Billiards in nearly isosceles triangles (joint with Rich Schwartz) Journal of Modern Dynamics 3 (2009), no. 2, 159--231. Abbreviated abstract: We prove that nearly isosceles triangles have periodic billiard paths. View original: from Journal of Modern Dynamics
[pdf] View Preprint: [pdf]
Lower bounds on growth rates of periodic billiard trajectories in some irrational polygons
Journal of Modern Dynamics 1 (2007), no. 4, 649--663. View original: from Journal of Modern Dynamics
[pdf] View Preprint: [pdf] Abbreviated abstract: Examples of irrational polygons where the growth rate of periodic trajectories is slightly super-linear are provided.
Periodic Billiard Paths in Right Triangles are Unstable
Geom. Dedicata 125 (2007), no. 1, 39--46. The original publication is available at www.springerlink.com. [Link] View Preprint: [pdf] [ps]
From Pappus' theorem to the twisted cubic
Geometriae Dedicata 110 (2005), 103--134. The original publication is available at www.springerlink.com. [Link] View Preprint: [pdf] [ps]
Preprints:
Generalized Staircases: Recurrence and Symmetry (joint with Barak Weiss) Abbreviated abstract: We study properties of Z-covers of translation surfaces. View Preprint: [pdf]
Another Veech Triangle View preprint: [pdf] [ps] Abstract: The triangle with angles (Pi/12, Pi/3, 7 Pi/12) has the lattice property.
Dynamics on an infinite surface with the lattice property View Preprint: [pdf]
Grid graphs and lattice surfaces View preprint: [pdf] An earlier version (with a different presentation) [pdf]
Notes:
Notes on deforming the staircase surface These are notes on a surface first thought about by Pascal Hubert and Barak Weiss.
View notes: [pdf]
Slides from talks:
Billiards in nearly isosceles triangles
Analysis Seminar,
DePaul University
October 1, 2008
[slides]
Some irrational polygons have many periodic billiard paths
Spring Topology and Dynamics Conference,
Milwaukee, Wisconsin,
March 15, 2008
[printable slides]
Billiards in right triangles are unstable
Geometry, Dynamics and Topology Day at Eastern Illinois University,
October 27, 2007
[abstract] [printable slides] [slides used]
On the stability of periodic billiard paths in triangles
Thesis defense,
Stony Brook. May 2006. View slides: [pdf]
Computation and Billiards in Triangles
Foundations of Computational Mathematics Conference,
Computational geometry and topology Workshop
Santander, Spain. 2005.
[Abstract] Slides:[pdf]
A note on comparing numbers in a real algebraic field View Preprint: [pdf]
Introduction to McBilliards with Rich Schwartz Documentation for the program McBilliards. 2004.
(This documentation is outdated, but may still be of interest.) View: [pdf] [ps]
