Zugehörigkeit:
Rice University/MPIM
Datum:
Don, 27/06/2024 - 15:00 - 16:00
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.
