Richard Evan Schwartz
Publications
preprints
On The Optimal Embedded Paper Mobius Band
preprint (2021) pdf
companion
program
Paper Moebius bands with T Patterns
preprint (2020) pdf
An Improved Bound on the Optimal Embedded Paper Mobius Band
preprint (2020) pdf
The Farthest Point Map on the Regular Octahedron
preprint (2020) pdf
Companion program download
On Area Growth in Sol
preprint (2020) pdf
The Spheres of Sol (joint with
Matei P. Coiculescu)
preprint (2019) pdf
Companion program download
Research Monographs
The Phase Transition in Five Point Energy Minimization
Research Monograph (2016)
pdf
Companion program download
The Plaid Model
Annals of Mathematics Studies 198 (2018)
pdf
Companion program download
The Projective Heat Map
A.M.S. Research Monograph (2016)
pdf
Companion program download
The Octagonal PETs
A.M.S. Research Monograph (2013)
pdf
Download the companion programs
OctaPET
and
BonePET
Outer Billiards on Kites
Annals of Mathematics Studies 171 (2009)
the publication
preprint arXiv version
companion online material
Spherical CR Geometry and Dehn Surgery
Annals of Mathematics Studies 165 (2007)
the publication
Papers
Descartes Circle Theorem, Steiner Porism, and Spherical Designs
(joint with Serge Tabachnikov)
American Math Monthly Vol 127 Issue 3 (2020)
A Trichotomy for Rectangles inscribed in a Jordan Loop
Geometriae Dedicata (2020) to appear
pdf
Inscribed Rectangle Coincidences
Advances in Geometry (2019) to appear.
pdf
Five Point Energy Minimization: A Summary
Journal of Consructive Approximation (2019) to appear
pdf
A Hyperbolic View of the Seven Circles Theorem
Math. Intelligencer (Joint with Kostiantin Drach) to appear
(2019)
pdf
Four Lines and a Rectangle
J. Exp Math. (2019) to appear
pdf
companion program
Square Turning Maps and their Compactifications
Geometria Dedicata (volume in honor of Bill Goldman's 60th) (2017)
pdf
Lenghtening a Tetrahedron
Geometriae Dedicata (to appear) (2014)
pdf
Companion program download
The Pentagram Integrals for Poncelet Families
Journal of Geometry and Physics (2014) pp 384-405
pdf
Pentagram Spirals
J. Exp Math. Vol 22, Issue 4 (2013)
pdf
Companion program
click here
Liouville-Arnold integrability of the pentagram map on closed polygons
Duke Mathematics Journal, Vol 162, Number 12 (2012) pp 2149-2196
pdf
(joint with
Valentin Ovsienko and
Sergei Tabachnikov )
The 5-Electron Case of Thomson's Problem
J. Experimental Math, vol 22, issue 2, (2013) pp 157-186
pdf
companion program Electron Champ
Outer Billiards on the Penrose Kite: Compactification and Renormalization
Journal of Modern Dynamics, Issue 3 (2012) pp 473-581
pdf
Companion applet:
The applet
download the program:
the program
The Pentagram Integrals for Inscribed Polygons
Electronic Journal of Combinatorics (2011) to appear
pdf or
companion program (download)
joint with Sergei Tabachnikov )
Outer Billiards and the Pinwheel Map
Journal of Modern Dynamics Issue 2 (2011) 255-283
pdf
Companion Applet:
Pinwheel
The Pentagram map: A discrete integrable system
Communications in Mathematical Physics 299 (2010) pp 409-446
pdf
The paper has a small omission. See
this erratum or our
sequel paper for a fix.
(joint with
Valentin Ovsienko and
Sergei Tabachnikov )
Elementary Surprises in Projective Geometry
Mathematical Intelligencer , 2010 (to appear)
pdf
joint with Sergei Tabachnikov )
companion applet
Billiards in Nearly Isosceles Triangles
Journal of Modern Dynamics, Vol 3 Number 2 (2009) pp 159-231
pdf
(joint with Pat Hooper)
Obtuse Triangular Billiards II:
100 Degrees Worth of Periodic Trajectories
Journal of Experimental Math , Vol 18, No 2 pp 137-171 (2008)
paper (.pdf) or
wordlist
or applet
Discrete Monodromy, Pentagrams, and the Method of Condensation
Journal of Fixed Point Theory and Applications
(Special edition in Honor of V.I. Arnold's 70th birthday) (2008)
.pdf
Unbounded Orbits for Outer Billiards
Journal of Modern Dynamics 3 (2007)
.pdf
Research Announcement:
E.R.A-M.S. Electronic Notices, Vol 14 (2007)
web link
or
.pdf
The Poncelet Grid
Advances in Geometry Vol 7 pp 157-175 (2006)
.pdf
Affine Subdivision,
Steerable Semigroups,
and Sphere Coverings
Quarterly Journal of Pure and Applied Mathematics
(Special volume in honor of G.A. Margulis' 60th Birthday.)
