Doonedu at 12:26, 12 March 2026

2026-03-12T12:26:45Z

New page

{{short description|Canadian-American mathematician (born 1974)}}
{{Use dmy dates|date=August 2014}}
{{Infobox scientist
| name = Manjul Bhargava
| honorific_suffix = {{post-nominals|country=GBR|FRS|size=100}}
| caption = Manjul Bhargava in 2014
| image = File:Manjul_Bhargava_FieldsMedal.jpg
| birth_date = {{birth date and age|1974|8|8|df=y}}
| birth_place = [[Hamilton, Ontario]], Canada
| workplaces = [[Princeton University]] [[Leiden University]] [[University of Hyderabad]]
| education = [[Harvard University]] ([[Bachelor of Arts|AB]]) [[Princeton University]] ([[Doctor of Philosophy|PhD]])
| thesis_title = Higher composition laws
| thesis_year = 2001
| thesis_url = https://www.proquest.com/docview/304722465
| doctoral_advisor = [[Andrew Wiles]]<ref name=mathgene>{{MathGenealogy}}</ref>
| doctoral_students = {{plainlist|1=
*[[Wei Ho]]
*[[Alison Miller]]
*[[Evan O'Dorney]]
*[[Melanie Wood]]
*[[Arul Shankar]]
*[[Piper Harron]]
}}
| known_for = [[Bhargava factorial]] [[Bhargava cube]] [[15 and 290 theorems]] [[average rank of elliptic curves]]
| awards = [[Fellow of the Royal Society]] (2019) [[Padma Bhushan]] (2015) [[Fields Medal]] (2014) [[Infosys Prize]] (2012) [[Fermat Prize]] (2011) [[Cole Prize]] (2008) [[Clay Research Award]] (2005) [[SASTRA Ramanujan Prize]] (2005) [[Blumenthal Award]] (2005) [[Merten M. Hasse Prize]] (2003) [[Morgan Prize]] (1996) [[Hoopes Prize]] (1996) [[Hertz Fellowship]] (1996)
| website = {{URL|https://www.math.princeton.edu/people/manjul-bhargava}}
}}

'''Manjul Bhargava''' {{post-nominals|country=GBR|FRS}} (born 8 August 1974)<ref>{{cite book |last=Gallian |first=Joseph A. |year=2009 |title=Contemporary Abstract Algebra |location=Belmont, CA |publisher=Cengage Learning |isbn=978-0-547-16509-7 |page=571 |url=https://books.google.com/books?id=CnH3mlOKpsMC&q=Contemporary%20Abstract%20Algebra&pg=PA571 }}</ref> is a [[Canadian Americans|Canadian-American]] mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at [[Princeton University]], the Stieltjes Professor of Number Theory<ref>{{cite press release|url=http://www.news.leiden.edu/news-2014/fields-medal-for-leiden-professor-of-number-theory-manjul-bhargava.html |title= Fields Medal for Leiden Professor of Number Theory Manjul Bhargava |date= 13 August 2014 |access-date= 13 August 2014}}</ref> 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".<ref>{{cite press release|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2014|publisher=International Mathematical Union|title=Fields Medal 2014|access-date=10 February 2021}}</ref><ref>{{Cite web|date=10 February 2021|title=Press Release - Manjul Bhargava|url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2014/news_release_bhargava.pdf|website=International Mathematical Unioin}}</ref><ref>{{Cite web|title=Fields Medallists 2014 awardees with brief citations {{!}} International Mathematical Union (IMU)|url=https://www.mathunion.org/imu-awards/fields-medal/fields-medal-2014/fields-medallists-2014-awardees-brief-citations|access-date=2021-02-09|website=www.mathunion.org}}</ref> He was also a member of the [[Padma Award]] committee in 2023.<ref>{{Cite web |date=April 2023 |title=Padma Awards Committee |url=https://www.mha.gov.in/sites/default/files/2023-04/PadmaAwardsCommittee_13042023.pdf |access-date=2024-08-21 |website=[[Ministry of Home Affairs (India)|Ministry of Home Affairs]] }}</ref>

