Manjul Bhargava

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Manjul Bhargava
Manjul Bhargava.jpg
Born (1974-08-08) 8 August 1974 (age 43)
Hamilton, Ontario
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
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 Wei Ho
Alison Miller
Arul Shankar
Melanie Wood
Ila Varma

Manjul Bhargava (born 8 August 1974)[1] is a Canadian-American mathematician of Indian origin. 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]

Education and career[edit]

Bhargava was born in Hamilton, Ontario, Canada of parents who had emigrated from India, and he grew up 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 2001-02,[7] and at Harvard University in 2002-03. 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 well-known scholar of Sanskrit and ancient Indian history.[9] He is an admirer of Sanskrit poetry.[10]


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.[11] A short list of his specific mathematical contributions are:

In 2015 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.[12]

Awards and honors[edit]

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 5-year 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]

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:

In 2011, he 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".[19]

In 2011, he delivered the Hedrick lectures of the MAA in Lexington, Kentucky.[20] He was also the 2011 Simons Lecturer at MIT.[21]

In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,[22] and became a fellow of the American Mathematical Society in its inaugural class of fellows.[23]

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".[24]

In 2013, he was elected to the National Academy of Sciences.[25]

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".[26]

In 2015, he was awarded the Padma Bhushan, the third highest civilian award of India.[27]

Selected publications[edit]

See also[edit]

Notes and references[edit]

  1. ^ Gallian, Joseph A. (2009). Contemporary Abstract Algebra(((((Vaishali))))). Belmont, CA: Cengage Learning. p. 571. ISBN 978-0-547-16509-7. 
  2. ^ "Fields Medal for Leiden Professor of Number Theory Manjul Bhargava" (Press release). 13 August 2014. Retrieved 13 August 2014. 
  3. ^ "List of all 2014 awardees with brief citations" (Press release). International Mathematical Union. Retrieved 12 August 2014. 
  4. ^ "At Play in the Fields of Math". Retrieved September 29, 2016. 
  5. ^ "Fareed Zakaria is India Abroad Person of the Year — India News". 2009-03-21. Retrieved 2014-08-14. 
  6. ^ "India Abroad — Archives 2003-2008". 2009-12-30. Retrieved 2014-08-14. 
  7. ^ "Institute for Advanced Study: A Community of Scholars". Retrieved 2014-08-14. 
  8. ^ "Bhargava strikes balance among many interests". 2003-12-08. Retrieved 2014-08-14. 
  9. ^ a b "Fields Medal Winner Bhargava". Business Insider. Retrieved 2014-08-14. 
  10. ^ Dasgupta, Sucheta (2014-08-18). "Interest at home, among NRIs resurrects Sanskrit". Times of India. Retrieved 18 August 2014. 
  11. ^ "Fellows and Scholars | Clay Mathematics Institute". Retrieved 2014-08-14. 
  12. ^ 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:1007.0052Freely accessible. doi:10.4007/annals.2015.181.2.4. 
  13. ^ "Meet Manjul Bhargava: The Fields Medal winner for mathematics, who is also a musician". The Economic Times. 2014-08-14. Retrieved 2017-04-03. 
  14. ^ "1996 AMS-MAA-SIAM Morgan Prize" (PDF). Retrieved 2014-08-14. 
  15. ^ "Hertz Foundation Fellows: Rare individuals elevate and inspire us through bold thinking and leadership.". Retrieved 2015-09-09. 
  16. ^ "About the MAA". Retrieved 2014-08-14. 
  17. ^ Bhargava GS '98 awarded Clay Research prize Archived 14 June 2011 at the Wayback Machine.
  18. ^ "2008 Cole Prize in Number Theory" (PDF). Retrieved 2014-08-14. 
  19. ^ Fermat Prize 2011 Archived 3 November 2011 at the Wayback Machine.
  20. ^ "Earle Raymond Hedrick Lecturers". Retrieved 2014-08-14. 
  21. ^ "MIT Mathematics | Simons". Retrieved 2014-08-14. 
  22. ^ "Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced". 2012-07-24. Retrieved 2014-08-14. 
  23. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
  24. ^ "Subrahmanyam, Chaudhuri get Infosys Prize". The Hindu. Bangalore. 24 November 2012. Retrieved 24 November 2012. 
  25. ^ "Professor Manjul Bhargava Has Been Elected to National Academy of Sciences". Retrieved 2014-08-14. 
  26. ^ "List of all 2014 awardees with brief citations". Retrieved 2014-08-24. 
  27. ^ "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. 

External links[edit]