Geodesics on modular surfaces and functional transcendence

Abstract: The approach to the André-Oort conjecture suggested by Pila-Zannier relies on the study of (complex) subvarieties of Shimura varieties (and their universal cover) from the viewpoint of functional transcendence. I will first recall the main results of this theory in the simplest case of the product of two modular curves. I will then deduce analogous theorems for real subvarieties of a modular curve seen as a real algebraic surface.

algebraic geometrynumber theory

Audience: researchers in the topic

Number Theory Seminars at Università degli Studi di Padova