Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

Let $X$ and $Y$ be algebraic varieties over $\mathbb C$ and let $\phi: X^{an} \rightarrow Y^{an}$ be a complex analytic map which is not algebraic. In this case, for most algebraic subvarieties $X_0 \subset X$, the image $\phi (X_0)$ is not algebraic. The pairs of algebraic subvarieties $(X_0 , Y_0)$ with $X_0 \subset X$ and $Y_0 \subset Y$ such that $\phi (X_0) = Y_0$ are called \emph{bi-algebraic} for $\phi$. Specific instances of bi-algebraic problems have played an important role in the resolution of conjectures in diophantine geometry and model theory over the past decade. In this talk, I will give a general overview of model-theoretic approaches to this type of problem coming from o-minimal and differential algebraic geometry. I will give a more detailed description of one approach to the problem in the case that $\phi$ is the uniformizing function of a discrete subgroup of $SL_2$.

Model Theory And Bi-Algebraic Geometry