In February 2026, he became the first president of the [[National Museum of Mathematics]] (MoMath) in New York city.<ref>{{Cite web | date=2026-03-12 | title=National Museum of Mathematics Names Fields Medalist Dr. Manjul Bhargava as First President | url=https://www.citybiz.co/article/812792/national-museum-of-mathematics-names-fields-medalist-dr-manjul-bhargava-as-first-president/ | access-date=2026-03-12}}</ref>

==Education and career==
Bhargava was born to an [[India]]n family in [[Hamilton, Ontario]], Canada, but grew up and attended school primarily on [[Long Island]], [[New York (state)|New York]]. His mother Mira Bhargava, a mathematician at [[Hofstra University]], was his first mathematics teacher.<ref>{{cite web|url=https://paw.princeton.edu/article/play-fields-math |title=At Play in the Fields of Math |date=21 January 2016 |access-date=September 29, 2016}}</ref><ref>{{cite web|url=http://news.rediff.com/specials/2009/mar/21/fareed-zakaria-is-india-abroad-person-of-the-year.htm |title=Fareed Zakaria is India Abroad Person of the Year — Rediff.com India News |publisher=News.rediff.com |date=2009-03-21 |access-date=2014-08-14}}</ref> He completed all of his high school math and [[computer science]] courses by age 14.<ref>{{cite web|url=http://www.indiaabroad-digital.com/indiaabroad/personoftheyear/?pg=29 |title=India Abroad — Archives 2003-2008 |publisher=Indiaabroad-digital.com |date=2009-12-30 |access-date=2014-08-14}}</ref> He attended [[Plainedge High School]] in [[North Massapequa, New York|North Massapequa]], and graduated in 1992 as the class [[valedictorian]]. He obtained his AB from [[Harvard University]] in 1996, where he was elected to [[Phi Beta Kappa]]. For his research as an undergraduate, he was awarded the 1996 [[Morgan Prize]]. Bhargava went on to pursue graduate studies at Princeton University, where he completed a doctoral dissertation titled "Higher composition laws" under the supervision of [[Andrew Wiles]] and received his PhD in 2001, with the support of a [[Hertz Foundation|Hertz Fellowship]].<ref>{{Cite book |last=Bhargava |first=Manjul |url=https://catalog.princeton.edu/catalog/3399787 |title=Higher composition laws |publisher=[[Princeton University]] |year=2001 |isbn=978-0-493-19386-1 |editor-last=Wiles |editor-first=Andrew |language=en}}</ref> He was a visiting scholar at the [[Institute for Advanced Study]] in 2001–02,<ref>{{cite web|url=http://www.ias.edu/people/cos/ |title=Institute for Advanced Study: A Community of Scholars |publisher=Ias.edu |access-date=2014-08-14}}</ref> 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 has also studied the [[tabla]] under gurus such as [[Zakir Hussain (musician)|Zakir Hussain]].<ref>{{cite web|url=https://www.princeton.edu/pr/pwb/03/1208/1b.shtml |title=Bhargava strikes balance among many interests |publisher=Princeton.edu |date=2003-12-08 |access-date=2014-08-14}}</ref> He also studied [[Sanskrit]] from his grandfather Purushottam Lal Bhargava, a scholar of Sanskrit and ancient Indian history.<ref>An International Conference in Honor of the 100th Birth Anniversary of Professor P. L. Bhargava {{usurped|1=[https://web.archive.org/web/20100304065219/http://plbhargava-conference.org/bio.htm]}}</ref><ref name="Fields Medal Winner Bhargava">{{cite web|url=http://www.businessinsider.com/fields-medal-winner-bhargava-2014-8 |title=Fields Medal Winner Bhargava |publisher=Business Insider |access-date=2014-08-14}}</ref> He is an admirer of Sanskrit poetry.<ref name="TOI-20140818">{{cite news|url=http://timesofindia.indiatimes.com/india/Interest-at-home-among-NRIs-resurrects-Sanskrit/articleshow/40354569.cms|title=Interest at home, among NRIs resurrects Sanskrit|last=Dasgupta|first=Sucheta|date=2014-08-18|work=Times of India|access-date=18 August 2014}}</ref>

==Career and research==
Bhargava’s PhD thesis generalized [[Gauss]]'s classical law for composition of [[binary quadratic form]]s to many other situations. One major use of his results is the parametrization of quartic and quintic orders in [[Algebraic number field|number fields]], thus allowing the study of the asymptotic behavior of the arithmetic properties of these orders and fields.

