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Padé approximations on Riemann Surfaces and applications

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

I will introduce different notions of (bi)orthogonality for a pairing associated to a measure on a contour in a Riemann surface and show how they are naturally related to suitable Pad ́e approximation problems thus generalizing the ordinary orthogonal polynomials. These objects can be framed in the context of a Riemann—Hilbert problem on Riemann surfaces, i.e. a vector bundle of degree 2g. This formulation is, in fact, of practical applications in at least three contexts: —) application of steepest descent methods,  —) construction of matrix orthogonal polynomials, —) constructions of KP/2 Toda tau functions that generalize Krichever’s construction. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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