Annual Report 2005 - Fields Institute - University of Toronto

in which one will ascend more rapidly. If so, one’s angle of
descent should be as steep as possible, subject to the constraint
that one must reach the updraft before hitting the
ground! Fortunately, modern gliders come equipped with
computers, and programs to help one make quick decisions.
Almgren described how to set up the glider control problem
mathematically, and indicated the type of solutions one
gets.
At this point Tourin took over, and tried to give the audience
a sense of the mathematics that goes into producing
a solution. The saw-toothed nature of the trajectories
means they are not smooth functions at all. She described
how the modern machinery of viscosity-solutions allows
one to circumvent this difficulty, and still pose a welldefined
mathematical problem having a unique solution.
She illustrated the utility of this approach by giving other
applications of exactly the same mathematical ideas, from
the propagation of flame fronts to solving for optimal asset
allocation in the presence of transaction costs.
An enthusiastic audience of over 200 attended the talk,
and kept the speakers busy answering questions for long
afterwards.
Clay/Fields Institute Public Lecture
Eric Zaslow
June 2, 2005
Held at Fields Institute
Physmatics
Mathematics and physics, once a wonderful marriage,
underwent a divorce, but now the relationship has reconciled
as “Physmatics” in large part due to String theory.
Eric Zaslow (Northwestern) provided a lecture based
Eric Zaslow
L e c t u r e s a n d S p e c i a l E v e n t s
Suite Vollard building
on this story, enjoyed by layperson and expert alike. His
slide presentation, interspersed with informative pictures,
quotations and analogies, traveled from the beginnings of
the interaction of physics and mathematics, to present day
investigations in String theory: an attempt to provide a
unified framework for the physics of the big and small. This
theory provides rich and unexpected predictions of duality
between mathematical objects of previous independent
importance.
The work of mathematicians to both put these predictions
inside the appropriate mathematical setting, and to furthermore
verify them, has in turn advanced the physics. It
is this interdependence of the two subjects that has been a
driving force in the aforementioned reconciliation.
Zaslow was a Clay Senior Scholar, in residence at the Fields/
Perimeter Institute thematic program on the Geometry
of String Theory. His participation in the program, and
his associated public lecture, were generously supported
by the Clay Mathematics Institute, based in Cambridge,
Massachusetts. In his lecture he surveyed the relationship
Fields Institute 2005 ANNUAL REPORT 40