His research also includes fundamental contributions to the [[representation theory]] of [[quadratic form]]s, to [[interpolation theory|interpolation problems]] and [[p-adic analysis]], to the study of [[ideal class group]]s of [[algebraic number field]]s, and to the arithmetic theory of [[elliptic curve]]s.<ref>{{cite web |url=http://www.claymath.org/fas/research_fellows/Bhargava/ |title=Fellows and Scholars | Clay Mathematics Institute |publisher=Claymath.org |access-date=2014-08-14 |archive-date=17 August 2014 |archive-url=https://web.archive.org/web/20140817060023/http://www.claymath.org/fas/research_fellows/Bhargava |url-status=dead }}</ref> A short list of his specific mathematical contributions are:

*Fourteen new Gauss-style composition laws.
*Determination of the asymptotic density of [[discriminant]]s of quartic and [[Algebraic number field|quintic number fields]].
*Proofs of the first-known cases of the [[Cohen-Lenstra-Martinet heuristics]] for [[ideal class group|class groups]].
*Proof of the [[15 and 290 theorems|15 theorem]], including an extension of the theorem to other number sets such as the odd numbers and the [[prime number]]s.
*Proof (with Jonathan Hanke) of the [[15 and 290 theorems|290 theorem]].
*A novel [[generalization]] of the [[factorial]] function, [[Bhargava factorial]],<ref name="Bhargava Factorial Function Generalization">{{cite journal | last=Bhargava | first=Manjul | title=The Factorial Function and Generalizations | journal=The American Mathematical Monthly | publisher=Informa UK Limited | volume=107 | issue=9 | year=2000 | issn=0002-9890 | doi=10.1080/00029890.2000.12005273 | pages=783–799| s2cid=18356188 }}</ref> providing an answer to a decades-old question of [[George Pólya]].<ref name="Walter de Gruyter GmbH pp. 97–116">{{cite journal | title=Über ganzwertige Polynome in algebraischen Zahlkörpern. | journal=Journal für die reine und angewandte Mathematik (Crelle's Journal) | publisher=Walter de Gruyter GmbH | volume=1919 | issue=149 | date=1919-01-01 | issn=0075-4102 | doi=10.1515/crll.1919.149.97 | pages=97–116| last1=Pólya | first1=Georg | s2cid=120316910 }}</ref>
*Proof (with Arul Shankar) that the average [[Rank of an elliptic curve|rank]] of all [[elliptic curve]]s 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 Swinnerton-Dyer conjecture]] for a positive proportion of elliptic curves.<ref>{{Cite journal |last1=Bhargava |first1=Manjul |author-link=Manjul Bhargava |last2=Shankar |first2=Arul |author-link2=Arul Shankar |title=Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 |year=2015 |journal=[[Annals of Mathematics]] |volume=181 |issue=2 |pages=587–621 |doi=10.4007/annals.2015.181.2.4 |arxiv=1007.0052|s2cid=1456959 }}</ref>

==Awards and honours==
[[File:Four_Fields_medallists_plus_epsilon.jpg|thumb|Four Fields medallists left to right ([[:en:Artur Avila|Artur Avila]], [[:en:Martin Hairer|Martin Hairer]] (at back), [[:en:Maryam Mirzakhani|Maryam Mirzakhani]], with Maryam's daughter Anahita) and Bhargava at the ICM 2014 in Seoul]]
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.

