Date: Wednesday, 19 April, 2023.
Time: 2:00 PM
Venue: Lecture Hall 1
Deformation space analogies between Kleinian reflection groups and rational maps
An intriguing dictionary exists between two branches of conformal
dynamics: the theory of Kleinian groups and dynamics of rational maps
on the Riemann sphere. We will describe an explicit correspondence
between certain Kleinian reflection groups and certain
anti-holomorphic rational maps acting on the Riemann sphere. This
correspondence has several dynamical and parameter space
consequences. To illustrate some of these, we will discuss striking
similarities between the deformation spaces of these two classes of
conformal dynamical systems, including an analogue of Thurston's
compactness theorem for anti-holomorphic rational maps and relations
between the global topology of the corresponding deformation spaces.