Moduli Spaces of Parabolic Connections and Parabolic Bundles and Geometric Langlands by M-H Saito
Explore the intricacies of moduli spaces and their connections to Geometric Langlands theory in this comprehensive lecture. Delve into A-parabolic connections, λ-connections, and their properties, including residues, local exponents, and the Fuchs relation. Examine parabolic and quasiparabolic bundles, stability conditions, and the construction of moduli spaces for stable parabolic connections and Higgs bundles. Investigate deformation theory, symplectic structures, and the relationship between parabolic connections and bundles. Analyze specific cases such as the Painlevé VI equation and results from Arinkin and Lysenko. Gain insights into the interplay between mathematics and theoretical physics in this advanced exploration of Quantum Fields, Geometry, and Representation Theory.