## Special Colloquium

James Freitag

UIC

Intersections of varieties with isogeny classes

**Abstract:**Fix $a \in \mathbb C$ and some element $g \in GL_2 (\mathbb C)$. How many $b \in \mathbb C$ are there so that the elliptic curves $E_a, \, E_b$ are isogenous and the elliptic curves $E_{g a} , E_{g b}$ are isogenous? This is a specific case of the general topic of understanding intersections of varieties with products of isogeny classes, where Andre-Pink conjecture completely classifies those varieties which contain infinitely many isogeny class points. In this talk we will discuss how the conjecture was proved with effective bounds using a combination of o-minimal geometry, algebraic differential equations, and model theory.

Friday December 8, 2017 at 3:00 PM in SEO 636