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ChuuLian Terng, 1999 AWMMAA invited lecturer 
AWMMAA Invited Address
Friday, August 4, 2000 8:30 a.m.  9:20
a.m. Grand Horizon Ballroom, Sunset Village, UCLA
"Finite Quantum Chaos"
Audrey Terras University of California, San
Diego
Audrey Terras of the University of California, San Diego will
deliver the AWMMAA Invited Address "Finite Quantum Chaos" on August 4, 2000 at
8:30 a.m. at the Mathfest to be held at the University of California, Los
Angeles (August 35, 2000).
Please also join us at the AWM Reception to be held
August 3, 2000 at 8:00 p.m. in the Grand Horizon Ballroom Terrace, Sunset
Village, UCLA.
Abstract
Physicists have long studied spectra of Schrödinger
operators and random matrices, thanks to the implications for quantum
mechanics. Analogously number theorists and geometers have investigated the
statistics of spectra of Laplacians on Riemannian manifolds associated with
arithmetic groups. Sarnak calls this "arithmetic quantum chaos." Equivalently
one studies the zeros of Selberg zeta functions. Parallels with the statistics
of the zeros of the Riemann zeta function have been evident for some time. Here
we survey what may be called "finite quantum chaos"  seeking connections with
the continuous theory. The results can also be formulated in terms of Ihara
zeta functions of graphs.
Biographical Information
Audrey Terras received her B.S. degree in Mathematics from the
University of Maryland, College Park in 1964 where she was inspired by the
lectures of Sigekatu Kuroda to become a number theorist. She was particularly
impressed by the use of analysis (in particular using zeta functions) to derive
algebraic results (e.g. about the structure of the ring of integers in an
algebraic number field). She received her M.A. (1966) and Ph.D. (1970) from
Yale University.
In 1972 she became an assistant professor of mathematics at the
University of California, San Diego. Now she is a full professor at UCSD where
she has had 20 Ph.D. students.
She is a fellow of the American Association for the Advancement
of Science and has served on that organization's mathematics section nominating
committee. She has served on the Council of the American Mathematical Society
and various AMS committees and was an editor of the Transactions of the
AMS. Currently she is an associate editor of book reviews for the
Bulletin of the AMS and the chair of the Western Section Program
Committee. She has served on various AWM committees in the past.
She has written three books: Harmonic Analysis on Symmetric
Spaces and Applications, Vols. I, II, SpringerVerlag, New York, 1985, 1988
and Fourier Analysis on Finite Groups and Applications, Cambridge
University Press, Cambridge, 1999. She also coedited, with Dennis Hejhal and
Peter Sarnak, the proceedings from a 1984 conference on Selberg's trace
formula. Her research interests include number theory; harmonic analysis on
symmetric spaces and finite groups along with its applications; special
functions; algebraic graph theory, especially zeta functions of graphs; and
Selberg's trace formula.
Current research involves finite analogues of the symmetric
spaces of her SpringerVerlag volumes. This led her to work on spectra of
graphs and hypergraphs attached to finite matrix groups, also coverings of
graphs and their zeta and Lfunctions. These functions are analogues of the
Riemann and Selberg zeta functions.
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