Non-Euclidean geometry, modular surface, and coding of geodesics

INSTRUCTOR: Svetlana Katok

COURSE SUMMARY:

In this mini-course we will explore connections between hyperbolic geometry, geodesics on the modular surface and various kinds of continued fractions. Particular topics will include: hyperbolic geometry (geodesics, isometries, hyperbolic area); modular group and its fundamental region; coding of geodesics on the modular surface via fundamental region and via various kinds of continued fractions.