Holomorphic Dynamics and Hyperbolic Geometry

Rational maps are self-maps of the Riemann sphere of the form z → p(z)/q(z) where p(z) and q(z) are polynomials. Kleinian groups are discrete subgroups of PSL(2,C), acting as isometries of 3-dimensional hyperbolic space and as conformal automorphisms of its boundary, the Riemann sphere. Both theories experienced remarkable advances in the last two decades of the 20th century and are very active areas of continuing research. The aim of the course is to introduce some of the main techniques and results in the two areas, emphasising the strong connections and parallels between them.