James Freitag, University of Illinois at Chicago
"Model theory, automorphic functions, and differential equations"
Given an analytic function, $f: \mathbb C^n \rightarrow \mathbb C^n$, we call an algebraic variety $V \subset \mathbb C^n$ bi-algebraic for $f$ if $f(V)$ is algebraic. Most varieties are not bi-algebraic, and identifying the collection should reveal certain aspects of the geometry of $f$. We will talk about several recent approaches to bi-algebraicity problems which involve model theory. We will also talk about how bi-algebraicity problems are related to several number theoretic applications - special points conjectures and transcendence problems. The results we discuss center around automorphic functions, but we will not assume any background on this topic.
MC 5501