3:00 p.m., Friday (October 20, 2006)
Our favourite classical linear PDEs - the Laplace, heat, wave,
and Schroedinger equations - all have natural geometric
(and hence nonlinear) generalizations for maps into manifolds -
the harmonic map, harmonic map heat-flow, wave map, and Schroedinger map
equations. Remarkably, these equations are also physically relevant,
for example in relativity (wave maps) and ferromagnetism (Schroedinger
maps). While the first three map equations have been mathematically popular
for some time now, the Schroedinger map problem has only very recently become
hot. I will give some general background about these
geometric equations, and then describe some recent work on asymptotic
behaviour and singularity formation in Schroedinger maps.
Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115).