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Geometric Phase in the Hopf Bundle - An Evans Function Method


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Colin Grudzien

University of North Carolina, Chapell Hill

Resumen:
Evans function analysis has become a standard method of calculating the stability of non-linear waves for PDE's, and building on the machinery of the Evans function, we have proven a related but alternative form of analysis. The Hopf bundle has an embedding in complex space, and locally is represented by the cross product of a circle and complex projective space - the dynamical system associated with the linearized operator for a PDE can thus induce a winding number through parallel transport in the fibre. Our method uses parallel transport to count the multiplicity of eigenvalues contained within a loop in the spectral plane.

Miércoles 5 de marzo, 2014
18:00 hrs.
Salón 203, Edificio Anexo, IIMAS

Informes: coloquiomym@gmail.com, o al 5622-3564.