## CRM/Fields Institute Prize Lecture

### James Arthur

*University of Toronto*

### Harmonic Analysis and Trace Formulas

April 16, 1997

Harmonic Analysis could be interpreted broadly as a general
principle which relates analytic and geometric objects. Examples occur throughout
many areas of mathematics. In group theory, the geometric objects are conjugacy
classes, the analytic objects are irreducible characters, and the two can
be related by means of trace formulas. We shall give a general introduction
to trace formulas, and their applications to group representations and number
theory.

*James Arthur* is currently a University Professor of mathematics at
the University of Toronto. He received his Ph.D. in mathematics at Yale University
in 1970, and taught at Princeton University, Yale University and Duke University
before coming to the University of Toronto in 1979. He has also worked at
the Institute for Advanced Study in Princeton, Institut des Hautes Études
Scientifiques in France and the Max-Planck Institut in Bonn. In 1994 he gave
the Hermann Weyl lectures at the Institute for Advanced Study. His research
interests are automorphic forms, number theory, representation theory and
harmonic analysis on real and p-adic groups. He is an associate editor of
the International Mathematics Research Notices, the Journal of the American
Mathematical Society and Journal für die reine und angewandte Mathematik.
He is a fellow of the Royal Society of Canada and a Fellow of the Royal Society
of London.