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Explore a comprehensive lecture on the Donagi-Pantev program for constructing Hecke eigensheaves in the geometric Langlands correspondence. Delve into the intricacies of parabolic logarithmic Higgs sheaves and their spectral varieties over Bun_G, viewed as Hitchin fibers within T^*(Bun_G). Examine known cases, potential challenges, and connections to Hitchin moduli space geometry. Gain insights from Carlos Simpson of Université Nice-Sophia Antopolis as he discusses various aspects of this construction in this 1-hour 14-minute talk presented at the Institut des Hautes Etudes Scientifiques (IHES).