.pdf
Obtuse Triangular Billiards I: Near the (2,3,6) Triangle
Journal of Experimental Mathematics (2006) Vol 15, Issue 2
.pdf
A Conformal Averaging Process on the Circle
Geometriae Dedicata Vol 117, Number 1 (2006)
.pdf
or the computer code
May, 2013: Stergios Antonakoudis found a much faster proof of the
main inequality in my paper. Click
here
A Better Proof of the Goldman-Parker
Conjecture
Geometry & Topology Vol 9 (2005) pp 1539-1602
.pdf or
Java applet
Modular Circle Quotients and PL
Limit Sets
Geometry&Topology
Volume 8 (2004) Paper 1 pp 1-34
The Density of Shapes in Three Dimensional
Barycentric Subdivision
Journal of Discrete and Computational Geometry
#30 (2003) 373-377
.pdf
Real Hyperbolic on the Outside,
Complex Hyperbolic on the Inside
Inventiones Mathematicae 151.2 (2003) 221-295
.pdf or
computer code
Complex Hyperbolic Triangle Groups
Proceedings of the International Congress of Mathematicians
(2002) Volume 1: Invited Lectures, pp 339-350
.pdf
Lucy and Lily: a
Game of Geometry and Number Theory
American Math Monthly
(Jan 2002) Vol 109.1, pp 13-20
.pdf
Circle Quotients and String Art
Topology
(2001) Vol 41.3 pp. 495-523
.pdf
The Pentagram Map is Recurrent
Journal of Experimental Mathematics
(2001) Vol 10.4 pp. 519-528
.pdf
Degenerating the Complex Hyperbolic Ideal Triangle
Groups
Acta Mathematica 186
(2001) Vol 186 p.105-154
.pdf
Ideal Triangle Groups, Dented Tori, and
Numerical Analysis
Annals of Mathematics
(2001) Vol 153 pp. 533-598
.pdf or
Desargues Theorem, Dynamics and Hyperplane
Arrangements
Geometriae Dedicata
(2001) Vol 87(1) pp. 261-283
.pdf
Symmetric Patterns of Geodesics and Automorphisms of
Surface Groups
Inventiones Mathematicae
(1997) Vol 128 pp. 177-199
.pdf
On the Integral Equation of a Third Order O.D.E.
Journal of Differential Equations
(1997) Vol 135 pp.183-191
Quasi-Isometric Rigidity and Diophantine Approximation
Acta Mathematica
(1996) Vol 177 pp. 75-112
The Large Scale Geometry of Hilbert Modular Groups
(with Benson Farb)
Journal of Differential Geometry
(1996) Vol 44 pp. 435-478
The Quasi-Isometry Classification of Rank One Lattices
I.H.E.S. Publications Mathematiques
(1995) Vol. 82 pp. 133-168
The Correlation of Length Spectra on two Hyperbolic Surfaces
(with Richard Sharp)
Communications in Mathematical Physics
(1993) Vol 153 pp. 323-330
Pappus's Theorem and the Modular Group
I.H.E.S. Publications Mathematiques
(1993) Vol. 78 pp. 187-206
A Projectively Natural Flow for Circle Diffeomorphisms
Inventiones mathematicae
(1992) Vol. 110 pp 627-647
The Pentagram Map
Journal of Experimental Mathematics
(1992) Vol 1 pp. 85-90
The Limit Sets of Some
Infinitely Generated Schottky Groups
Transactions of the American Math Society
(1992) Vol 355 pp. 865-875
Stuff I Will Probably Never Publish
Outer Billiards, Polytope Exchange Transformations, and
Quarter Turn Compositions
preprint (2011)
pdf
Outer Billiards, The Arithmetic Graph, and the Octagon
preprint (2010)
pdf
Companion programs:
OctoMap 1
and
OctoMap 2
Outer Billiards, Arithmetic Graphs, and multigrid flows
(2008) research notes
pdf
Introduction to McBilliards
(somewhat outdated) program documentation (2004),
joint with Pat Hooper
.pdf
or
the Mc Billiards program
Billiards Obtuse and Irrational,
light and breezy article (2005)
.pdf
Dented Tori
interactive document (1999)
C/tk program
A Dynamical Theorem in Projective Geometry
interacrive research announcement (1997)
HTML
Proving Disjointness with Foliated Patches
speculative technical notes (1999)
.pdf
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