CMSA Differential Geometry and Physics Seminar: Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons

I will begin by explaining a dimension reduction result for Tian’s generalized ASD instantons over product manifolds, which generalizes work of Yuanqi Wang on codimension-one reduction and includes the cases of G2 and Spin(7) instantons as well as degree zero Hermitian-Yang-Mills connections. The proof is inspired by a simple observation about the Yang-Mills energy and suggests a natural adiabatic picture for these generalized ASD connections. I will describe ongoing work towards establishing such an adiabatic scheme, emphasizing some of the complications that arise in the general case and explaining what can be said for G2 instantons. Everything I will talk about is joint work with my collaborator Langte Ma.