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Title:
Minimal surfaces in hyperbolic spaces and their Higgs bundles
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Abstract:
One of the pieces of the non-abelian Hodge correspondence says that stable Higgs bundles parametrise equivariant (or "twisted") harmonic maps from the Poincare disc into a noncompact symmetric space. Since minimal surfaces are conformal harmonic maps this means we can use Higgs bundles to parametrise minimal surfaces. In fact this allows us to define a moduli space of equivariant minimal surfaces and study its structure. We only know the details for low dimensional hyperbolic spaces (real and complex) at the moment, but these give a good picture of what to expect in a little more generality. I will explain how this works for 3 and 4 dimensional real hyperbolic space. This is joint work with John Loftin (Rutgers-Newark).
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