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Higher solutions of Hitchin's self-duality equations Heller, Lynn
Description
Solutions of Hitchin's self-duality equations correspond to special real sections in the Deligne-Hitchin moduli space -- twistor lines. A question posed by Simpson in 1995 asks whether all real sections give rise to global solutions of the self-duality equations. An armative answer would allow for complex analytic procedure to obtain solutions of the self- duality equations. The purpose of my talks is to explain the construction of counter examples given by certain (branched) Willmore surfaces in 3-space (with monodromy) via the generalized Whitham flow. Though these higher solutions do not give rise to global solutions of the self- duality equations on the whole Riemann surface M, they are solutions on an open dense subset of it. This suggest a deeper connection between Willmore surfaces, i.e., a rank 4 harmonic map theory, with the rank 2 self-duality theory.
Item Metadata
Title |
Higher solutions of Hitchin's self-duality equations
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-07-05T11:00
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Description |
Solutions of Hitchin's self-duality equations correspond to special real sections
in the Deligne-Hitchin moduli space -- twistor lines. A question posed by Simpson in 1995
asks whether all real sections give rise to global solutions of the self-duality equations. An
armative answer would allow for complex analytic procedure to obtain solutions of the self-
duality equations. The purpose of my talks is to explain the construction of counter examples
given by certain (branched) Willmore surfaces in 3-space (with monodromy) via the generalized
Whitham flow. Though these higher solutions do not give rise to global solutions of the self-
duality equations on the whole Riemann surface M, they are solutions on an open dense subset
of it. This suggest a deeper connection between Willmore surfaces, i.e., a rank 4 harmonic map
theory, with the rank 2 self-duality theory.
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Extent |
51.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Hannover
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Series | |
Date Available |
2019-03-29
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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 |
10.14288/1.0377655
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International