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 tudes Scientifiques in France and the Max-Planck Institut in Bonn.