# Manjul Bhargava

Manjul Bhargava | |
---|---|

Born | Hamilton, Ontario | 8 August 1974

Nationality | Canada / United States |

Institutions | Princeton University Leiden University University of Hyderabad |

Alma mater | Harvard University Princeton University |

Doctoral advisor | Andrew Wiles |

Doctoral students | Wei Ho Alison Miller Arul Shankar Melanie Wood |

Known for | higher composition laws 15 and 290 theorems factorial function average rank 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) Blumenthal Award (2005) Hasse Prize (2003) Morgan Prize (1996) Hoopes Prize (1996) Hertz Fellowship (1996) |

### Biography

Manjul Bhargava (given birth to 8 August 1974) is definitely a Canadian-American mathematician of Indian origin. He’s the R. Brandon Fradd Teacher of Mathematics at Princeton College or university, the Stieltjes Teacher of Quantity Theory at Leiden College or university, and also keeps Adjunct Professorships in the Tata Institute of Fundamental Study, the Indian Institute of Technology Bombay, as well as the College or university of Hyderabad. He’s known mainly for his efforts to quantity theory. Bhargava was awarded the Areas Medal in 2014. Based on the International Mathematical Union citation, he was granted the reward “for developing effective new strategies in the geometry of amounts, which he put on count bands of little rank also to bound the common rank of elliptic curves”.

### Education and career

Bhargava was created in Hamilton, Ontario, Canada of parents who all had emigrated from India, and he was raised primarily in Long Isle, NY. His mom Mira Bhargava, a mathematician at Hofstra School, was his initial mathematics instructor. He completed most of his senior high school mathematics and computer research courses by age group 14. He went to Plainedge SENIOR HIGH SCHOOL in North Massapequa, and graduated in 1992 as the course valedictorian. He attained his B.A. from Harvard School in 1996. For his analysis as an undergraduate, he was honored the 1996 Morgan Award. Bhargava continued to get his doctorate from Princeton in 2001, supervised by Andrew Wiles and funded with a Hertz Fellowship. He was a going to scholar on the Institute for Advanced Research in 2001-02, with Harvard College or university in 2002-03. Princeton appointed him being a tenured Total Teacher in 2003. He was appointed towards the Stieltjes Seat in Leiden College or university this year 2010.Bhargava can be an accomplished tabla participant, having studied under experts such as for example Zakir Hussain. He also researched Sanskrit from his grandfather Purushottam Lal Bhargava, a well-known scholar of Sanskrit and historic Indian history. He's an admirer of Sanskrit poetry.

### Contributions

His PhD thesis generalized Gauss's classical rules for structure of binary quadratic forms to numerous other circumstances. One major usage of his outcomes may be the parametrization of quartic and quintic purchases in number areas, thus allowing the analysis of asymptotic behavior of arithmetic properties of the purchases and fields.His research also contains fundamental contributions towards the representation theory of quadratic forms, to interpolation complications and p-adic evaluation, to the analysis of ideal course sets of algebraic amount fields, also to the arithmetic theory of elliptic curves. A brief set of his particular mathematical efforts are: Fourteen brand-new Gauss-style composition laws and regulations. Determination from the asymptotic density of discriminants of quartic and quintic amount fields. Proofs from the initial known cases from the Cohen-Lenstra-Martinet heuristics for course groups. Proof the 15 theorem, including an expansion from the theorem to various other amount sets like the unusual numbers as well as the leading numbers. Resistant (with Jonathan Hanke) from the 290 theorem. A book generalization from the factorial function, Bhargava factorial, resolving a decades-old conjecture by George Pólya. Resistant (with Arul Shankar) that the common rank of most elliptic curves over Q (when purchased by elevation) is certainly bounded. Resistant that a lot of hyperelliptic curves over Q haven't any rational points.In 2015 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for the positive proportion of elliptic curves.

