p. 571. ISBN 9780547165097.
 ^ "Fields Medal for Leiden Professor of Number Theory Manjul Bhargava" (Press release). 13 August 2014. Retrieved 13 August 2014.
 ^ "List of all 2014 awardees with brief citations" (Press release). International Mathematical Union. Retrieved 12 August 2014.
 ^ "At Play in the Fields of Math". Retrieved September 29, 2016.
 ^ "Fareed Zakaria is India Abroad Person of the Year — Rediff.com India News". News.rediff.com. 20090321. Retrieved 20140814.
 ^ "India Abroad — Archives 20032008". Indiaabroaddigital.com. 20091230. Retrieved 20140814.
 ^ "Institute for Advanced Study: A Community of Scholars". Ias.edu. Retrieved 20140814.
 ^ "Bhargava strikes balance among many interests". Princeton.edu. 20031208. Retrieved 20140814.
 ^ ^{a} ^{b} "Fields Medal Winner Bhargava". Business Insider. Retrieved 20140814.
 ^ Dasgupta, Sucheta (20140818). "Interest at home, among NRIs resurrects Sanskrit". Times of India. Retrieved 18 August 2014.
 ^ "Fellows and Scholars  Clay Mathematics Institute". Claymath.org. Retrieved 20140814.
 ^ Bhargava, Manjul; Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0". Annals of Mathematics. 181 (2): 587–621. arXiv:1007.0052. doi:10.4007/annals.2015.181.2.4.
 ^ "Meet Manjul Bhargava: The Fields Medal winner for mathematics, who is also a musician". The Economic Times. 20140814. Retrieved 20170403.
 ^ "1996 AMSMAASIAM Morgan Prize" (PDF). Retrieved 20140814.
 ^ "Hertz Foundation Fellows: Rare individuals elevate and inspire us through bold thinking and leadership". Retrieved 20150909.
 ^ "About the MAA". Maa.org. Retrieved 20140814.
 ^ Bhargava GS '98 awarded Clay Research prize Archived 14 June 2011 at the Wayback Machine.
 ^ "2008 Cole Prize in Number Theory" (PDF). Retrieved 20140814.
 ^ Rajesh Karkera (20090322), The India Abroad Face of the Future Award  Manjul Bhargava, retrieved 20180717
 ^ Rajesh Karkera (20150613), The India Abroad Publisher's Special Award for Excellence 2014: Manjul Bhargava, retrieved 20180717
 ^ Fermat Prize 2011 Archived 3 November 2011 at the Wayback Machine.
 ^ "Earle Raymond Hedrick Lecturers". Maa.org. Retrieved 20140814.
 ^ "MIT Mathematics  Simons". Math.mit.edu. Archived from the original on 3 February 2014. Retrieved 14 August 2014.
 ^ "Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced". Foundationcenter.org. 20120724. Retrieved 20140814.
 ^ List of Fellows of the American Mathematical Society, retrieved 20121110.
 ^ "Subrahmanyam, Chaudhuri get Infosys Prize". The Hindu. Bangalore. 24 November 2012. Retrieved 24 November 2012.
 ^ "Professor Manjul Bhargava Has Been Elected to National Academy of Sciences". Math.princeton.edu. Archived from the original on 23 October 2014. Retrieved 14 August 2014.
 ^ "List of all 2014 awardees with brief citations". mathunion.org. Retrieved 20140824.
 ^ "This Year's Padma Awards announced". Ministry of Home Affairs. 25 January 2015. Archived from the original on 26 January 2015. Retrieved 2 February 2015.
 ^ MoMath Announces First Distinguished Chair for the Public Dissemination of Mathematics The National Museum of Mathematics, August 2, 2018
External links
 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
 1974 births
 Living people
 21stcentury Indian mathematicians
 Canadian mathematicians
 Canadian people of Indian descent
 Clay Research Award recipients
 Fellows of the American Mathematical Society
 Members of the United States National Academy of Sciences
 Foreign Fellows of the Indian National Science Academy
 Indian number theorists
 Fields Medalists
 Harvard University alumni
 Institute for Advanced Study visiting scholars
 Morgan Prize winners
 Leiden University faculty
 Princeton University alumni
 Princeton University faculty
 Recipients of the Infosys Prize
 Recipients of the SASTRA Ramanujan Prize
 People from Hamilton, Ontario
 People from North Massapequa, New York
 American academics of Indian descent
 Recipients of the Padma Bhushan in science & engineering
 Simons Investigator