Alladi Ramakrishnan Hall

An Introduction to Holomorphic Dynamics

Malavika Mukundan

University of Michigan

Holomorphic dynamics is the study of iterating holomorphic self-maps f of a Riemann surface X. In this talk we will give an overview of dynamical objects of interest - the Fatou and Julia sets, and explore what happens when X is the plane or the Riemann sphere. When X is the sphere, special maps that satisfy a property called postcritical finiteness can be studied by techniques from Teichmuller theory; we will briefly explain the philosophy behind this connection.