I was born in Los Angeles, in 1966. I got my BS in Mathematics from UCLA in 1987 and
my PhD in Mathematics from Princeton in 1991. I was a speaker at the International
Congress of Mathematicians in 2002 and a Guggenheim Fellow in 2003. My hobbies
include comic book writing, computer programming, cycling, classical music, and
reading. I am married and have 2 daughters.
Schwartz, Richard Evan The pentagram integrals for Poncelet families. Journal of Geometry and Physics/Journal of Geometry and Physics. 2015; 87 : 432-449. |
Hooper, W. Patrick, Schwartz, Richard Erratum: Billiards in nearly isosceles triangles. Journal of Modern Dynamics/Journal of Modern Dynamics. 2014; 8 (1) : 133-137. |
Schwartz, Richard Evan Lengthening a tetrahedron. Geometriae Dedicata/Geometriae Dedicata. 2014; 174 (1) : 121-144. |
Ovsienko, Valentin, Schwartz, Richard Evan, Tabachnikov, Serge Liouville–Arnold integrability of the pentagram map on closed polygons. Duke Math. J./Duke Math. J.. 2013; 162 (12) : 2149-2196. |
Schwartz, Richard Evan Pentagram Spirals. Experimental Mathematics/Experimental Mathematics. 2013; 22 (4) : 384-405. |
Schwartz, Richard Evan The Five-Electron Case of Thomson’s Problem. Experimental Mathematics/Experimental Mathematics. 2013; 22 (2) : 157-186. |
Schwartz, Richard Outer billiards and the pinwheel map. Journal of Modern Dynamics/Journal of Modern Dynamics. 2011; 5 (2) : 255-283. |
Schwartz, Richard Outer billiards on the Penrose kite: Compactification and renormalization. Journal of Modern Dynamics/Journal of Modern Dynamics. 2011; 5 (3) : 473-581. |
Schwartz, Richard Evan, Tabachnikov, Serge Elementary Surprises in Projective Geometry. Math Intelligencer/The Mathematical Intelligencer. 2010; 32 (3) : 31-34. |
Ovsienko, Valentin, Schwartz, Richard, Tabachnikov, Serge The Pentagram Map: A Discrete Integrable System. Commun. Math. Phys./Commun. Math. Phys.. 2010; 299 (2) : 409-446. |
Hooper, W., Schwartz, Richard Billiards in nearly isosceles triangles. Journal of Modern Dynamics/Journal of Modern Dynamics. 2009; 3 (2) : 159-231. |
Schwartz, Richard Evan Obtuse Triangular Billiards II: One Hundred Degrees Worth of Periodic Trajectories. Experimental Mathematics/Experimental Mathematics. 2009; 18 (2) : 137-171. |
Ovsienko, Valentin, Schwartz, Richard, Tabachnikov, Serge Quasiperiodic motion for the pentagram map. Electronic Research Announcements in Mathematical Sciences/Electronic Research Announcements in Mathematical Sciences. 2009; 16 (0) : 1-8. |
Schwartz, Richard Evan Discrete monodromy, pentagrams, and the method of condensation. J. fixed point theory appl./J. fixed point theory appl.. 2008; 3 (2) : 379-409. |
Schwartz, Richard Evan Affine Subdivision, Steerable Semigroups, and Sphere Coverings. Pure and Applied Mathematics Quarterly/Pure and Applied Mathematics Quarterly. 2007; 3 (4) : 897-926. |
Schwartz, Richard Evan The Poncelet grid. Advances in Geometry/Advances in Geometry. 2007; 7 (2) |
Schwartz, Richard Unbounded orbits for outer billiards I. Journal of Modern Dynamics/Journal of Modern Dynamics. 2007; 1 (3) : 371-424. |
Schwartz, Richard Evan A Conformal Averaging Process on the Circle. Geometriae Dedicata/Geometriae Dedicata. 2006; 117 (1) : 19-46. |
Schwartz, Richard Evan Obtuse Triangular Billiards I: Near the (2, 3, 6) Triangle. Experimental Mathematics/Experimental Mathematics. 2006; 15 (2) : 161-182. |
Schwartz, Richard Evan A better proof of the Goldman–Parker conjecture. Geom. Topol./Geom. Topol.. 2005; 9 (3) : 1539-1601. |
Schwartz, Richard Evan Modular circle quotients and PL limit sets. Geom. Topol./Geom. Topol.. 2004; 8 (1) : 1-34. |
Spherical CR Geometry and Dehn Surgery (research monograph) Annals of Mathematics Studies
Complex Hyperbolic Triangle Groups, Proceedings of the International Congress of Mathematicians
Real Hyperbolic on the Outside, Complex Hyperbolic on the Outside Inventiones Mathematicae
Ideal Triangle Groups, Dented Tori, and Numerical Analysis, Annals of Math
Symmetric Patterns of Geodesics and Automorphisms of Surface groups inventiones mathematicae
Quasi-Isometric Rigidity and Diophantine Approximation Acta Mathematica
The quasi-isometry classification of rank one lattices Publications IHES
Pappus's Theorem and the Modular Group Publications IHES
Year | Degree | Institution |
---|---|---|
1991 | PhD | Princeton University |
1987 | BS | University of California, Los Angeles |
National Merit Scholarship, 1984-87
National Science Foundation Graduate Fellowship, 1987-90
Alfred P. Sloan Dissertation Fellowship, 1990-91
National Science Foundation Postdoctoral Fellowship, 1993-95
Alfred P. Sloan Research Fellowship, 1996-2000
Invited speaker, International Congress of Mathematicians, 2002
John Simon Guggenheim Fellow, 2003
Simons Fellow, 2012,2016
Fellow of the American Math Society
MATH 0760 - Introduction to Higher Mathematics |
MATH 1230 - Graph Theory |
MATH 1410 - Topology |
MATH 1530 - Abstract Algebra |
MATH 1540 - Topics in Abstract Algebra |