3:00 p.m., Friday (October 20, 2006)

MATX 1100

Stephen Gustafson

Schroedinger maps

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).

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