Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons

Explore dimension reduction techniques and adiabatic limits in the context of generalized anti-self-dual (ASD) instantons through this differential geometry and physics seminar lecture. Learn about a dimension reduction result for Tian's generalized ASD instantons over product manifolds, which extends Yuanqi Wang's work on codimension-one reduction and encompasses G2 and Spin(7) instantons as well as degree zero Hermitian-Yang-Mills connections. Discover how the proof draws inspiration from observations about Yang-Mills energy and naturally leads to an adiabatic framework for these generalized ASD connections. Examine ongoing research toward establishing such an adiabatic scheme, including the complications that emerge in general cases and specific insights applicable to G2 instantons. Gain understanding of advanced topics in differential geometry and mathematical physics through collaborative research findings developed with Langte Ma.