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Algebro-geometric solutions to Painleve VI and Schlesinger systems Shramchenko, Vasilisa
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.
Item Metadata
| Title |
Algebro-geometric solutions to Painleve VI and Schlesinger systems
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2016-10-05T10:59
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| 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.
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| Extent |
45 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: Universite de Sherbrooke
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| Series | |
| Date Available |
2017-04-05
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0343486
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International