Manjul Bhargava
Encyclopedia
Manjul Bhargava (born August 8, 1974) 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
.
and his father is a chemist. Bhargava grew up in Long Island
, NY. Manjul Bhargava completed all of his high school math and computer courses by age 14. 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. He is still the youngest standing tenured full professor at Princeton.
Bhargava is also an accomplished tabla
player, having studied under gurus such as Zakir Hussain
. . He has also studied Sanskrit
. His grandfather Dr. Purushottam Lal Bhargava is a well-known scholar of Sanskrit and ancient Indian history.
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. A short list of his specific mathematical contributions are:
In July 2010 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture
for a positive proportion of elliptic curves.
(professor at Princeton at age 24).
Bhargava has won several awards for his research, including the Morgan Prize
in 1996, the Merten M. Hasse Prize from the MAA
in 2003, 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:
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
. The citation reads:
In 2011, Bhargava was awarded the Fermat Prize
for his work on various generalizations of Davenport-Heilbronn estimates and its recent remarkable results (with Arul Shankar) on the average rank of elliptic curves
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. He is known primarily for his research contributions to algebraic number theory
Algebraic number theory
Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number field K/Q, and studying their algebraic properties such as factorization,...
and representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
.
Biography
Bhargava's mother, Mira Bhargava, is a mathematician at Hofstra UniversityHofstra University
Hofstra University is a private, nonsectarian institution of higher learning located in the Village of Hempstead, New York, United States, about east of New York City: less than an hour away by train or car...
and his father is a chemist. Bhargava grew up in Long Island
Long Island
Long Island is an island located in the southeast part of the U.S. state of New York, just east of Manhattan. Stretching northeast into the Atlantic Ocean, Long Island contains four counties, two of which are boroughs of New York City , and two of which are mainly suburban...
, NY. Manjul Bhargava completed all of his high school math and computer courses by age 14. He attended Plainedge High School, graduating in 1992 as the class valedictorian. He obtained his B.A. from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1996 and received his doctorate from Princeton in 2001, working under Andrew Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
. 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. He is still the youngest standing tenured full professor at Princeton.
Bhargava is also an accomplished tabla
Tabla
The tabla is a popular Indian percussion instrument used in Hindustani classical music and in popular and devotional music of the Indian subcontinent. The instrument consists of a pair of hand drums of contrasting sizes and timbres...
player, having studied under gurus such as Zakir Hussain
Zakir Hussain (musician)
Zakir Hussain , , is an Indian tabla player, musical producer, film actor and composer.-Early life:Hussain was born in Mumbai, India to the legendary tabla player Alla Rakha. He attended St...
. . He has also studied Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
. 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. 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 theorem15 theoremThe 15 theorem of John H. Conway and W. A. Schneeberger , proved in 1993, states that if an integral quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers...
, including an extension of the theorem to other number sets such as the odd numbers and the prime numberPrime numberA prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s. - Proof of the 290 theorem.
- A novel generalizationGeneralizationA generalization of a concept is an extension of the concept to less-specific criteria. It is a foundational element of logic and human reasoning. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements. As such, it...
of the factorial function, resolving a decades-old conjecture by George PólyaGeorge PólyaGeorge Pólya was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory...
.
In July 2010 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture
Birch and Swinnerton-Dyer conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture is an open problem in the field of number theory. Its status as one of the most challenging mathematical questions has become widely recognized; the conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay...
for a positive proportion of elliptic curves.
Awards and Honors
Bhargava is the second youngest full professor in Princeton University's history, after Charles FeffermanCharles Fefferman
Charles Louis Fefferman is an American mathematician at Princeton University. His primary field of research is mathematical analysis....
(professor at Princeton at age 24).
Bhargava has won several awards for his research, including the Morgan Prize
Morgan Prize
The Morgan Prize in Mathematics may refer to:* Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student awarded jointly by the American Mathematical Society, Mathematical Association of America and Society for Industrial and Applied Mathematics* De Morgan...
in 1996, the Merten M. Hasse Prize from the MAA
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
in 2003, a Clay
Clay Mathematics Institute
The Clay Mathematics Institute is a private, non-profit foundation, based in Cambridge, Massachusetts. The Institute is dedicated to increasing and disseminating mathematical knowledge. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998...
Research Fellowship, the Clay Research Award
Clay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
in 2005, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics in 2005.
Peter Sarnak
Peter Sarnak
Peter Clive Sarnak is a South African-born mathematician. He has been Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Andrew Wiles, and is an editor of the Annals of Mathematics...
of Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
has said of Bhargava:
He was named one of Popular Science
Popular Science
Popular Science is an American monthly magazine founded in 1872 carrying articles for the general reader on science and technology subjects. Popular Science has won over 58 awards, including the ASME awards for its journalistic excellence in both 2003 and 2004...
Magazine’s “Brilliant 10” in November 2002. He recently won the American Mathematical Society
American Mathematical Society
The American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
's Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
and the $10,000 SASTRA Ramanujan Prize
SASTRA Ramanujan Prize
The SASTRA Ramanujan Prize, founded by Shanmugha Arts, Science, Technology & Research Academy University in Kumbakonam, India, Srinivasa Ramanujan's hometown, is awarded every year to a young mathematician judged to have done outstanding work in Ramanujan's fields of interest...
, shared with Kannan Soundararajan
Kannan Soundararajan
Kannan Soundararajan is an Indian mathematician. He currently is a professor of mathematics at Stanford University. Before moving to Stanford in 2006, he was a faculty at University of Michigan where he pursued his undergraduate studies...
, awarded by SASTRA in 2005 at Tanjavur, India, for his outstanding contributions to number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
.
In 2008, Bhargava was awarded the Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
. The citation reads:
In 2011, Bhargava was awarded the Fermat Prize
Fermat Prize
The Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive:* Statements of variational principles* Foundations of probability and analytic geometry* Number theory....
for his work on various generalizations of Davenport-Heilbronn estimates and its recent remarkable results (with Arul Shankar) on the average rank of elliptic curves