**Indian Institute of Technology Bombay**

**Popular Lecture Series in Mathematics**

**Mathematics Association of
IIT Bombay and
Bombay Mathematical Colloquium**

March 11, 2004

Prof. Manjul Bhargava

Princeton University, New Jersey, USA,

will speak on

**The Representation of Integers by
Quadratic**** ****Forms**

on

Friday, 19th March 2004

at 5-05 pm to 6-30 pm

Venue: IRCC Auditorium (Institute Auditorium)

Abstract:

The
classical "Four Squares Theorem" of Lagrange asserts that any
positive integer can be expressed as the sum of four squares; that is, the
quadratic form a^{2} + b^{2} + c^{2} + d^{2}
represents all (positive) integers.
When does a general quadratic form represent all integers? When does it represent all odd
integers? When does it represent all
primes? We will show how all these
questions turn out to have very simple and surprising answers.

**About the speaker**:
At Harvard University, Manjul Bhargava won the AMS Morgan Prize for
outstanding research in Mathematics by an undergraduate. He obtained
his Ph.D. in 2001 from Princeton University
under the guidance of Andrew Wiles.
In his Ph.D. thesis, he did some outstanding work on a 200-year-old
problem.
He is included in the
“Brilliant-10” list in 2002 by the magazine Popular Science.
He won the
Merten Hasse Prize for 2003 for his writing in non-technical magazines
and journals. He is also an accomplished Tabla
Player and a linguist.

At
28, he is a professor at Princeton University.
For more about Manjul
Bhargava, see the article
here.