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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.
