We will begin our talk with vortex equations ($\tau$-vortex equations). We then show that the vortex equations are a dimensional reduction of the Hermitian-Yang-Mills equation.
Vortex equation, Hermitian-Yang-Mills equation, Vortex bundle
References:


[GP93]     Oscar García-Prada. Invariant connections and vortices. Comm. Math. Phys., 156(3):527-546, 1993.
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