### Awards and honors

Bhargava offers won several honours for his analysis, one of the most prestigious getting the Areas Medal, the best award in neuro-scientific mathematics, which he won in 2014.Bhargava may be the third youngest full teacher in Princeton University's background, after Charles Fefferman and John Pardon.Furthermore, he earned the Morgan Prize and Hertz Fellowship in 1996, a Clay 5-year Analysis Fellowship, the Merten M. Hasse Award in the MAA in 2003, the Clay Analysis Prize in 2005, as well as the Leonard M. and Eleanor B. Blumenthal Prize for the Advancement of Analysis in Pure Mathematics in 2005.Peter Sarnak of Princeton School has said of Bhargava: “ In mathematics he's towards the top end. For a man so young I cannot remember anybody therefore embellished at his age group. He certainly began using a bang and hasn't let it reach his mind, which is uncommon. Obviously he couldn't perform what he will if he wasn't outstanding. It's his remarkable talent that's therefore striking ”He was named among Popular Science Newspaper’s "Brilliant 10" in November 2002. He gained the $10,000 SASTRA Ramanujan Award, distributed to Kannan Soundararajan, honored by SASTRA in 2005 at Thanjavur, India, for his excellent contributions to amount theory.In 2008, Bhargava was awarded the American Mathematical Society's Cole Prize. The citation reads: “ Bhargava’s primary and astonishing contribution may be the breakthrough of laws and regulations of structure on types of higher level. His methods and insights into this issue are dazzling; also in the event regarded by Gauss, they result in a fresh and clearer display of this theory ”In 2011, he was awarded the Fermat Prize for "several generalizations from the Davenport-Heilbronn quotes as well as for his startling latest outcomes (with Arul Shankar) on the common ranking of elliptic curves".In 2011, he delivered the Hedrick lectures from the MAA in Lexington, Kentucky. He was also the 2011 Simons Lecturer at MIT.In 2012, Bhargava was called an inaugural receiver of the Simons Investigator Award, and became a fellow from the American Mathematical Culture in its inaugural class of fellows.He was awarded the 2012 Infosys Award in mathematics for his "extraordinarily primary function in algebraic amount theory, which includes revolutionized how number areas and elliptic curves are counted".In 2013, he was elected towards the Country wide Academy of Sciences.In 2014, Bhargava was awarded the Fields Medal on the International Congress of Mathematicians in Seoul for "growing powerful new strategies in the geometry of numbers, which he put on count bands of small ranking and to destined the average ranking of elliptic curves".In 2015, he was awarded the Padma Bhushan, the 3rd highest civilian award of India.

### Selected publications

Bhargava, Manjul (2000). "The Factorial Function and Generalizations" (PDF). The American Mathematical Once a month. 107 (9): 783–799. doi:10.2307/2695734. Bhargava, Manjul (2004). "Higher Structure Laws I: A FRESH Take on Gauss Structure, and Quadratic Generalizations" (PDF). THE HISTORY of Mathematics. 159: 217–250. doi:10.4007/annals.2004.159.217. Bhargava, Manjul (2004). "Higher Structure Laws and regulations II: On Cubic Analogues of Gauss Structure" (PDF). THE HISTORY of Mathematics. 159 (2): 865–886. doi:10.4007/annals.2004.159.865. Bhargava, Manjul (2004). "Higher Structure Laws and regulations III: The Parametrization of Quartic Bands" (PDF). THE HISTORY of Mathematics. 159 (3): 1329–1360. doi:10.4007/annals.2004.159.1329. Bhargava, Manjul (2005). "The density of discriminants of quartic bands and areas" (PDF). THE HISTORY of Mathematics. 162: 1031–1063. doi:10.4007/annals.2005.162.1031. Bhargava, Manjul (2008). "Higher structure laws and regulations IV: The parametrization of quintic bands" (PDF). THE HISTORY of Mathematics. 167: 53–94. doi:10.4007/annals.2008.167.53. Bhargava, Manjul (2010). "The density of discriminants of quintic bands and areas" (PDF). THE HISTORY of Mathematics. 172: 1559–1591. doi:10.4007/annals.2010.172.1559. Bhargava, Manjul; Satriano, Matthew (2014). "On a concept of "Galois closure" for extensions of bands". Journal from the Western Mathematical Culture. 16 (9): 1881–1913. MR 3273311. arXiv:1006.2562v1 . doi:10.4171/JEMS/478. Bhargava, Manjul; Shankar, Arul (2015). "Binary quartic forms having bounded invariants, as well as the boundedness of the common rank of elliptic curves". Annals of Mathematics. 181 (1): 191–242. MR 3272925. doi:10.4007/annals.2015.181.1.3. Bhargava, Manjul; Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, as well as the existence of the positive percentage 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

