Manjul Bhargava Thesis

I wish to express our appreciation to Professor Andrews for sponsoring the Ramanujan Colloquium.

Born 8 August 1974, Hamilton, Ontario, Canada Fields Medal (2014) “for developing 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.” Manjul Bhargava was born in Canada but grew up in Long Island, New York.

Manjul Bhargava found methods to compose forms of higher order (with exponents larger than 2 in the exponents of the polynomials) in a similar way as Gauss did for the quadratic forms, and he even described these methods by means of a general theory. Hanke he also proved a number theoretic conjecture of John Horton Conway (*1937) dealing with a certain subclass of integral quadratic forms.

Bhargava also focused on one of the Millenium Problems, the conjecture of Birch and Swinnerton-Dyer which is a statement about elliptic curves, certain polynomials of degree 3.

The Ramanujan Colloquium will be held in the Spring during the two months when Professor Andrews is here.

The First Ramanujan Colloquium will be on Monday, March 19, 2007 by Professor Manjul Bhargava of Princeton University.

The Department has one of the strongest programs in areas of mathematics influenced by Ramanujan and the presence of Professor Andrews has raised the stature of this program significantly.

Thus it was felt that it would be well worthwhile to launch this new colloquium series.

Distinguished Visiting Professor George Andrews has generously offered to sponsor this colloquium for the first four years.This prize is awarded to mathematicians not exceeding the age of 32 for outstanding contributions to areas influenced by Ramanujan.In his talk at SASTRA in Ramanujan’s hometown Kumbakonam, India, on Ramanujan’s birthday, December 22, 2005, Bhargava announced the complete solution to a problem of Ramanujan on universal quadratic forms.Manjul Bhargava works in the field of number theory.He became famous with a series of four papers in the “Annals of Mathematics” in which he generalized the composition of binary integral quadratic forms.He was a child prodigy; his mother was a maths teacher, his father worked as a chemist.After high school, Bhargava studied at Harvard University (Bachelor 1996). studies at Princeton, advised by number theorist Andrew Wiles who is famous for his proof of Fermat’s Last Theorem from the 1990s.(They have little to do with ellipses, but are formulas that have been found when computing the length of ellipses.) Bhargava proved together with Arul Shankar among others that a positive measure of elliptic curves over the rational numbers satisfies the conjecture of Birch and Swinnerton-Dyer. For Manjul Bhargava, the counting numbers don't simply line themselves up in a demure row.Hasse Prize for Exposition of the Mathematical Association of America (2003).He is also an accomplished tabla player who has performed in concert halls, and he is an admirer of Sanskrit poetry.

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