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April 24, 2014 — Chris Hall soon will roam the halls where a mathematical giant once stood.

Hall, a University of Wyoming associate professor in the Department of Mathematics, has been selected for the prestigious von Neumann Fellowship at Princeton University’s Institute for Advanced Study. Up to eight of these fellowships are available each year.

“I'm excited about the fellowship because Princeton is one of the few places I can easily find people to talk to about my work,” Hall says. “Some of the best number theorists in the world are there, and I anticipate a very productive year.”

Hall’s primary research area is arithmetic geometry. Math topics of interest include elliptic curves, abelian varieties, big monodromy and compatible systems.

“Elliptic curves is a narrow field in the sense you won’t find people in every single math department,” he says. “Number theory is generally one of the really hard topics. The reason not many people are working on them is the complexity of the problems.”

John von Neumann, for whom the fellowship is named, was a Hungarian-born American mathematician (1903-1957) who made major contributions to a vast range of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics and game theory, computer science, numerical analysis, hydrodynamics of explosions and statistics. He was a principal member of the Manhattan Project and the Institute for Advanced Study at Princeton.

“The prestige of the award owes mainly to the prestige of the Institute for Advanced Study itself,” says Hall, who received his doctorate in mathematics from Princeton in 2003.

The Institute for Advanced Study began in 1933 with 23 members in the School of Mathematics. It has grown to include more than 7,000 historians, mathematicians, natural scientists and social scientists that make up the institute’s community of scholars, according to Leon Levy, institute director.

Hall was nominated for the fellowship by Emmanuel Kowalski, a mathematician at ETH Zurich in Zurich, Switzerland, with whom Hall had co-written a couple of research papers. The Institute for Advanced Study then contacted Hall and asked him to apply for the fellowship.

**A period of
numbers**

To conduct his fellowship, Hall will take a leave of absence from UW starting this September through June 2014. During his fellowship, Hall will participate in a yearlong mathematical theme, attend weekly lectures, give occasional talks, finish some of his current research and write papers, and begin new work. During his stay, he will receive housing and a stipend.

Hall also plans to attempt to solve one of six mathematical problems referred to as “millennium prize problems.” Each problem, listed by the Clay Mathematics Institute, currently has a $1 million bounty. Hall is most interested in the Birch and Swinnerton-Dyer (BSD) Conjecture, an open problem in the field of number theory.

“This problem has been around and unsolved since the late ‘60s and is of intense interest to me,” Hall says. “There are two ways to attach a number to an elliptic curve. One uses algebra and the other uses analysis. The conjecture boldly asserts that these numbers are the same.”

Hall’s decision to attend Princeton for his master’s degree and doctorate was a goal to study under Andrew Wiles, a British mathematician most noted for proving Fermat’s Last Theorem, which involves elliptic curves.

“I went to Princeton because that’s where Wiles was,” says Hall, who received his bachelor’s degree in computer science from the University of Colorado-Boulder. “I knew that would be the best place for me to learn about elliptic curves.”

Ultimately, Hall did not study under Wiles. But he was mentored by other notable mathematicians, including Nicholas Katz and Peter Sarnak.

Now, he will have another opportunity to mingle among notable mathematicians.

“It’s one of the few places I can go to be with people who truly have experience in this,” Hall says. “I want to see what other people are thinking about and to find new projects to work on.”

**Photo: **

Chris Hall, a UW associate professor of
mathematics, has been selected for a von Neumann Fellowship at Princeton
University. He will begin his fellowship this fall.