He received the [[Morgan Prize]] in 1996.<ref>{{cite web|url=https://www.ams.org/notices/199612/comm-morgan.pdf |title=1996 AMS-MAA-SIAM Morgan Prize |access-date=2014-08-14}}</ref> and [[Hertz Fellowship]]<ref>{{cite web|url=http://www.hertzfoundation.org/dx/fellows/fellows.aspx |title=Hertz Foundation Fellows: Rare individuals elevate and inspire us through bold thinking and leadership. |access-date=2015-09-09}}</ref> He was named one of ''[[Popular Science]]'' magazine's "Brilliant 10" in November 2002. He then received a [[Clay Mathematics Institute|Clay]] 5-year Research Fellowship and the Merten M. Hasse Prize from the [[Mathematical Association of America|MAA]] in 2003,<ref>{{cite web |url=http://www.maa.org/awards/hasse.html |title=About the MAA |publisher=Maa.org |access-date=2014-08-14 |archive-date=10 September 1999 |archive-url=https://web.archive.org/web/19990910005212/http://www.maa.org/awards/hasse.html |url-status=dead }}</ref> the [[Clay Research Award]], the [[SASTRA Ramanujan Prize]], 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:<ref>[http://www.dailyprincetonian.com/2005/10/11/13413/ Bhargava GS '98 awarded Clay Research prize] {{webarchive |url=https://web.archive.org/web/20110614221559/http://www.dailyprincetonian.com/2005/10/11/13413/ |date=14 June 2011 }}</ref>

{{blockquote|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.}}

In 2008, Bhargava was awarded the [[American Mathematical Society]]'s [[Cole Prize]].<ref>{{Cite journal |date=April 2008 |title=2008 Cole Prize in Number Theory |url=https://www.ams.org/notices/200804/tx080400497p.pdf |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |volume=55 |issue=4 |pages=497–498}}</ref> The citation reads:

{{blockquote|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.<ref>{{Citation|last=Rajesh Karkera|title=The India Abroad Face of the Future Award - Manjul Bhargava|date=2009-03-22|url=https://www.youtube.com/watch?v=pimiDwd0E_A |archive-url=https://ghostarchive.org/varchive/youtube/20211214/pimiDwd0E_A |archive-date=2021-12-14 |url-status=live|access-date=2018-07-17}}{{cbignore}}</ref> In 2014, the same publication gave the India Abroad Publisher's Prize for Special Excellence.<ref>{{Citation|last=Rajesh Karkera|title=The India Abroad Publisher's Special Award for Excellence 2014: Manjul Bhargava|date=2015-06-13|url=https://www.youtube.com/watch?v=2JJYi0OilWM |archive-url=https://ghostarchive.org/varchive/youtube/20211214/2JJYi0OilWM |archive-date=2021-12-14 |url-status=live|access-date=2018-07-17}}{{cbignore}}</ref>

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".<ref>[http://www.math.univ-toulouse.fr/PrixFermat Fermat Prize 2011] {{webarchive |url=https://web.archive.org/web/20111103125517/http://www.math.univ-toulouse.fr/PrixFermat |date=3 November 2011 }}</ref> In 2012, Bhargava was named an inaugural recipient of the Simons Investigator Award,<ref>{{cite web|url=http://foundationcenter.org/pnd/news/story.jhtml?id=386600006 |title=Simons Investigator Award Recipients in Math, Physics, and Computer Science Announced |publisher=Foundationcenter.org |date=2012-07-24 |access-date=2014-08-14}}</ref> and became a fellow of the [[American Mathematical Society]] in its inaugural class of fellows.<ref>{{Cite web |title=List of Fellows of the American Mathematical Society |url=https://www.ams.org/cgi-bin/fellows/fellows.cgi |access-date=2012-11-10 |website=[[American Mathematical Society]]}}</ref> 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".<ref name="hindu">{{cite news
| url=http://www.thehindu.com/news/subrahmanyam-chaudhuri-get-infosys-prize/article4127589.ece
| title=Subrahmanyam, Chaudhuri get Infosys Prize
| work=[[The Hindu]]
| date=24 November 2012
| access-date=24 November 2012
| location=[[Bangalore]]}}</ref>

In 2013, he was elected to the [[National Academy of Sciences]].<ref name="princeton1">{{cite web |url=http://www.math.princeton.edu/news/home-page/professor-manjul-bhargava-has-been-elected-national-academy-sciences |title=Professor Manjul Bhargava Has Been Elected to National Academy of Sciences |publisher=Math.princeton.edu |access-date=2014-08-14 |url-status=dead |archive-url=https://web.archive.org/web/20141023054921/http://www.math.princeton.edu/news/home-page/professor-manjul-bhargava-has-been-elected-national-academy-sciences |archive-date=23 October 2014 |df=dmy-all }}</ref>

