Pure Mathematics Colloquium - Holomorphic correspondences: matings, pinchings, tilings

Dates

Tuesday, March 7, 2023 - 14:00 to 15:00

Speaker:   Shaun Bullett (Queen Mary University of Londond)

Title:     Holomorphic correspondences: matings, pinchings, tilings

Abstract:

The multivalued dynamical system generated by the non-identity covering transformations of a pair of rational maps (P,Q) on the Riemann sphere, of degrees p and q, may be viewed as an iterated holomorphic r-to-r correspondence, where r=(p-1)(q-1). Under suitable conditions this behaves as a mating between a rational map of degree (p-1)(q-1) and a Kleinian group freely generated by a pair of elements of PSL(2,C) of orders p and q. 

I will give an overview of some of the ideas involved in constructing matings between rational maps and Kleinian groups, and proving results about these and their moduli spaces, highlighting recent work and open questions.