The Yang-Mills-Higgs fields are critical points of the famous Yang-Mills-Higgs functional which plays a fundamental role in quantum field theories. It is known that the isolated singularities of two dimensional YMH fieds are in general not removable. In this talk, we will give a sharp estimate of the singular YMH fields, namely, we establish a precise relation between the order of singularity and the limiting holonomy around that point. This is a recent joint work with Bo Chen.
