Complex Analysis, Dynamics and Geometry Seminar

Invariant graphs and curves appear naturally in various aspects of complex dynamics. For instance, Hubbard trees are used to classify all postcritically finite polynomials, while Thurston obstructions, which are certain invariant multicurves, appear in the celebrated Thurston characterization of rational maps. Concentrating on specific families of postcritically finite rational maps, I will discuss how invariant graphs can be used to analyze dynamics of simple closed curves under the pullback by the map as well as algebraic properties (such as growth and amenability) of the associated iterated monodromy groups. Speaker(s): Mikhail Hlushchanka (UCLA)