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## Schwartz, Richard Evan

Compute Distance To:
 Author ID: schwartz.richard-evan Published as: Schwartz, Richard; Schwartz, Richard Evan External Links: MGP · Wikidata · GND
 Documents Indexed: 60 Publications since 1992, including 10 Books
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#### Co-Authors

 47 single-authored 8 Tabachnikov, Serge L. 4 Ovsienko, Valentin Yu. 2 Hooper, W. Patrick 1 Drach, Kostiantyn 1 Farb, Benson 1 Morier-Genoud, Sophie 1 Sharp, Richard W.
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#### Serials

 6 Experimental Mathematics 5 Geometriae Dedicata 5 Journal of Modern Dynamics 4 The Mathematical Intelligencer 3 Inventiones Mathematicae 3 Annals of Mathematics Studies 2 American Mathematical Monthly 2 Communications in Mathematical Physics 2 Acta Mathematica 2 Publications Mathématiques 2 Geometry & Topology 2 Mathematical Surveys and Monographs 2 Electronic Research Announcements in Mathematical Sciences 1 Journal of Geometry and Physics 1 Duke Mathematical Journal 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Topology 1 Transactions of the American Mathematical Society 1 Constructive Approximation 1 Discrete & Computational Geometry 1 The Electronic Journal of Combinatorics 1 Annals of Mathematics. Second Series 1 Advances in Geometry 1 Pure and Applied Mathematics Quarterly 1 Student Mathematical Library 1 Journal of Fixed Point Theory and Applications 1 Forum of Mathematics, Sigma
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#### Fields

 24 Dynamical systems and ergodic theory (37-XX) 17 Geometry (51-XX) 16 Convex and discrete geometry (52-XX) 9 Manifolds and cell complexes (57-XX) 6 General and overarching topics; collections (00-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Differential geometry (53-XX) 5 Topological groups, Lie groups (22-XX) 4 Group theory and generalizations (20-XX) 3 Combinatorics (05-XX) 3 Functions of a complex variable (30-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

47 Publications have been cited 456 times in 236 Documents Cited by Year
The quasi-isometry classification of rank one lattices. Zbl 0852.22010
Schwartz, Richard Evan
1995
The pentagram map: a discrete integrable system. Zbl 1209.37063
Ovsienko, Valentin; Schwartz, Richard; Tabachnikov, Serge
2010
The pentagram map. Zbl 0765.52004
Schwartz, Richard
1992
Discrete monodromy, pentagrams, and the method of condensation. Zbl 1148.51001
Schwartz, Richard Evan
2008
The five-electron case of Thomson’s problem. Zbl 1269.78003
Schwartz, Richard Evan
2013
Complex hyperbolic triangle groups. Zbl 1022.53034
Schwartz, Richard Evan
2002
The large-scale geometry of Hilbert modular groups. Zbl 0871.11035
Farb, Benson; Schwartz, Richard
1996
Liouville-Arnold integrability of the pentagram map on closed polygons. Zbl 1315.37035
Ovsienko, Valentin; Schwartz, Richard Evan; Tabachnikov, Serge
2013
The Poncelet grid. Zbl 1123.51027
Schwartz, Richard Evan
2007
Outer billiards on kites. Zbl 1205.37001
Schwartz, Richard Evan
2009
Quasi-isometric rigidity and Diophantine approximation. Zbl 1029.11038
Schwartz, Richard Evan
1996
Spherical CR geometry and Dehn surgery. Zbl 1116.57016
Schwartz, Richard Evan
2007
Elementary surprises in projective geometry. Zbl 1204.51024
Schwartz, Richard Evan; Tabachnikov, Serge
2010
Obtuse triangular billiards. II: One hundred degrees worth of periodic trajectories. Zbl 1417.37154
Schwartz, Richard Evan
2009
Ideal triangle groups, dented tori, and numerical analysis. Zbl 1055.20040
Schwartz, Richard Evan
2001
Real hyperbolic on the outside, complex hyperbolic on the inside. Zbl 1039.32030
Schwartz, Richard Evan
2003
Linear difference equations, frieze patterns, and the combinatorial Gale transform. Zbl 1297.39004
Morier-Genoud, Sophie; Ovsienko, Valentin; Schwartz, Richard Evan; Tabachnikov, Serge
2014
Unbounded orbits for outer billiards. I. Zbl 1130.37021
Schwartz, Richard Evan
2007
The pentagram map is recurrent. Zbl 1013.52003
Schwartz, Richard Evan
2001
Degenerating the complex hyperbolic ideal triangle groups. Zbl 0998.53050
Schwartz, Richard Evan
2001
Pappus’s theorem and the modular group. Zbl 0806.57004
Schwartz, Richard
1993
Symmetric patterns of geodesics and automorphisms of surface groups. Zbl 0884.58021
Schwartz, Richard Evan
1997
The octogonal PETs. Zbl 1308.37022
Schwartz, Richard Evan
2014
Quasiperiodic motion for the pentagram map. Zbl 1163.37019
Ovsienko, Valentin; Schwartz, Richard; Tabachnikov, Serge
2009
Obtuse triangular billiards. I: Near the $$(2,3,6)$$ triangle. Zbl 1112.37030
Schwartz, Richard Evan
2006
Billiards in nearly isosceles triangles. Zbl 1203.37073
Hooper, W. Patrick; Schwartz, Richard Evan
2009
Centers of mass of Poncelet polygons, 200 years after. Zbl 1351.01013
Schwartz, Richard; Tabachnikov, Sergei
2016
Outer billiards on the Penrose kite: compactification and renormalization. Zbl 1277.37070
Schwartz, Richard Evan
2011
The pentagram integrals on inscribed polygons. Zbl 1246.37091
Schwartz, Richard Evan; Tabachnikov, Serge
2011
A better proof of the Goldman-Parker conjecture. Zbl 1098.20034
Schwartz, Richard Evan
2005
A projectively natural flow for circle diffeomorphisms. Zbl 0773.58022
Schwartz, Richard
1992
Outer billiards and the pinwheel map. Zbl 1268.37056
Schwartz, Richard Evan
2011
Mostly surfaces. Zbl 1237.30002
Schwartz, Richard Evan
2011
Desargues theorem, dynamics, and hyperplane arrangements. Zbl 0996.51002
Schwartz, Richard Evan
2001
The correlation of length spectra of two hyperbolic surfaces. Zbl 0772.58045
Schwartz, Richard; Sharp, