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Hodge theory, unlikely intersections and o-minimal geometry

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Kenneth Chiu
Rice University/MPIM
Thu, 27/06/2024 - 15:00 - 16:00
MPIM Lecture Hall
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We will begin with an introduction of the key notions in Hodge theory. We will then explain how Hodge theory is used to prove results (called Ax-Schanuel) about transcendental degrees of function fields. When phrased geometrically, it roughly says that if the intersection of a given algebraic variety and the graph of a period mapping is "unlikely", then this intersection should be related to group orbits of Hodge structures. Since period mappings are transcendental, to prove Ax-Schanuel results one needs a theory that interpolates algebraic geometry and analytic geometry. We will give an introduction of o-minimal geometry and mention their applications. If time permits, we will discuss speculations on p-adic transcendence.


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