Special Colloquium

Xuemiao Chen, University of Maryland

"Singularities of Hermitian-Yang-Mills connections"

The study of Yang-Mills connections has been proven successful through the celebrated works of Donaldson on smooth four manifolds. 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 through the well-known Donaldson-Uhlenbeck-Yau theorem. In higher dimensions, the compactification turns out to be extremely subtle and complicated, especially due to the appearance of higher codimensional singularities. We will first state a singular version of the Donaldson-Uhlenbeck-Yau theorem over normal varieties. Then we will prove a local Donaldson-Uhlenbeck-Yau theorem for the study of singularities of Hermitian-Yang-Mills connections.

Zoom link: https://uwaterloo.zoom.us/j/99159090516?pwd=Y1REWmRLd3B4cFhraE1kR0ZTU3JJZz09