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Navigating moduli space with complex twists

Curtis McMullen — 2013

Journal of the European Mathematical Society

We discuss a common framework for studying twists of Riemann surfaces coming from earthquakes, Teichmüller theory and Schiffer variations, and use it to analyze geodesics in the moduli space of isoperiodic 1-forms.

Trees and the dynamics of polynomials

Laura G. DeMarcoCurtis T. McMullen — 2008

Annales scientifiques de l'École Normale Supérieure

In this paper we study branched coverings of metrized, simplicial trees F : T T which arise from polynomial maps f : with disconnected Julia sets. We show that the collection of all such trees, up to scale, forms a contractible space T D compactifying the moduli space of polynomials of degree D ; that F records the asymptotic behavior of the multipliers of f ; and that any meromorphic family of polynomials over Δ * can be completed by a unique tree at its central fiber. In the cubic case we give a combinatorial...

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