
CRM/Fields Institute Prize Lecture 2000
ISRAEL MICHAEL SIGAL
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 longterm
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 groundbreaking 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.

