## Manjul Bhargava

### Princeton University

Primary Section: 11, Mathematics Membership Type: Member (elected 2013) |

### Biosketch

Manjul Bhargava is the R. Brandon Fradd Professor of Mathematics at Princeton University. He earned his AB in Mathematics from Harvard University in 1996 and PhD from Princeton University in 2001. After a year each at the Institute for Advanced Study and Harvard University, he joined the faculty at Princeton University as Professor of Mathematics in 2003. He was the first five-year Research Fellow of the Clay Mathematics Institute during 2000-05, and is currently a Simons Foundation Fellow.

His primary research interests lie in number theory, representation theory, and arithmetic geometry. His research includes the study of integer values taken by quadratic forms, composition laws on spaces of higher degree forms, and rational points on "elliptic curves" (i.e., rational solutions (x,y) to equations of the form y^2 = x^3 + A x + B).

### Research Interests

Using varied techniques from algebra, analysis, and geometry, Bhargava addresses basic questions in number theory. Examples include: when does a positive-definite quadratic form with integer coefficients take every possible positive integer value? What is the probability that an elliptic curve equation y^2 = x^3 + A x + B has a rational solution (x,y)? What is the probability that a random integer polynomial of large degree takes a square value? Bhargava uses such questions as a starting point to study the structure of the integers, higher degree polynomials and forms over the integers, and related arithmetic and geometric objects.