Differential Geometry Seminar: Singularities of Hermitian-Yang-Mills connections

Seminar | November 5 | 3:10-4 p.m. | 939 Evans Hall

 Xuemiao Chen, Stony Brook (visiting Berkeley)

 Department of Mathematics

Abstract: The celebrated Donaldson-Uhlenbeck-Yau theorem builds the correspondence between irreducible Hermitian-Yang-Mills (HYM) connections and slope stability for holomorphic vector bundles over a Kahler manifold. Singular HYM connections naturally occur when one tries to compactify the moduli space of HYM connections. For singular HYM connections, the tangent cones at any singular point are known to exist. In this talk, I will show how to characterize algebraically the tangent cones at an isolated singularity in some special case. This can be viewed as a local Donaldson-Uhlenbeck-Yau theorem. The talk is based on joint work with Song Sun.