In 2014, Bhargava was awarded the [[Fields Medal]] at the [[International Congress of Mathematicians]] in [[Seoul]]<ref name="Fields Medal Winner Bhargava"/> 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".<ref>{{cite web |url=http://www.mathunion.org/general/prizes/2014/prize-citations/ |title=List of all 2014 awardees with brief citations |publisher=mathunion.org |access-date=2014-08-24 |archive-date=11 November 2017 |archive-url=https://web.archive.org/web/20171111174206/http://www.mathunion.org/general/prizes/2014/prize-citations |url-status=dead }}</ref>

In 2015, he was awarded the [[Padma Bhushan]], the third-highest civilian award of India.<ref name="Padma Bhushan">{{cite web |url=http://pib.nic.in/newsite/PrintRelease.aspx?relid=114952 |title=This Year's Padma Awards announced |publisher=[[Ministry of Home Affairs (India)|Ministry of Home Affairs]] |date=25 January 2015 |access-date=2 February 2015 |url-status=dead |archive-url=https://web.archive.org/web/20150128022143/http://pib.nic.in/newsite/PrintRelease.aspx?relid=114952 |archive-date=28 January 2015 }}</ref>

In 2017, Bhargava was elected as a member of the [[American Academy of Arts and Sciences]].<ref>{{Cite web|title=Manjul Bhargava|url=https://www.amacad.org/person/manjul-bhargava|website=American Academy of Arts & Sciences|language=en|access-date=2020-05-13}}</ref> 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.<ref>[https://www.prweb.com/releases/momath_announces_first_distinguished_chair_for_the_public_dissemination_of_mathematics_first_visiting_professorship_in_u_s_dedicated_to_raising_public_awareness_of_math/prweb15669001.htm MoMath Announces First Distinguished Chair for the Public Dissemination of Mathematics] The National Museum of Mathematics, August 2, 2018</ref> Bhargava was conferred a Fellowship at the Royal Society in 2019.<ref>{{cite web|url=https://royalsociety.org/news/2019/04/royal-society-announces-2019-fellows|title=Distinguished scientists elected as Fellows and Foreign Members of the Royal Society}}</ref>

