# Papers for Sarah C. Koch

**Papers**
*Braiding Cantor Julia sets and the topology of the shift locus*
(with J. Bavard, D. Calegari, Y. M. He and A. Walker)

In preparation, 2017.

*On the postcritical set of a rational map* (with L.
DeMarco and C. McMullen)

Submitted, 2017.

*Eigenvalues of the Thurston operator*
(with X. Buff and A. Epstein)

Submitted, 2017.

*On balanced planar graphs, following W. Thurston* (with Tan Lei)

Submitted to the Thurston Memorial Conference Proceedings, 2015.

*Origami, affine maps, and complex dynamics*
(with W. Floyd, G. Kelsey, R. Lodge, W. Parry, K. Pilgrim, and E. Saenz)

Arnold Mathematical Journal

Vol. 3, 2017.

*A disconnected deformation space of rational maps* (with E.
Hironaka)

Journal of Modern Dynamics

Vol. 11, 2017.

*Roots, Schottky Semigroups, and a proof of
Bandt's
conjecture* (with D. Calegari and A. Walker)

Ergodic Theory Dynamical Systems

Vol. 37, 2017.

*Computing dynamical degrees of maps on
moduli space* (with R. Roeder)

Ergodic Theory and Dynamical Systems

Vol. 36, 2016.

*Pullback invariants of Thurston maps* (with K.
Pilgrim and N.
Selinger)

Transactions of the American Mathematical Society

Vol. 368, No. 7, 2016.

*An analytic construction of the Deligne-Mumford compactification of the moduli space of
curves*
(with J. H. Hubbard)

Journal of Differential Geometry

Vol. 98, No. 2, 2014.

*Teichmüller theory and critically finite endomorphisms*

Advances in Mathematics

Vol. 248, 2013.

*Böttcher coordinates* (with X. Buff and A. Epstein)

Indiana University Mathematics Journal

Vol. 61, No. 5 2012.

*Twisted matings and equipotential gluings* (with X.
Buff
and A. Epstein)

Annales de la faculté des sciences de Toulouse

Sér. 6 Vol. 21 No. S5 2012.

*Questions about polynomial matings* (with X.
Buff, A. Epstein, D. Meyer, K. Pilgrim, M. Rees, and Tan Lei)

Annales de la faculté des sciences de Toulouse

Sér. 6 Vol. 21 No. S5 2012.

*On a Theorem of Kas and Schlessinger* (with O. Antolín-Camarena)

Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces.

Contemporary Mathematics, 575. American Mathematical Society, 2012.

*Iterated monodromy for a two-dimensional map* (with J. Belk)

In the tradition of Ahlfors-Bers V.

Contemporary Mathematics, 510. American Mathematical Society, 2010.

*On Thurston's Pullback Map* (with X. Buff, A. Epstein and K. Pilgrim)

Complex Dynamics, Families and Friends, 561-583, AK Peters, Wellesley, MA, 2009.

*SaddleDrop: a tool for studying dynamics in $\C^2$*

Teichmüller theory and moduli problems, 465-479, Ramanujan Math. Soc. Lect. Notes Ser., 10, Ramanujan Math.
Soc., 2010.

**PhD Theses**
*A new link between Teichmüller theory and complex dynamics*, Cornell University, 2008.

*Teichmüller theory and applications to endomorphisms of $\P^n$*, Université de Provence,
2007.