Chennai Mathematical Institute


Lecture Announcement
Date: Wednesday, 19 April, 2023.
Time: 2:00 PM
Venue: Lecture Hall 1
Deformation space analogies between Kleinian reflection groups and rational maps

Sabyasachi Mukherjee


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.
Time permitting, we will touch upon analytic aspects of the above correspondence.