Manjul Bhargava

Canadian American mathematician

Manjul Bhargava (born 8 August 1974) is a Canadian American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory 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". He was also a member of prestigious Padma award committee 2023.

Bhargava was born to an Indian family in Hamilton, Ontario, Canada, but grew up and attended school primarily on Long Island, New York. His mother Mira Bhargava, a mathematician at Hofstra University, was his first mathematics teacher. He completed all of his high school math and computer science courses by age 14. He attended Plainedge High School in North Massapequa, and graduated in 1992 as the class valedictorian. He obtained his AB from Harvard University in 1996. 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 Fellowship. He was a visiting scholar at the Institute for Advanced Study in 2001–02, 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. He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a well known scholar of Sanskrit and ancient Indian history. He is an admirer of Sanskrit poetry.

Bhargava’s 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 the asymptotic behavior of the 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. A short list of his specific mathematical contributions are:

Fourteen 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 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, providing an answer to a decades old question of 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 Swinnerton Dyer conjecture for a positive proportion of elliptic curves.