April 19, 2014

CRM/Fields Institute Prize Lecture 2000


Professor Sigal is a mathematical physicist, bringing the problems of physics and chemistry, especially the deep problems of the nature of matter, to mathematics. As such, he works in the part of mathematics concerned with modeling basic physical phenomena. While the models themselves can be deceptively simple, it turns out to be extraordinarily difficult to establish that they do in fact replicate experimentally known phenomena, an effort that has motivated the development of a large part of deep mathematical analysis.

Sigal's work goes to the very heart of quantum theory, that is, the long-term behaviour of particles under interactions. His work has primarily centered on the Schroedinger equation, which is at the heart of mathematical models of atoms and molecules. In the 1920's, Schroedinger formulated what has become the standard equation for quantum mechanics. It created a whole new field of mathematics dealing with the behaviour of the Schroedinger operators; that is with the general behaviour of the solutions. For fifty years, one major unsolvable problem remained. The theorem established through a series of papers by Sigal and his former postdoctoral student, Soffer, provided the first completely rigorous solution.

In recent years Professor Sigal has made ground-breaking contributions to the theory of interaction between light and matter, know as Quantum Electrodynamics. A basic set of equations to explain the interaction between electrons and photons was first proposed by Physics Nobel laureates Feynmann, Schwiger and Tomonaga around 1950. Their work created a need for a precise, consistent mathematical description of the theory and for over 40 years this task seemed to be beyond reach. Sigal's recent contribution is the first convincing attempt to provide a consistent mathematical description of Quantum Electrodynamics and represent a revolutionary approach to the subject.

Professor Sigal is currently a professor at the University of Toronto. He received his PhD from Tel Aviv University. His work has been rewarded by many honours; including several invited lectures to the International Congress on Mathematical Physics and the International Congress of Mathematicians, as well as the editorship of two of the most respected journals in the field, Reviews in Mathematical Physics and Duke Mathematical Journal. He is also a Fellow of the Royal Society of Canada and received the John L. Synge Award as the outstanding Canadian mathematician in 1993.