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.

Preprints

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

Publications

Cutting sequences on square-tiled surfaces
To appear in Geometriae Dedicata.
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.
Preprint
Pseudo-Anosov eigenfoliations on Panov planes
(with M. Schmoll)
Electronic Research Announcements in Mathematical Sciences, 21 (2014), 89 -- 108.

In Progress

An interval exchange transformation on a fractal surface
with R. Niemeyer
Compositions of scaling involutions and measure-preserving transformations