Vortrag von Florian Beck (Tübingen)
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Spectral curves of harmonic maps
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| When |
Feb 19, 2013 from 01:15 PM to 02:15 PM |
| Where | Raum 404, Eckerstr. 1 |
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To each harmonic map from a complex one-dimensional torus to the special unitary group SU(2) (respectively the 3-sphere) one can associate a hyperelliptic Riemann surface, the so-called spectral curve. This construction, mainly due to Hitchin, allows one to study such maps essentially by algebro-geometric methods. Its drawback is that it cannot be applied to higher genus. However, Heller has recently carried out an analogous construction for an example of higher genus, Lawson's surface of genus two, for the first time. We sketch an important step in this construction, the abelianization of certain flat connections over Lawson's surface.
Summer School "Geometric, Algebraic and Combinatorial Methods in Modular Representation Theory", July 23-27, 2018