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BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

High codimension phenomena for Hermitian Yang-Mills connections Li, Yang

Description

I will discuss my recent work constructing a non-conical singular Hermitian Yang-Mills connection on a homogeneous reflexive sheaf over $\mathbb{C}^3$, which is supposed to model the generic situation of bubbling phenomenon when the Fueter section has a zero. This example in particular shows that the uniqueness part of the Hitchin-Kobayashi correspondence does not extend naively to noncompact manifolds. A variant of this construction gives a sequence of HYM connections on the unit ball in $\mathbb{C}^3$ with uniformly bounded $L^2$ curvature, but the number of codimension 6 singularities tends to infinity along the sequence. This illustrates the substantial difficulty of the compactification problem in higher dimensional gauge theory.

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