Courses / ActivitiesCanceled: Harmonic trinoids in complex projective spaces
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I will talk about a construction of harmonic maps from a thrice-punctured sphere to complex projective space. Since such harmonic maps are characterized by the Toda field equations, integrable systems methods can be applied, that is, the problem of nonlinear PDE can be converted to a problem of linear ODE with parameter. Then the main difficulty is the monodromy problem, the global behavior of solutions of the linear ODE. I use generalized hypergeometric equations and solve the monodromy problem for particular cases.
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Shimpei Kobayashi
2011-03-15
10:00:00 - 11:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
I will talk about a construction of harmonic maps from a thrice-punctured sphere to complex projective space. Since such harmonic maps are characterized by the Toda field equations, integrable systems methods can be applied, that is, the problem of nonlinear PDE can be converted to a problem of linear ODE with parameter. Then the main difficulty is the monodromy problem, the global behavior of solutions of the linear ODE. I use generalized hypergeometric equations and solve the monodromy problem for particular cases.