Also in 1996 Bhargava received the AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student for work he began at the Duluth REU and expanded on in his senior thesis. A year before he obtained his Ph.D. from Princeton on a Hertz Fellowship, Manjul was also appointed as the first Clay Mathematics Institute Long-Term Prize Fellow and a Visiting Fellow at Princeton University. This past year he was a visiting professor at Harvard.
Manjul's research interests include algebraic number theory, combinatorics, and representation theory. The paper for which he won the Hasse Prize, “The factorial function and generalizations,” published in the American Mathematical Monthly (November 2000), explains his new generalization of the factorial function and its connections with some classical problems in number theory, ring theory, and combinatorics. His work on the factorial function unifies and generalizes the results of about 20 previous papers, many by well-known mathematicians.
One of Bhargava's recent accomplishments has to do with the so-called “Fifteen Theorem”, which was originally proved by Conway and Schneeberger in 1993. It states that if a positive definite quadratic form whose associated symmetric matrix has integer values represents all positive integers up to 15, then it is “universal,” that is, it represents all positive integers. Bhargava not only simplified the Conway-Schneeberger proof, but also generalized the result in several beautiful ways. Another of Bhargava's achievements, which was the basis for his thesis, is a generalization of Gauss's 1801 law of composition of binary forms. Manjul showed that Gauss's composition is only one of at least 14 such composition laws.
Andrew Wiles, Manjul's Ph.D. advisor, is quoted in the Popular Science article as saying Bhargava's thesis was one of the strongest he's seen in 20 years. Also quoted in the article is Princeton professor Peter Sarnak: “We are watching him very closely. He is going to be a superstar. He's amazingly mature mathematically. He is changing the subject in a fundamental way.”
In addition to doing mathematics, Manjul is also an accomplished tabla player, and performs extensively in the New York and Boston areas. He also enjoys nature hiking, running, tennis, and spending time with friends.