==Selected publications==

* {{cite journal
| last = Bhargava
| first = Manjul
| url = https://maa.org/sites/default/files/pdf/upload_library/22/Hasse/00029890.di021346.02p0064l.pdf
| archive-url = https://web.archive.org/web/20160303182741/https://maa.org/sites/default/files/pdf/upload_library/22/Hasse/00029890.di021346.02p0064l.pdf
| url-status = dead
| archive-date = 2016-03-03
| title = The Factorial Function and Generalizations
| journal = The American Mathematical Monthly
| volume = 107
| year = 2000
| pages = 783–799
| doi = 10.2307/2695734
| issue = 9
| jstor = 2695734
| citeseerx = 10.1.1.585.2265
}}
* {{cite journal
| last = Bhargava
| first = Manjul
| url = http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n1-p03.pdf
| title = Higher Composition Laws I: A New View on Gauss Composition, and Quadratic Generalizations
| journal = Annals of Mathematics
| volume = 159
| year = 2004
| pages = 217–250
| doi = 10.4007/annals.2004.159.217
| doi-access = free
}}
* {{cite journal
| last = Bhargava
| first = Manjul
| url = http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n2-p09.pdf
| title = Higher Composition Laws II: On Cubic Analogues of Gauss Composition
| journal = Annals of Mathematics
| volume = 159
| year = 2004
| pages = 865–886
| doi = 10.4007/annals.2004.159.865
| issue = 2
| doi-access = free
}}
* {{cite journal
| last = Bhargava
| first = Manjul
| url = http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n3-p08.pdf
| title = Higher Composition Laws III: The Parametrization of Quartic Rings
| journal = Annals of Mathematics
| volume = 159
| year = 2004
| pages = 1329–1360
| doi = 10.4007/annals.2004.159.1329
| issue = 3
| doi-access = free
}}
* {{cite journal
| last = Bhargava
| first = Manjul
| url = http://annals.math.princeton.edu/wp-content/uploads/annals-v162-n2-p10.pdf
| title = The density of discriminants of quartic rings and fields
| journal = Annals of Mathematics
| volume = 162
| issue = 2
| year = 2005
| pages = 1031–1063
| doi = 10.4007/annals.2005.162.1031
| s2cid = 53482033
| doi-access = free
}}
* {{cite journal
| last = Bhargava
| first = Manjul
| url = http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n1-p02.pdf
| title = Higher composition laws IV: The parametrization of quintic rings
| journal = Annals of Mathematics
| volume = 167
| year = 2008
| pages = 53–94
| doi = 10.4007/annals.2008.167.53
| doi-access = free
}}
* {{cite journal
| last = Bhargava
| first = Manjul
| url = http://annals.math.princeton.edu/wp-content/uploads/annals-v172-n3-p02-p.pdf
| title = The density of discriminants of quintic rings and fields
| journal = Annals of Mathematics
| volume = 172
| issue = 3
| year = 2010
| pages = 1559–1591
| doi = 10.4007/annals.2010.172.1559
| arxiv = 1005.5578
| bibcode = 2010arXiv1005.5578B
}}
* {{cite journal
|last1=Bhargava
|first1=Manjul
|last2=Satriano
|first2=Matthew
|title=On a notion of "Galois closure" for extensions of rings
|year=2014
|journal = [[Journal of the European Mathematical Society]]
|mr=3273311
|doi=10.4171/JEMS/478
|arxiv=1006.2562
|volume=16
|issue=9
|pages=1881–1913
|s2cid=18493502
}}
* {{cite journal | last1=Bhargava | first1=Manjul | last2=Shankar | first2=Arul | title=Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves | year=2015 | journal=[[Annals of Mathematics]] | volume=181 | issue=1 | pages=191–242 | mr=3272925 | doi=10.4007/annals.2015.181.1.3| arxiv=1006.1002 | s2cid=111383310 }}
* {{Cite journal |last1=Bhargava |first1=Manjul |last2=Shankar |first2=Arul |title=Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 |year=2015 |journal=[[Annals of Mathematics]] |volume=181 |issue=2 |pages=587–621 |doi=10.4007/annals.2015.181.2.4 |arxiv=1007.0052|s2cid=1456959 }}

==See also==
* [[Indians in the New York City metropolitan area]]

==References==
{{Reflist|2}}

==External links==
*[https://www.npr.org/templates/story/story.php?storyId=4111253 Manjul Bhargava at NPR]
*[http://www.icts.res.in/people/9/details/41/ Manjul Bhargava at ICTS]
*[https://web.archive.org/web/20061116002458/http://www.hindu.com/2005/10/14/stories/2005101405840500.htm Article in The Hindu on Bhargava winning the SASTRA prize]
*[https://www.princeton.edu/pr/pwb/03/1208/1b.shtml Princeton University article by Steven Schultz]

{{FRS 2019}}
{{PadmaBhushanAwardRecipients 2010–19}}
{{Fields medalists}}
{{Recipients of SASTRA Ramanujan Prize winners|state=collapsed}}
{{Authority control}}
{{Portal bar|Mathematics|Biography}}

{{DEFAULTSORT:Bhargava, Manjul}}
[[Category:1974 births]]
[[Category:Living people]]
[[Category:21st-century Indian mathematicians]]
[[Category:Canadian mathematicians]]
[[Category:Canadian people of Indian descent]]
[[Category:Clay Research Award recipients]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Foreign fellows of the Indian National Science Academy]]
[[Category:Indian number theorists]]
[[Category:Fields Medalists]]
[[Category:Harvard University alumni]]
[[Category:Institute for Advanced Study visiting scholars]]
[[Category:Academic staff of Leiden University]]
[[Category:Princeton University alumni]]
[[Category:Princeton University faculty]]
[[Category:Academics from Hamilton, Ontario]]
[[Category:People from North Massapequa, New York]]
[[Category:American academics of Indian descent]]
[[Category:Recipients of the Padma Bhushan in science & engineering]]
[[Category:Simons Investigator]]
[[Category:Canadian fellows of the Royal Society]]
[[Category:Indian fellows of the Royal Society]]

Manjul Bhargava - Revision history

Doonedu at 12:26, 12 March 2026