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SUMMARY:Padé approximations on Riemann Surfaces and applications - Marco 
 Bertola (Concordia University)
DTSTART:20220824T143000Z
DTEND:20220824T153000Z
UID:TALK177545@talks.cam.ac.uk
DESCRIPTION: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&mdash\;Hilbert problem on Riemann su
 rfaces\, i.e. a vector bundle of degree&nbsp\;2g. This formulation is\, in
  fact\, of practical applications in at least three contexts:\n&mdash\;)&n
 bsp\;application of steepest descent methods\,&nbsp\;\n&mdash\;) construct
 ion of matrix orthogonal polynomials\,\n&mdash\;) constructions of KP/2 To
 da tau functions that generalize Krichever&rsquo\;s construction.&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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