Sarah Koch

An analytic construction of the Deligne-Mumford compactification of the moduli space of curves

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves. Their compactification is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmueller space by the action of the mapping class group gives a compactification of the moduli space. We put an analytic structure on this compact quotient and prove that with respect to this structure, it is canonically isomorphic (as an analytic space) to the Deligne-Mumford compactification.

On the postcritical set of a rational map

The postcritical set P ( f ) of a rational map

On Thurston's pullback map

f:{\mathbb P}^1\rightarrow {\mathbb P}^1

Pullback invariants of Thurston maps

f : P 1 → P 1 is the smallest forward invariant subset of

Roots, Schottky semigroups, and a proof of Bandt's conjecture

{\mathbb P}^1

Computing dynamical degrees of rational maps on moduli space

P 1 that contains the critical values of f . In this paper we show that every finite set