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Explore conjectures aimed at identifying linear differential equations derived from Gauss-Manin connections in this 54-minute lecture from the Hausdorff Center for Mathematics. Delve into the Katz-Grothendieck, André, and Bombieri-Dwork conjectures, and examine a refined criterion for detecting differential equations originating from families of hypergeometric Calabi-Yau varieties. Conclude with an explanation of the classification list for Heun and Painlevé VI equations, gaining insights into the intricate world of algebraic geometry and differential equations.
