# Virginia Tech mathematician named AAAS fellow

November 02, 2000(Blacksburg, Va., November 3, 2000) -- Frank S. Quinn, professor of mathematics at Virginia Tech, has been awarded the distinction of fellow of the American Association for the Advancement of Science (AAAS) in recognition of his efforts in advancing science.

Founded in 1848, AAAS represents the world's largest federation of scientists, with more than 143,000 members and 276 affiliated societies. AAAS conducts programs in the areas of science policy, science education, and international scientific cooperation, and publishes the prestigious peer-reviewed journal, Science. Quinn will be among only 251 scientists to be recognized as new fellows on Feb. 17, 2001 at the AAAS annual meeting in San Francisco.

He was recognized for "pioneering research in low-dimensional topology and in controlled topology resulting in outstanding insights and accomplishments, including the 4-dimensional annulus conjecture," according to the AAAS Council.

We are all familiar with 2 dimensional topology, including paper and computer screens, and with 3 dimensions, or 3-D. Topologists study objects in higher dimensions as well, Quinn explains. "Although 5 dimensions and higher are mind-boggling in a way, they are more uniform than the low dimensions, so theory is more manageable," he says.

As an undergraduate and master's student at the University of Virginia, and then as a doctoral student at Princeton, where topology was a "hot" topic, Quinn studied the high dimensional theories. He went on to develop a branch now known as "controlled" topology. As this subject matured he turned to the challenge of the difficult dimensions in the low range, and what is known as the "annulus conjecture."

A 2-dimensional "annulus" is the washer-shaped region between two concentric circles. The conjecture is that if the inner circle is replaced by an arbitrarily-shaped simple closed curve, no matter how distorted, the region between the circle and curve is still abstractly the same as the standard annulus. This 2-dimensional case was proved nearly a century ago.

There is a 3-D analog. The standard 3-dimensional annulus is the region between two concentric spheres in 3-D space, such as a ball within a ball. The conjecture asserts that if the inner sphere is replaced by one that is very distorted -- think of a prune -- the region between it and the outer sphere is still abstractly the same as the standard annulus. The 3-D case is much harder than 2-D and was not proved until the 1950's.

The analogous conjecture for dimensions 5 and above was proved about 1970, shortly after Quinn finished his studies at Princeton. Dimension 4 was then the final unknown case. Quinn, who joined Virginia Tec's faculty in 1977, focused his research on this conjecture and finally proved it true in the early 1980s.

This theoretical work is important in understanding mathematical structures. It is expected to eventually connect with high-energy physics such as string theory, but such connections are probably still decades away.

As a result of his discovery, Quinn received the Virginia Outstanding Faculty Member Award in 1987 and received the Virginia Tech Alumni Research Award and a University Distinguished Professorship in 1985. His more recent work is also drawing wide attention. Last year he was a visiting professor at Harvard and he has been invited to give the Cairns lecture at the University of Illinois in November. This summer he will be one of the principal lecturers at a European Union conference in Trieste, Italy.

At Virginia Tech, he is part of the computer testing project in the math department. "Our goal is to have computer-based testing in as many courses as possible. This will reduce routine burdens on faculty members so that they can spend more time with students." He also directs a number of graduate students.

Quinn grew up in Charlottesville, Virginia.

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PR CONTACT:Susan Trulove(540) 231-5646 STrulove@vt.edu

Faculty contact: Frank Quinn

fquinn@vt.edu or 1-540-231-8274

Virginia Tech

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