Title of the course: Hyperbolic geometry of the unit disc
Instructor: Dr. Ahmed Yekta Ökten
Institution: University of Rome Tor Vergata
Dates: 31 August – 6 September 2026
Prerequisites: Advanced calculus, basic knowledge of complex numbers
Level: Advanced undergraduate, graduate
Abstract: We start this course by defining the notion of holomorphic functions and give their basic properties. We then prove the Schwarz-Pick lemma for the holomorphic functions on the unit disc. With the help of the Schwarz-Pick lemma we construct the hyperbolic (Poincar´e) distance and study its properties. We will then state the Riemann mapping theorem and extend the definition of the hyperbolic metric to any simply connected domain not equal to C itself. If time permits, we will conclude by studying the dynamics of the self maps of the disc and give proof of the Denjoy-Wolff theorem with an easy application of the hyperbolic distance.
Language: English