Math’s Hassett wins almost $1M in support

Math’s Hassett wins almost $1M in support

BY JADE BOYD
Rice News staff

In theoretical mathematics, progress depends not upon expensive supercomputers or laboratories but on brainpower.

Brendan Hassett

“We don’t require expensive equipment in our discipline, so funding is really all about developing and supporting people,” said Brendan Hassett, associate professor of mathematics, who scored a major coup for Rice this spring by winning almost $1 million in National Science Foundation (NSF) funding for postdoctoral researchers and graduate students at Rice and three other institutions.

Million-dollar grants don’t come along every day in mathematics, and department chair Michael Wolf said focused research group grants like this are among the most competitive mathematics awards handed out by the NSF.

“Very few of the awards are given, and the competition is very intense,” Wolf said. “Dr. Hassett’s winning is an indication both of the superb quality of his scholarship and of his strong and growing reputation in the field of algebraic geometry.”

Hassett said the funds will pay for a series of meetings over the next three years aimed at generating breakthroughs in a specific area of algebraic geometry that is ripe for innovation. Hassett, the principal investigator on the grant, is joined by collaborators Yuri Tschinkel of New York University’s Courant Institute of Mathematics, Johan de Jong of Columbia University and Jason Starr of the Massachusetts Institute of Technology.

Solving algebra problems is something every high school math student does from time to time. Most people probably recall seeing an equation that contains variables like x and y and being given a problem like “Solve for x if y=1.” That’s an example of a specific solution, one that is applicable only in the specific case when y=1. Hassett and colleagues are interested in solving problems too, but they are interested in parametric solutions — general solutions that account for all possible specific solutions — and often they are interested in finding parametric solutions for not just one equation but for an entire class of equations. Finding these overarching solutions requires the use of a combination of geometric and algebraic methods.

“The problems we study are similar to those addressed by experimental scientists,” Hassett said. “Imagine you are collecting data from an experiment, but some of the variables are dependent. For example, they might satisfy a mathematical constraint coming from a general scientific principle. Our goal is to find a curve fitting the data and compatible with the constraint.”

It has been said that algebraic geometry starts where equation-solving leaves off. The concepts and techniques that are required to understand the totality of solutions of a system of equations are radically different from those involved in generating specific solutions. Geometric insight can be used to solve equations that would stymie even the fastest supercomputers. The key is to visualize the solutions in space, where they can be manipulated geometrically.

Wolf said another measure of Hassett’s high standing in the field is the fact that he was recently chosen as a lead organizer of one of the largest gatherings of algebraic geometry researchers in recent years. The meetings, which will stretch over three months in spring 2009, will bring together hundreds of leading scholars for a series of in-depth discussions at the University of California–Berkeley’s Mathematical Sciences Research Institute, one of the nation’s leading mathematics institutes.