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
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(with R. Niemeyer)
Submitted for publication
Pre-print available on the arXiv.
Publications
- Cutting sequences on square-tiled surfaces
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Geometriae Dedicata, 190 (2017), 53 -- 80.
Full text available for online reading; pre-print available on the arXiv - Hyperelliptic translation surfaces and folded tori
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(with M. Schmoll)
Topology and its Applications, 161 (2014), 73 -- 94.
Preprint - Pseudo-Anosov eigenfoliations on Panov planes
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(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