Manjul Bhargava: Fields Medal Winner - 2014:
Manjul Bhargava became the first person of Indian origin to win the Fields Medal, at the International Congress of Mathematicians 2014 held in Seoul. Mr. Bhargava, a professor of mathematics (number theory) at Princeton University, was among the four winners who have been awarded the Fields Medal. Fields medal is awarded every four years to the mathematicians below or upto the age of 40 years. Fields medal is considered as the Nobel Prize for mathematics. Manjul Bhargava won this presitigious award 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".
Born in 1974 in Hamilton, Ontario, Canada, Manjul Bhargava grew up in the US and also spent much time in India. He received his PhD in 2001 from Princeton University and became a professor in 2003. Mira Bhargava, his mother, is herself a rare female mathematician, teaching at Hofstra University.
Manjul has won the Fermat Prize in 2011 with his PhD student, Arul Shankar. Manjul's own PhD advisor was Andrew Wiles, famous for proving Fermat's last theorem. Mr. Bhargava was awarded the 2012 Infosys Prize in mathematics for his work in "algebraic number theory". This theory has directed a way in which number fields and elliptic curves are counted. Mr. Bhargava's honours include the Merten Hasse Prize of the Mathematical Association of America (2003), the SASTRA Ramanujan Prize (2005), the Cole Prize in Number Theory of the American Mathematical Society (2008). He was elected to the US National Academy of Sciences in 2013.
Manjul Bhargava is not only facinated by the numbers, he is also an accomplished tabla player (tutored by Zakir Hussain). He also studied Sanskrit from his grandfather Purushottam Lal Bhargava, a well-known scholar of Sanskrit and ancient Indian history.
- 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, resolving a decades-old conjecture by George Pólya.
- Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded.
- In July 2010 Manjul Bhargava and Arul Shankar proved the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.