Colloquium
4:00 p.m., Monday (January 12th)
Math Bldg. Room 203
Robert McCann
University of Toronto
Phase transitions and symmetrybreaking in singular diffusion
Physical dynamics divide naturally into the dissipative and
conservative extremes, in which friction either dominates or
becomes irrelevant. Otto's work heralded a breakthrough in
our ability to realize dissipative dynamical systems as
infinite dimensional Riemannian gradient flows. Here we
exploit this point of view to analyze the long time behaviour
of the nonlinear (fast) diffusion equation, used to model heat
transport, population spreading, fluid seepage, curvature flows,
and avalanches in sandpiles  as a prototype from the dissipative
regime. The spectrum of the entropy is explicitly determined,
and the dynamics are found to undergo a phase transition in
which rotational symmetry is broken as the strength of the
nonlinearity is varied.
Refreshments will be served at 3:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
