|Date:||Tue, April 4, 2017|
|Place:||Research I Seminar Room|
Abstract: In the formal mating of two quadratic polynomials, we have two filled Julia sets on the sphere, and external rays connecting them. Ray-equivalence classes are fundamental to define or to describe various notions of mating. The talk will give some general explanations and focus on a few examples, where ray connections provide specific phenomena:
* Discontinuity of mating when both polynomials are varied.
* Shared matings with precisely known multiplicity.
* Direct construction of topological matings by bounding the diameter of ray connections.
* Hausdorff obstructions, which prevent a topological mating.