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Title:
Vortices and the Morse theory of the Yang-Mills-Higgs functional
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Abstract:
Vortices appear as energy minimisers of the Yang–Mills–Higgs functional. In previous work (joint with Richard Wentworth), we used the Morse theory of this functional to compute topological invariants of moduli spaces of rank 2 vortices on Riemann surfaces. After discussing this, I will then describe some more recent work in which the vortex equations appear as linearised solutions of a reverse heat flow on the space of Higgs bundles (in the sense studied by Hitchin and Simpson). Spaces of flow lines for this energy functional have an interesting algebro-geometric structure, and
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