AbstractSupergeometry is an extension of geometry to include dimensions with anti-commutingcoordinates as motivated by high energy physics. In this talk, l wil give an introduction to themathematical treatment of supergeometry: supercommutative rings, supermanifolds, mapsbetween supermanifolds, their tangent bundles and split models.l will also introduce superRiemann surfaces which are holomorp...
AbstractThe non-abelian Hodge theory identifies moduli spaces of representations with moduli spaces of Higgs bundles through solutions to Hitchin's selfduality equations. On the one hand, this enables one to relate geometric structures on surfaces with algebraic geometry, and on the other hand, one obtains interesting hyper-Kähler metrics on the solution spaces. In my talk, I will explain how t...
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