Singularities of Hermitian-Yang-Mills connections and singular Donaldson-Uhlenbeck-Yau theorem

Singularities of Hermitian-Yang-Mills connections and singular Donaldson-Uhlenbeck-Yau theorem

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Xuemiao Chen, University of Maryland, College Park

Online Talk

Zoom linkhttps://princeton.zoom.us/j/594605776

The study of Yang-Mills connections in dimension four has been proven to be successful through the celebrated works of Donaldson. A key analytic aspect is the understanding of the compactification of the moduli space of Yang-Mills connections. The study of Hermitian-Yang-Mills connections enriches the picture by bridging with algebraic geometry. In higher dimensions, the compactification turns out to be extremely subtle and complicated, especially due to the appearance of higher codimensional singularities. In this talk, we will study such singularities through a notion of tangent cones for singular Hermitian-Yang-Mills connections.

Then I will talk about a version of the Donaldson-Uhlenbeck-Yau theorem over normal varieties.