The Alfred P. Sloan Foundation has named a University of Virginia mathematician who specializes in untying mathematical knots – the abstract equivalent of untangling shoelaces that have no ends – as a Sloan Research Fellow for 2014.
Benjamin Webster, an assistant professor of mathematics, is an expert in algebraic geometry, representation theory and topology. The work is basic research, “not aimed at solving any particularly real-world problem,” he said, but related areas of mathematics have found applications in everything from Global Positioning System devices to cell phones and quantum computing.
“The reason the Sloan Foundation supports basic work like mine is so that pieces of knowledge are already in place to be used when we discover we need them – using ideas that hadn’t been originally developed for a specific purpose,” he said.
Awarded annually since 1955, Sloan Fellowships are given to early-career scientists and scholars whose achievements and potential identify them as rising stars – the next generation of scientific leaders with capacity for substantially contributing to and possibly changing their fields.
This year’s fellows, 126 of them selected from 61 colleges and universities in the United States and Canada, represent a broad range of scientific areas: chemistry, computer science, economics, mathematics, evolutionary and computational molecular biology, neuroscience, ocean sciences and physics. Each receives a $50,000 grant to further their research.
Webster is the only winner this year from U.Va. He joins two other Sloan Fellows currently on the math faculty, Michael Hill and Mikhail Ershov, both 2011 winners. The department has won six Sloan fellowships over the years.
Webster plans to use the Sloan funding for travel to conferences, graduate student support and possibly to organize a conference. He also is a current National Science Foundation Early Career Development grant-winner.
“Ben is extremely impressive, not only in the particular research he has done, but also in the breadth and vision he has shown across a great deal of mathematics,” said Craig Huneke, chair of the U.Va. mathematics department and Webster’s nominator. “He has demonstrated a deep conceptual understanding of the ‘big picture,’ is highly productive, and some of his research is foundational in nature.
“On top of everything else, he is a great teacher.”
As a simple example of the types of problems Webster teases through, he gave the following:
“Imagine that you tangled up your shoelaces, and then someone played a prank on you and fused the two ends together. Can you untangle them without cutting them open? Probably not, but it’s hard to be sure; after all, rubber bands can get pretty wound up, but you can always untangle them.
“It’s impossible to check by just trial and error; there will always be some combination you haven’t tried. Instead, what you have to do is extract some easier-to-understand piece of information (like a number) from your shoelace fused into a loop that measures something about how it’s tangled. If I had such a thing, I could look at the value I get on my shoelaces, and the value I get on an untangled loop, and if they’re different, then I’m sure I have to cut my laces.”
What interests Webster about this type of problem – and why it’s important – are the possibilities for variants.
“I find surprising appearances of knots in other areas of mathematics, which has allowed me to get more and more information about precisely how a knot is tangled up,” he said.
Webster came to U.Va. last year from Northeastern University and currently is a visiting scholar at Université Paris Diderot - Paris 7 on a grant from Fondation Sciences Mathématiques de Paris. He has taught at the University of Oregon and the Massachusetts Institute of Technology. He did his postdoctoral fellowship at the Institute for Advanced Study in Princeton, N.J., and earned his Ph.D. in 2007 from the University of California at Berkeley.
Past Sloan Research Fellows have gone on to notable careers and include such intellectual luminaries as physicist Richard Feynman and game theorist John Nash. Since the beginning of the program nearly 60 years ago, 42 fellows have received Nobel Prizes, 16 have won the Fields Medal in mathematics, 13 have won the John Bates Clark Medal in economics and 63 have received the National Medal of Science.
“For more than half a century, the Sloan Foundation has been proud to honor the best young scientific minds and support them during a crucial phase of their careers when early funding and recognition can really make a difference,” Sloan Foundation President Paul L. Joskow said. “These researchers are pushing the boundaries of scientific knowledge in unprecedented ways.”