




Plenary Speakers / Conférenciers principaux
 MARTIN GOLUBITSKY, University of Houston
Oscillations in coupled systems and animal gaits

Collins and Stewart noted that many quadruped gaits can be
described by spatiotemporal symmetries. For example, when a
horse paces it moves both left legs in unison and then both
right legs and so on. The motion is described by two symmetries:
Interchange front and back legs, and swap left and right legs
with a halfperiod phase shift.
Central pattern generators (CPGs) in the neural system are thought
to send time periodic signals to the `legs'. We model CPGs by
coupled systems of differential equations with symmetries based on
leg permuation. We describe how periodic solutions with prescribed
spatiotemporal symmetry can be formed in symmetric systems;
construct a CPG architecture that naturally produces quadrupedal
gait rhythms; and make several testable predictions about gaits.
This is joint work with Luciano Buono, Jim Collins, and Ian Stewart.
 JOHN OCKENDON, Oxford University
Simulating mathematics in industry

This talk will illustrate how a few basic mathematical ideas can help
industry understand some of its problems in a helpful and quantitative
way. What transcends all successful mathematics in industry is the
construction of a consistent, accessible theoretical framework within
which a class of processes can be placed. Examples of such frameworks
will include several stages of glass manufacture, the electrical
heating of metals and wave propagation around stealthy objects. This
range of topics will also help me show how to set about stimulating
mathematics in industry and, also how to find ``stimulating mathematics
in industry''.
 ARTURO PIANZOLA, University of Alberta, Edmonton, Alberta T6G 2G1
Local triviality and infinite dimensional Lie algebras

Using the beautiful classification of complex finite dimensional simple
Lie algebras for inspiration, my intention is to explain how some
fundamental questions about an interesting family of infinite
dimensional Lie algebras (which includes the affine KacMoody case),
can be answered by using principal fibrations.
I will use many examples, stay away from technicalities, and try to
convey to a general audience what some of the central ideas at hand
are.
 DAVID PIMM, Faculty of Education, University of Alberta, Edmonton, AB T6G 2G5
Interactions between language and mathematics: fluency,
understanding and time

In this talk, I will take a look at some significant ways in which
language interacts with mathematics (despite Dutch philosopher of
mathematics L. E. J. Brouwer's claim that `Mathematics is a
languageless activity of the human mind, having its origin in a move in
time'), illustrated with some examples from mathematics classrooms. In
particular, I will cautiously revisit the stillsmouldering debate
about mathematical fluency vs mathematical understanding (and I use the
term `vs' advisedly) and offer some reasons connected with the nature
of symbols themselves for why these need to be twin goals of any
mathematics education. Lastly, I will try out some new (i.e.
unrefined) thoughts about connections between the language of
mathematics, the nature of mathematical knowledge and time.
 RICHARD SCHOEN, Stanford University
Constructing calibrated submanifolds

Calibrated submanifolds include complex submanifolds of Kähler
manifolds as well as special lagrangian submanifolds. This latter class
of submanifolds is of substantial interest in string theory. This talk
will give a general introduction to the subject with particular
emphasis on existence questions special lagrangian and minimal
lagrangian submanifolds. We will describe deformation results, gluing
methods, heat equation methods, and variational methods for
constructing them.
 DAN VOICULESCU, University of California, Berkeley, California 947203840, USA
Free entropy

Shannon's informationtheoretic entropy has an analogue in a highly
noncommutative probabilistic context, the free entropy of free
probability theory. There are important connections to random matrix
theory and applications to the solution of a number of problems on von
Neumann algebras.

