Title	Algebro-geometric solutions to Painleve VI and Schlesinger systems
Creator	Shramchenko, Vasilisa
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2016-10-05T10:59
Description	A method of constructing algebro-geometric solutions of rank two Schlesinger systems is presented. For an elliptic curve given as a ramified double covering of $CP^1$, a meromorphic differential is constructed with the following property: the common projection of its two zeros on the base of the covering, regarded as a function of the only moving branch point of the covering, is a solution of the Painleve VI $(1/8,-1/8,1/8,3/8)$ equation. This differential provides an invariant formulation of a classical Okamoto transformation for the Painleve VI equations. This approach is motivated by an observation of Hitchin connecting algebraic solutions of a Painleve VI equation to the Poncelet polygons in the plane. The research is partially supported by the NSF grant 1444147 and NSERC discovery grant.
Extent	45 minutes
Subject	Mathematics; Ordinary differential equations; Dynamical systems and ergodic theory; Dynamical systems
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Universite de Sherbrooke
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2017-04-06
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0343486
URI	http://hdl.handle.net/2429/61128
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Faculty
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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Algebro-geometric solutions to Painleve VI and Schlesinger systems Shramchenko, Vasilisa

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