AWM-MAA 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 AWM-MAA 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 3-5, 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, Springer-Verlag, New York, 1985, 1988 and Fourier Analysis on Finite Groups and Applications, Cambridge University Press, Cambridge, 1999. She also co-edited, 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 Springer-Verlag 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 L-functions. These functions are analogues of the Riemann and Selberg zeta functions.