Report for the Academic Years 1987-1988 and 1988-1989

THE SCHOOL OF NATURAL SCIENCES
was jeopardized with the withdrawal of National Science Foundation support for
the John von Neumann Supercomputer Center in Princeton. The project is
now being continued in Japan. Professor Hut also continues to study the evolu-
tion of globular clusters in collaboration with colleagues at Princeton University,
the Harvard-Smithsonian Center for Astrophysics, Munich, Utrecht, Tokyo,
Kyoto and elsewhere.
FRANK WILCZEK, who joined the faculty in January 1989, pursued research in
three principal areas. Working with Professor Edward Witten, Yi-Hong Chen
and Bert Halperin, he demonstrated that ideal gases of certain kinds of anyons are
superconducting at zero temperature. This work has since been extended in several
directions, notably to give new insight into the quantized Hall effect. Professor
Wilczek worked on several topics and published several papers relating to the
quantum mechanics of cosmic strings and quantum hairs on black holes. Finally,
with Curt Callan of Princeton University, he has begun a program to investigate
several problems of physics that are difficult or obscure in flat space on spaces of
constant negative curvature, where they seem to simphfy.
EDWARD WITTEN, who joined the faculty in 1987, has spent most of the last
three years working on geometrical applications of quantum field theory. The
main successes have been a physical reinterpretation of "Donaldson theory" of
four-dimensional geometry; a new description of the "Jones polynomial" of
three-dimensional knot theory that for the first time explains its symmetries; and
new interpretations and insights concerning general relativity in two and three
dimensions. In the course of this work, many physical ideas have been applied
to problems in geometry for the first time, and vice versa. These developments,
some of which were forecast and advocated by former Institute Professor Sir
Michael Atiyah at the string theory workshop at the Institute in 1987—88, have
shown that many structures usually studied by string theorists in two dimensions
have important analogs in the "physical dimensions," three and four. Professor
Witten's explanation of the Jones polynomial involved ingredients similar to
ideas of Professor Frank Wilczek about fractional statistics particles in 2 + 1
dimensions. The realization of this led to a collaboration of Wilczek and Witten
[with Yi-Hong Chen and Bert Halperin] on theories of high—temperature super-
conductivity.
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