Colloquium abstracts

Mahan Mj
April 15, 2021

Combining rational maps and Kleinian groups via orbit equivalence:  We develop a new orbit equivalence framework for holomorphically combining the dynamics of complex polynomials with that of Kleinian surface groups. We show that the only torsion-free Fuchsian groups that can be thus combined are punctured sphere groups. We describe a new class of maps that are topologically orbit-equivalent to Fuchsian punctured sphere groups. We call these higher Bowen-Series maps. The existence of this class ensures that, unlike in higher dimensions, topological orbit equivalence rigidity fails for Fuchsian groups acting on the circle. We also classify the collection of Kleinian Bers' boundary groups that are combinable in our framework. This is joint work with Sabyasachi Mukherjee.