4 papers
Monodromy Groups of Dessins d'Enfant on Rational Polygonal Billiards Surfaces
Richard A. Moy, Jason Schmurr, Japheth Varlack
A dessin d'enfant, or dessin, is a bicolored graph embedded into a Riemann surface, and the monodromy group is an algebraic invariant of the dessin generated by rotations of edges…
Monodromy Groups of Dessins d'Enfant on Rational Triangular Billiards Surfaces
Madison Mabe, Richard A. Moy, Jason Schmurr +1
A dessin d'enfant, or dessin, is a bicolored graph embedded into a Riemann surface, and the monodromy group is an algebraic invariant of the dessin generated by rotations of edges…
Cayley Graphs on Billiard Surfaces, and Their Genus
Jason Schmurr, Jaime Lynne McCartney, Joanna Grzegrzolka
In this article we discuss a connection between two famous constructions in mathematics: a Cayley graph of a group and a (rational) billiard surface. For each rational billiard sur…
Translation Covers Among Triangular Billiard Surfaces
Jason Schmurr
We identify all translation covers among triangular billiard surfaces. Our main tools are the holonomy field of Kenyon and Smillie and a geometric property of translation surfaces,…