TATA INSTITUTE OF FUNDAMENTAL RESEARCH

ASET COLLOQUIUM

Topic SUMS AND SQUARES OF THE “290-THEOREM” Speaker Prof. Manjul Bhargava Princeton University, Princeton Clay Mathematics Institute, Cambridge, and Tata Institute of Fundamental Research, Mumbai Date Friday, February 27, 2009 Time 4 p.m. Venue Lecture Theatre AG 66 Tata Institute of Fundamental Research Homi Bhabha Road, Colaba Mumbai 400005

The famous "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four square numbers. That is, the quadratic form a2 + b2 + c2 + d2 "represent" 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? All these questions turn out to have very simple and surprising answers.

Manjul Bhargava (b 1974) is the youngest full professor of mathematics at Princeton University. His research interests span algebraic number theory, combinatorics, and representation theory. He graduated from Harvard University in 1996 and received his doctorate from Princeton in 2001, working under Andrew Wiles. His breakthrough Ph.D. thesis surprised the mathematical community by generalizing the classical Gauss composition law for quadratic forms to many other situations.

Bhargava has won several awards for his research, including the AMS–MAA–SIAM Frank and Brennie Morgan Prize, a Clay Research Fellowship, the Clay Research Award in 2005, and the Leonard M. and Eleanor B. Blumenthal Award for the Advancement of Research in Pure Mathematics. He was named one of Popular Science Magazine’s “Brilliant 10” in November 2002. He recently won the American Mathematical Society's Cole Prize in number theory and the SASTRA Ramanujan Prize for his outstanding contributions to number theory.

Manjul is also a very good tabla player, having studied under Zakir Hussain. Non-TIFR members wishing to attend the lecture are requested to send a mail to [email protected] and also come with a photo-identify card.