Introduction to holomorphic dynamics
Abstract: 1D holomorphic dynamics focuses on the study of the dynamics of holomorphic functions in the plane. The main protagonist in these studies is the Julia set, which represents the chaotic part of the system. First we are going to present a general introduction to the topic and later talk about the dynamics of quadratic polynomials, which have fueled much of the contemporary advancements in the field. If time permits we will also try to explore the connection with hyperbolic geometry in the plane and hyperbolic 3-manifolds.