Manjul Bhargava

Revision as of 09:06, 14 August 2014

The pinnacle: The Fields Medal 2014

Indian-origin wizard wins 'Nobel Prize' of Mathematics

Chidanand Rajghatta,TNN | Aug 13, 2014 The Times of India

Manjul Bhargava was among the four winners of the 2014 Fields Medal, widely considered the Nobel Prize for Mathematics that has been mostly dominated by white men (Americans, Russians, French, and Britons: 38 medals between them) since it was instituted in 1936.

The award going to Princeton University's Manjul Bhargava, a Canadian-American maths wizard was no surprise. Although he is the first person of Indian origin, he was the hot favourite in pre-award polls among peers. Which is not surprising for someone who became a tenured full professor within two years of finishing graduate school, an Ivy League record, and the second youngest full professor in Princeton's history.

In early August 2014 as speculation heated up about possible 2014 winners of Fields Medal, an online poll put Bhargava on top with 516 votes

The award

One to four Fields Medals are awarded once every four years to mathematicians under the age of 40 years at the International Congres of the International Mathematical Union (IMU), which meets every four years. (Hyderabad hosted it in 2010). Seoul is the venue of the 2014 presentation

The award is the highest recognition in the world of mathematics.

The Fields Medal Citation

Manjul Bhargava

is awarded a Fields Medal 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.

Bhargava’s thesis provided a reformulation of Gauss’s law for the composition of two binary quadratic forms. He showed that the orbits of the group SL(2, Z)3 on the tensor product of three copies of the standard integral representation correspond to quadratic rings (rings of rank 2 over Z) together with three ideal classes whose product is trivial. This recovers Gauss’s composition law in an original and computationally effective manner. He then studied orbits in more complicated integral representations, which correspond to cubic, quartic, and quintic rings, and counted the number of such rings with bounded discriminant.

Bhargava next turned to the study of representations with a polynomial ring of invariants. The simplest such representation is given by the action of PGL(2, Z) on the space of binary quartic forms. This has two independent invariants, which are related to the moduli of elliptic curves. Together with his student Arul Shankar, Bhargava used delicate estimates on the number of integral orbits of bounded height to bound the average rank of elliptic curves. Generalizing these methods to curves of higher genus, he recently showed that most hyperelliptic curves of genus at least two have no rational points.

Bhargava’s work is based both on a deep understanding of the representations of arithmetic groups and a unique blend of algebraic and analytic expertise.

Manjul Bhargava’s work

Mathematics offers solutions to everyday issues from airline scheduling to Internet security, even though many practitioners pursue esoteric problems described in dense language incomprehensible to the layman. Bhargava's PhD thesis is said to have helped in the "determination of the asymptotic density of discriminants of quartic and quintic number fields."

Previous prizes and honours

Recognition came early. He has often recounted how in Grade 3, he became curious about how many oranges it takes to make a pyramid.

Manjul has also collaborated with many Indian mathematicians, and his work with fellow Princeton scholar Arul Shankar, his PhD student, won them the Fermat Prize in 2011. Manjul's own PhD advisor was Andrew Wiles, famous for proving Fermat's last theorem.

Bhargava 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." That came on top of almost every other top prize in maths, from the SASTRA Ramanujan Prize in 2005 to the American mathematical Society's Cole Prize in 2008. So the Fields Medal comes as no great surprise to the mathematical community in the US or in India.

Family

Although a Canadian-American who was born in Hamilton, Ontario, Bhargava is no stranger to India or to Indian mathematicians. Indeed, his mother, Mira Bhargava, is herself a rare female mathematician, teaching at Hofstra University (another well-known female Indian-American mathematician is Bhama Srinivasan at the University of Chicago).

His mathematician mother and chemist father were well-to-do: they indulged him with oranges till he figured out the pyramid answer, which was not long coming.

Other interests

That's not all. Before you think all he does is crunch numbers, Bhargava is also an accomplished tabla player (tutored by Zakir Hussain) and has the number on Sanskrit, which he learned from his grandfather Purushottam Lal Bhargava, was the head of the Sanskrit department of the University of Rajasthan, during family visits to Jaipur. He sees close links between his three loves noting how beats of tabla and rhythms of Sanskrit poetry are highly mathematical.