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Explore a 58-minute lecture by Carlos Simpson on Higgs bundles for Hecke eigensheaves in the geometric Langlands program, focusing specifically on rank 2 local systems on curves of genus 2. Learn about joint work with Ron Donagi and Tony Pantev examining the moduli space of bundles with two connected components: P³ and the intersection of two quadrics in P⁵. Discover the search for Higgs bundles on these spaces with parabolic structure and logarithmic poles along the wobbly locus, the geometry of the wobbly locus and its singularities, and the application of the Dolbeault higher direct image construction for calculating Hecke operators. This mathematical talk was recorded during the "Families of Kähler spaces" thematic meeting at the Centre International de Rencontres Mathématiques (Marseille, France) in April 2025.
