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3:00 pm Monday, December 9, 2013 Special Geometry Analysis Seminar: Compatibility of holomorphic and unitary decompositions of Higgs bundlesby Brian Collier (UIUC) in HB227- Higgs bundles are holomorphic vector bundles with an auxiliary field, called a Higgs field, over a Riemann surface $\Sigma$. Through the nonabelian Hodge theorem the moduli space of polystable Higgs bundles is homeomorphic to the character variety of $\Sigma$. One direction of the homeomorphism is given by a Kobayashi-Hitchin correspondence relating polystable Higgs bundles to solutions of certain gauge theoretic equations which yield a special metric and a flat connection. In this talk we will review some Higgs bundle basics and examine when a holomorphic splitting is unitary with respect to the special metric.
Submitted by mwolf@rice.edu |