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Geometry and Topology Seminar

Friday, May 11, 2018
3:00pm to 5:00pm
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Building 15, Room 104
Geometry of weightless Kapustin-Witten solutions on the plane
Steven Rayan, Department of Mathematics & Statistics, University of Saskatchewan,
The Kapustin-Witten equations are an analogue of the Hitchin equations for a four-manifold. On a compact Kaehler manifold, the solutions are slope-stable Higgs bundles that are Simpson-integrable. On the projective plane, we need the additional data of a parabolic structure along a curve in order to attain a well-defined, nonempty moduli space. By twisting by the divisor of the curve and forgetting the weights, we arrive at a larger moduli space into which the Kapustin-Witten spaces are embedded. We use classical facts about holomorphic bundles on the plane to construct interesting loci within this moduli space.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].