## Manjul Bhargava Receives Hasse Prize at MathFest

#### By Joseph Gallian

At the August 2003 MathFest in Boulder Manjul Bhargava received the MAA's Hasse Prize for exposition. It has been quite a year for Manjul. In November 2002 he was the only mathematician among

*Popular Science's* “Brilliant 10”, the publication's first annual celebration of ten scientists who are shaking up their fields. (The article is available online at

http://www.popsci.com/science/article/0,12543,364881,00.html) In January 2003 he was selected to be one of the AMS/MAA one hour invited speakers at the January 2004 Joint Meetings in Phoenix. Then came offers of tenured Associate Professorships from the top Ivy League schools. Shortly thereafter, these offers were increased to full professorships. It is believed that the two years from thesis to full professorship offers is the shortest period ever for an Ivy League school. In June he accepted the professorship from Princeton and also was appointed to the editorial board of the

*Journal of Number Theory*.

Manjul Bhargava lecturing on

the Fifteen Theorem.

Awards are not new to the 29-year-old Bhargava, who is the son of a chemist father and mathematician mother, Mira Bhargava, a professor at Hofstra University. In high school Manjul was the winner of the First Annual New York State Science Talent Search. As an undergraduate at Harvard he won the Hoopes Prize for his outstanding senior thesis and (three times!) the Derek Bok Award for Excellence in Teaching. He was selected to lead the commencement of the 1600 Harvard graduates of the class of 1996.

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.