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Delve into the second lecture of Raphaël Belliard's series on the quantum geometry of Fuchsian systems, presented at the TRSalento school from September 5-16, 2022. Explore advanced concepts and theories in this comprehensive two-hour session, building upon the foundations laid in the previous lecture. Gain deeper insights into the intricate relationship between quantum mechanics and geometric structures in Fuchsian systems. Access additional resources and materials related to this topic by visiting the official school website at https://sites.google.com/view/tr-salento-2022/.