February 16, 2011 — The Alfred P. Sloan Foundation has named two mathematicians in the University of Virginia's College of Arts & Sciences – Mikhail Ershov, assistant professor of mathematics, and Michael Hill, associate professor of mathematics – as Sloan Research Fellows for 2011.

Awarded annually since 1955, the fellowships are given to early-career scientists and scholars in recognition of their achievements and potential for substantially contributing to their fields.

Drawn from 54 colleges and universities in the U.S. and Canada, this year's 118 fellows represent a broad range of scientific research areas. Ershov and Hill are the only two this year in any field from any university in Virginia, and are among only 20 mathematicians
selected nationally.

"We are enjoying this news around here," Nicholas Kuhn, professor of mathematics, said. "It is a nice confirmation of the quality of our younger faculty."

Michael Hill

Hill works in the area of topology: the study of geometric objects like curves, surfaces and their higher dimensional analogs. His particular subfield is algebraic topology, which studies such objects by means of algebraic invariants, combining insights from a wide swath of modern mathematics.

"He was already earning a reputation as one of a strong new generation of topology researchers when, in April 2009, he, together with collaborators Michael Hopkins of Harvard and Doug Ravenel of the University of Rochester, announced a solution to the 'Kervaire Invariant One' problem," Kuhn said. "Since the 1960s, this subtle question about spheres had been perhaps the most famous open problem in high-dimensional geometric topology."

Kuhn added that the research, which has since been the subject of conferences around the world, is "a tour-de-force of conceptual and computational methods. It is one of the most spectacular recent results in the world of mathematics."

Hill came to U.Va. as a Whyburn Instructor after earning his Ph.D. in mathematics from the Massachusetts Institute of Technology in 2006.

Mikhail Ershov

Ershov is recognized for outstanding research contributions to various aspects of group theory. "Groups" in mathematics describe symmetries of various objects of algebraic or geometric nature. Ershov specializes in understanding groups defined by generators and relations, a subject known as combinatorial group theory. In his still-early career he has attracted worldwide attention for his work on Golod-Shafarevich groups and the Nottingham group.

Professor Pierre de la Harpe of the University of Geneva, one of the world’s leading authorities in group theory, said of Ershov: "I find it remarkable that, only five years after his Ph.D., he can be cited as an expert on several subjects: Kazhdan Property (T), Kac-Moody theory, pro-p groups in general and Nottingham group in particular. There is no doubt that Mikhail Ershov has both the original ideas and the technical expertise to become a leading mathematician."

In the last two years Ershov has given colloquium talks at Rutgers and Yale universities and Imperial College, plus numerous seminar talks. He also has co-organized two conferences, including one at U.Va. on "Arithmetic Groups and their Applications in Combinatorics, Geometry and Topology."

Ershov came to the United States from Moscow State University in 1998 to earn a master's degree from Brandeis University. He earned his Ph.D. in mathematics from Yale in 2005 and joined the U.Va. mathematics faculty in 2007.
 
"The scientists and researchers selected for this year's Sloan Research Fellowships represent the very brightest rising stars of this generation of scholars," said Paul L. Joskow, president of the Alfred P. Sloan Foundation. "The foundation is proud to be able to support their work at this important stage in their careers."

Administered and funded by the Sloan Foundation, the fellowships are awarded in close cooperation with the scientific community. Potential fellows must be nominated for recognition by their peers and are subsequently selected by an independent panel of senior scholars.

The $50,000 fellowships are awarded in chemistry, computer science, economics, mathematics, evolutionary and computational molecular biology, neuroscience, and physics.

The Alfred P. Sloan Foundation is a philanthropic, not-for-profit, grant-making institution based in New York City. Established in 1934 by Alfred Pritchard Sloan Jr., then president and chief executive officer of the General Motors Corporation, the foundation makes grants in support of original research and education in science, technology, engineering, mathematics and economic performance.