Modular forms and diophantine analysis

Seminar of Mathematics
Abstract:
The theory of modular forms has interactions with many fields in mathematics and beyond. Nowadays integrals of modular functions along hyperbolic geodesics are being very much exploited because of their many applications to problems in arithmetic, geometry, and the theory of modular forms itself. First I will consider some of these recent results. Then I will discuss a new approach in the study of these modular objects that relies on diophantine approximation, and the new insights it brings.
The talk is aimed at a general audience and I will not assume knowledge of modular forms.