An infinite surface with the lattice property Ⅱ: Dynamics of pseudo-Anosovs
Journal of Modern Dynamics, 14 (2019) no. 1, 243--276, doi: 10.3934/jmd.2019009. Preprint:arXiv:1803.01741
Immersions and translation structures I: The space of structures on the pointed disk,
Conformal Geometry and Dynamics, 22 (2018), 235-270, doi: 10.1090/ecgd/326. Preprint:arXiv:1309.4795.
The Invariant Measures of some Infinite Interval Exchange Maps
Geometry & Topology 19 (2015) 1895-2038,
doi: 10.2140/gt.2015.19.1895. Abbreviated abstract: We study classify the locally finite ergodic invariant measures of some skew rotations and other infinite interval exchange maps. View Preprint: [pdf]
Another Veech Triangle Proceedings of the AMS,
141 (2013), no. 3, 857-865, doi: 10.1090/S0002-9947-2013-06139-9.
Published version: [pdf] View preprint: [pdf] Abstract: The triangle with angles (Pi/12, Pi/3, 7 Pi/12) has the lattice property.
Billiards in nearly isosceles triangles 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:
Immersions and the space of all translation structures View Preprint: [pdf]
The Necker cube surface
with Pavel Javornik,
Preprint: arXiv:2310.03115.
Dynamics on an infinite surface with the lattice property (Subsumed by An infinite surface with the lattice property I and II). View Preprint: [pdf]
A note on comparing numbers in a real algebraic field View note: [pdf]
Introduction to McBilliards with Documentation for the program McBilliards. 2004.
(This documentation is outdated, but may still be of interest.) View: [pdf] [ps]
The rel leaf and real-rel ray of the Arnoux-Yoccoz surface in genus 3 with Barak Weiss
This work was subsumed by "Rel leaves of the Arnoux-Yoccoz surfaces" which proves the results of this paper in arbitrary genus. It may be of interest to people with special interest in the genus three case. Available on the arXiv.
Truchet Tilings and Renormalization View Preprint: [pdf]
Conference Proceedings:
Immersions and the space of all translation surfaces
Abstracts from the workshop held May 23-29, 2014. Organised by
Howard Masur,
Martin Moller and Anton Zorich. View preprint: [pdf]
Renormalization of Polygon Exchange Maps arising from Corner Percolation Abstracts from the workshop held May 8-14, 2011. Organised by
Howard Masur,
Martin Moller and Anton Zorich.
Oberwolfach Reports 25 (2011), 1384–779. View preprint: [pdf]
Slides and handouts from talks:
Geodesic representatives on surfaces without metrics
RTG Colloquium
January 16, 2024, Universität Heidelberg
[pdf slides]
Geodesic representatives on surfaces without metrics
Séminaire Rauzy
October 20, 2023, Institut de Mathématiques de Marseille
[pdf slides]
Hidden symmetries of the dodecahedron
Hyperbolic Geometry Seminar
October 27, 2020, CUNY
[pdf slides]
Infinite nilpotent covers of square-tiled surfaces
Workshop on Dynamics and Moduli Spaces of Translation Surfaces
October 22 - 26, 2018, The Fields Institute
[html slides]
[pdf slides]
Dynamics of Pseudo-Anosovs on a limit of Veech's surfaces
Workshop on Dynamical Systems and Related Topics, In Memor of Bill Veech, University of Maryland, April 6, 2018
[svg slides] (Use up/down arrows to navigate) [pdf version]
Periodicity and ergodicity in the trihexagonal tiling
2017 Joint Mathematics Meeting, Atlanta, GA, January 7, 2017
[svg slides] (Use up/down arrows to navigate)
Periodicity and ergodicity in the trihexagonal tiling
Midwest Dynamical Systems Seminar, Indianapolis, IN, November 4-6, 2016.
[svg slides] (Use up/down arrows to navigate)
[Tiling billiards app of Alex St. Laurent]
Immersions and the space of all translation surfaces
Flat Surfaces and Dynamics of Moduli Space, Oaxaca, Mexico. May 12th, 2016.
[pdf slide] [pdf handout]
Piecewise isometric dynamics on the square pillowcase
Ergodic Theory and Statistical Mechanics,
Princeton University,
November 13th, 2014.
[svg slides] [inferior pdf slides]
Topologizing the space of all translation surfaces
Complex Analysis and Dynamics Seminar, CUNY Graduate Center, 4 Apr 2014.
[svg slides] [pdf of slides]
Immersions and the space of all translation surfaces
Oberwolfach conference on flat surfaces.
[svg slides]
Notes on Veech triangle groups
These notes explain how to construct translation surfaces with Veech triangle groups.
Teichmuller theory trimester,
The Hausdorff Institute in Bonn, Germany
June 2010.
[notes]
Infinite genus surfaces admitting two affine multi-twists
CCSU Teichmuller Theory Conference,
Central Connecticut State University
April 25, 2010
[slides]
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]
