Dr. Manjul Bhargava, Professor
 (Ref:http://en.wikipedia.org/wiki/Manjul_Bhargava [1])
Dr. Manjul Bhargava, born August 8, 1974 in Canada. Bhargava grew up
primarily in the USA and also spent much time in India. He obtained his B.A.
from Harvard in 1996. For his research as an undergraduate, he was awarded the
1996 Morgan Prize. He received his PhD in 2001,from Princeton University, under
the direction of Andrew Wiles. Bhargava became a professor at Princeton in
2003. Prof. Bhargava’s contribution in number theory has had a unique influence
on the maths research and its community.  

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Prof. Bhargava is not only a great mathematician but also an accomplished
tabla player too, he is the pupil of great guru (Ustad/Teacher) Zakir Hussain Sahab. He is very close to Indian culture and also learn studied Sanskrit from
his grandfather, who is a reputed and well known pandit of Sanskrit and Indian
History. Prof. Bhargava is an outstanding communicator, he has won several teaching awards, and his lucid and
elegant writing has garnered a prize for exposition.
 Dr. Manjul Bhargava, Professor
Recently, Prof. Manjul Bhargava has been awarded the
prestigious Fields Medal at the International Mathematical Union’s (IMU)
International Congress of Mathematicians, ICM, in Seoul. The Fields Medal is
considered as the Nobel Prize of Mathematics for being traditionally regarded
as the most prestigious award in the field of mathematics.
Prof. Bhargava was awarded the medal for
developing powerful new methods in geometry of numbers, which he applied to
count rings of small rank and to bound the average rank of elliptic curves.

techniques and insights … are dazzling; even in the case considered by Gauss,
they lead to a new and clearer presentation of that theory”, the Cole
Prize citation says.

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Bhargava had stopped with this discovery, his work would already be quite
remarkable. But Bhargava has gone on to use his composition laws to solve a new
case of one of the fundamental questions of number theory, that of asymptotic
enumeration of number fields of given degree, as the discriminant grows. Bhargava
used his new composition laws to solve the degree 4 case, brilliantly
overcoming very serious analytic problems that had completely blocked all
previous work on the problem.”[2].


 Dr. Manjul Bhargava, Professor

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 [1]: 

  • 14 new Gauss-style composition laws.
  • Determination of the asymptotic density of discriminates
    of quadratic and quintic number fields.
  • Proofs of the first known cases of the Cohen-Lenstra-Martinent
    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 Polya.
  • Proof (with Arul Shankar) that the average rank of all elliptic curves over Q
    (when ordered by height) is bounded.

How Bhargava follow and extend the work of work of Brahmagupta in
628 C.E. and Carl
Friedrich Gauss
(1777-1855) ? 


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A very interesting reality is behind of this that how
does a graduate student read the monumental Disquisitiones Arithmeticae, a book about number
theory by Carl Friedrich Gauss, get inspiration and keep the idea
in his mind and how that idea takes a shape when he was playing with the Rubik’s
cubes [3]. Read more..
Leonard M. and Eleanor B. Blumenthal Award for the
Advancement of Research in Pure
Mathematics, January 2005. 
Packard Foundation Fellowship in Science and Engineering,
November 2004.
The Mathematical Association of America’s Merten M.
Hasse Prize for Exposition, August 2003. 
Named one of Popular Science Magazine’s “Brilliant 10”,
November 2002.
Named first Five-Year Long-Term Prize Fellow of the
Clay Mathematics Institute, 2000.
AMS–MAA–SIAM Frank and Brennie Morgan Prize for
Outstanding Undergraduate Research in Mathematics, 1997.
Hertz Foundation Graduate Fellowship in Mathematics,
Hoopes Prize for Excellence in Scholarly Work and
Research, Harvard University, 1996.
Harvard University Salutatorian, 1996.
Elected Phi Beta Kappa, Harvard University, 1995.
Three–time recipient of the Derek Bok Award for
Excellence in Teaching; nominated for Levin-son Teaching Prize, Harvard
University, 1993–1995.
Detur Prize for Outstanding Academic Achievement, Harvard
University, 1993.
Winner of the New York State Science Talent Search,
Plainedge High School Valedictorian, 1992

Research Positions [4]

Professor, Princeton University, July 2003–.
Visiting Assistant Professor, Harvard University, Spring
Visiting Mathematician, Princeton University, Fall 2001–Fall
Clay Mathematics Institute, Cambridge, 2000–.
AT&T Labs Research, Florham Park, NJ, Summer 1997.
Center for Communications Research, Princeton, Summer 1996.
Duluth Summer Research Program, Summer 1995.
National Security Agency, Summer 1994.

Bhargava has recently made a great advance in the arithmetic theory of elliptic
curves. Together with his student, Arul Shankar, he determines the average order
of the Selmer group Sel(E, m)for an elliptic curve Eover Q, when m= 2,3,4,5 [5].

also used his expansion of the geometry of numbers to look at the more general
case of higher degree hyperelliptic curves.[6]


Link of his research papers: