Explore a lecture on parabolic Higgs bundles and their connection to Hecke eigensheaves in the geometric Langlands program. Delve into the collaborative work of Carlos Simpson, Ron Donagi, and Tony Pantev, focusing on their conjectural program for constructing Hecke eigensheaves using nonabelian Hodge theory. Examine the case of a genus 2 curve, investigating how a rank 2 local system on the curve relates to a rank 8 local system on the moduli stack of rank 2 bundles. Discover the description of the associated parabolic logarithmic Higgs bundle and its spectral variety, which is revealed to be the Hitchin fiber corresponding to the input local system.
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Moduli Spaces of Parabolic Connections and Parabolic Bundles and Geometric Langlands by M-H Saito
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Asymptotics in Hitchin's Moduli Space
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Twistor Space for Moduli of Local Systems on Open Curves
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Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices
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Higgs Bundles and the Topology of Higher Teichmüller Spaces
