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The Shape of Thurston's Master Teapot
Harrison Bray, Diana Davis, Kathryn Lindsey +1
We establish basic geometric and topological properties of Thurston's Master Teapot and the Thurston set for superattracting unimodal self-maps of intervals. In particular, the Mas…
How to hear the shape of a billiard table
Aaron Calderon, Solly Coles, Diana Davis +2
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods…
Cutting sequences, regular polygons, and the Veech group
Diana Davis
We describe the cutting sequences associated to geodesic flow on regular polygons, in terms of a combinatorial process called "derivation." This work is an extension of some of the…
Lines in positive genus: An introduction to flat surfaces
Diana Davis
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple thing…