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Explore the intersection of algebraic geometry and model theory in this advanced mathematical lecture examining algebraic flat connections through the lens of o-minimality. Delve into the proof that an algebraic flat connection has ℝan, exp-definable flat sections if and only if it is regular singular with unitary monodromy eigenvalues at infinity, building upon and refining previous work by Bakker–Mullane. Discover how this result provides an o-minimal characterization of classical properties of the Gauß-Manin connection, offering new insights into fundamental geometric structures. Learn about the collaborative research conducted with Moritz Kerz that advances our understanding of the relationship between algebraic flat connections and definability in o-minimal structures. Gain exposure to cutting-edge developments in this specialized area of mathematics, including recent progress and ongoing challenges in the field, as presented by a leading expert from Copenhagen University and Harvard University at the Institute for Advanced Study's Workshop on Special Cycles and Related Topics.
