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Complex Analysis and Geometry Seminar

Adiabatic limits of ASD connections on collapsing K3 surfaces

Ved Datar, Indian Institute of Science, Bangalore

Location:  Hill 705
Date & time: Friday, 12 April 2019 at 10:30AM - 11:30AM

Abstract:  I will talk about recent joint work with Adam Jacob and Yuguang Zhang on a convergence result for a family of Yang-Mills connections over an elliptic K3 surface as the fibres collapse. We show that outside a finite number of fibres, the curvatures of the connections are uniformly bounded (with respect to fixed background metrics), and that the connections converge in L^{1,p} to a limiting connection whose restriction to a generic fibre is a flat connection. This solves a conjecture of Fukaya in dimension two, and is a vector bundle analog of the work of Gross-Wilson and Gross-Tosatti-Zhang on the collapsing behaviour of Ricci flat metrics in degenerating Kahler classes.

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