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DTSTAMP:20250806T012616Z
DESCRIPTION:Title: Padé approximants on Riemann surfaces and KP tau functio
 ns.\n\nAbstract: The talk has two relatively distinct but connected goals\
 ; the first is to define the notion of Padé approximation of Weyl-Stieltje
 s transforms on an arbitrary compact Riemann surface of higher genus. The 
 data consists of a contour in the Riemann surface and a measure on it\, to
 gether with the additional datum of a local coordinate near a point and a 
 divisor of degree g. The denominators of the resulting Padé–like approxima
 tion also satisfy an orthogonality relation and are sections of appropriat
 e line bundles. A Riemann–Hilbert problem for a square matrix of rank two 
 is shown to characterize these orthogonal sections\, in a similar fashion 
 to the ordinary orthogonal polynomial case.  \n	\n	The second part extends t
 his idea to explore its connection to integrable systems. The same data ca
 n be used to define a pairing between two sequences of line bundles. The l
 ocus in the deformation space where the pairing becomes degenerate for fix
 ed degree coincides with the zeros of a “tau” function. We show how this t
 au function satisfies the Kadomtsev–Petviashvili hierarchy with respect to
  either deformation parameters\, and a certain modification of the 2–Toda 
 hierarchy when considering the w\n\nWeb -Please fill in this form: https:/
 /forms.gle/S1NcNQ8BxkzfAXcj9\n\n \n
DTSTART:20210330T193000Z
DTEND:20210330T203000Z
SUMMARY:Marco Bertola  (Concordia)
URL:/mathstat/channels/event/marco-bertola-concordia-3
 29602
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