Differential Geometry Seminar: Adiabatic limits of Yang-Mills connections on collapsing K3 surfaces

Seminar | November 26 | 3:10-4 p.m. | 939 Evans Hall

 Adam Jacob, UC-Davis

 Department of Mathematics

In this talk I will discuss the vector bundle analogue of the degeneration problem for Ricci flat K3 surfaces considered by Gross-WIlson (and later Gross-Tosatti-Zhang). Namely, given an elliptically fibered K3 surface equipped with complex vector bundle, what are the convergence properties of a family of SU(n) ASD Yang-Mills connections as the elliptic fibers collapse? Under certain geometric assumptions, I will demonstrate $W^{1,p}$ convergence away from a finite number of fibers, and show how the limit is uniquely determined by the sequence of holomorphic structures. This is joint work with Ved Datar and Yuguang Zhang.