Research Overview

My research interests essentially lie at the intersection of geometry and dynamics. In general I am interested in how the geometry of a space can affect the types of dynamical systems that live on that space. More specifically I am interested in the various dynamical systems associated to translation surfaces and their moduli.

For more detailed information, see my research statement.


The wild, elusive singularities of the T-fractal
(with R. Niemeyer)
Submitted for publication
Pre-print available on the arXiv.


Cutting sequences on square-tiled surfaces
Geometriae Dedicata, 190 (2017), 53 -- 80.
Full text available for online reading; pre-print available on the arXiv
Hyperelliptic translation surfaces and folded tori
(with M. Schmoll)
Topology and its Applications, 161 (2014), 73 -- 94.
Pseudo-Anosov eigenfoliations on Panov planes
(with M. Schmoll)
Electronic Research Announcements in Mathematical Sciences, 21 (2014), 89 -- 108.

In Progress

Haupt's theorem for strata
with M. Bainbridge, C. Judge, and I. Park
Compositions of scaling involutions and measure-preserving transformations