Research Papers
Rich Schwartz' homepage


Preprints

  • Modular Cantor Sets and Projective Geometry
    (2008) in progress

  • Outer Billiards on Kites
    (2008) research monograph
    pdf or interactive guide

  • Billiards in Nearly Isosceles Triangles
    (2008) preprint (w/ Pat Hooper)
    pdf

    Publications

  • Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories
    Journal of Experimental Math (2008) to appear
    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

  • Unbounded Orbits for Outer Billiards: Research Announcement
    E.R.A-M.S. (A.M.S.) Electronic Notices, Vol 14 (2007)
    web link or .pdf

  • The Poncelet Grid
    Advances in Geometry Vol 7 (2007) 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

  • Spherical CR Geometry and Dehn Surgery
    research monograph
    Annals of Mathematics Studies 165 (2007)
    .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

  • 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

    Other Documents