Bhargava cube Bhargava factorial

### Notes and references

^ Gallian, Joseph A. (2009). Modern Abstract Algebra(((((Vaishali))))). Belmont, CA: Cengage Learning. p. 571. ISBN 978-0-547-16509-7. ^ "Areas Medal for Leiden Teacher of Amount Theory Manjul Bhargava" (News release). 13 August 2014. Retrieved 13 August 2014. ^ "Set of all 2014 awardees with short citations" (News release). International Mathematical Union. Retrieved 12 August 2014. ^ "At Play in the Areas of Mathematics". Retrieved Sept 29, 2016. ^ "Fareed Zakaria is normally India Overseas Person from the Calendar year — Rediff.com India Information". Information.rediff.com. 2009-03-21. Retrieved 2014-08-14. ^ "India Overseas — Archives 2003-2008". Indiaabroad-digital.com. 2009-12-30. Retrieved 2014-08-14. ^ "Institute for Advanced Research: A Community of Scholars". Ias.edu. Retrieved 2014-08-14. ^ "Bhargava hits stability among many passions". Princeton.edu. 2003-12-08. Retrieved 2014-08-14. ^ "Areas Medal Champion Bhargava". Business Insider. Retrieved 2014-08-14. ^ Dasgupta, Sucheta (2014-08-18). "Curiosity in the home, among NRIs resurrects Sanskrit". Situations of India. Retrieved 18 August 2014. ^ "Fellows and Scholars | Clay Mathematics Institute". Claymath.org. Retrieved 2014-08-14. ^ Bhargava, Manjul; Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, as well as the existence of the positive percentage of elliptic curves having rank 0". Annals of Mathematics. 181 (2): 587–621. arXiv:1007.0052 . doi:10.4007/annals.2015.181.2.4. ^ "Match Manjul Bhargava: The Areas Medal champion for mathematics, who's also a musician". The Financial Situations. 2014-08-14. Retrieved 2017-04-03. ^ "1996 AMS-MAA-SIAM Morgan Award" (PDF). Retrieved 2014-08-14. ^ "Hertz Base Fellows: Rare people elevate and motivate us through vivid thinking and command.". Retrieved 2015-09-09. ^ "About the MAA". Maa.org. Retrieved 2014-08-14. ^ Bhargava GS '98 honored Clay Research award Archived 14 June 2011 on the Wayback Machine. ^ "2008 Cole Award in Amount Theory" (PDF). Retrieved 2014-08-14. ^ Fermat Award 2011 Archived 3 November 2011 on the Wayback Machine. ^ "Earle Raymond Hedrick Lecturers". Maa.org. Retrieved 2014-08-14. ^ "MIT Mathematics | Simons". Mathematics.mit.edu. Retrieved 2014-08-14. ^ "Simons Investigator Award Recipients in Mathematics, Physics, and Pc Research Announced". Foundationcenter.org. 2012-07-24. Retrieved 2014-08-14. ^ Set of Fellows from the American Mathematical Culture, retrieved 2012-11-10. ^ "Subrahmanyam, Chaudhuri obtain Infosys Award". The Hindu. Bangalore. 24 November 2012. Retrieved 24 November 2012. ^ "Teacher Manjul Bhargava CONTINUES TO BE Elected to Country wide Academy of Sciences". Mathematics.princeton.edu. Retrieved 2014-08-14. ^ "Set of all 2014 awardees with short citations". mathunion.org. Retrieved 2014-08-24. ^ "This Year's Padma Honours announced". Ministry of House Affairs. 25 January 2015. Archived from the initial on 26 January 2015. Retrieved 2 Feb 2015.