## Colloquium - James Freitag - Model Theory and Automorphic Functions

### Description

HH/305

Speaker: James Freitag (University of Illinois at Chicago)

Title: Model theory and automorphic functions

Abstract: 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 tobi-algebraicity problems which involve model theory, o-minimality, and differential equations. 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.

Coffee and Cookies will be served in the lounge (Hamilton Hall 216) at 3:00 pm. Everyone is welcome.

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