Indian Institute of Technology Bombay

Popular Lecture Series in Mathematics

Mathematics Association of IIT Bombay


Bombay Mathematical Colloquium


March 11, 2004

Prof. Manjul Bhargava

Princeton University, New Jersey, USA,

will speak on

The Representation of Integers by Quadratic Forms


Friday, 19th March 2004

at 5-05 pm to 6-30 pm

 Venue: IRCC Auditorium (Institute Auditorium)





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 a2 + b2 + c2 + d2 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.