Andrey Gogolev will teach an online mini-course on hyperbolic geometry. This mini-course will be an educational one and there will be many HW problems. Only basic mathematical literacy will be required, and high schoolers are very welcome; even though some knowledge of calculus will be useful at some point.

Hyperbolic space is a central geometric concept which is ubiquitous in modern mathematics. However, only 200 years ago it was a hard-to-believe-in, exotic counter-example to Euclid’s 5th postulate. In this mini-course we will start with basic definitions and discuss fundamental properties of hyperbolic space such as its geometry and isometries, associated holomorphic structure, behavior at infinity, etc. At the very end we will touch on some modern research topics such as the moduli space of Riemann surfaces.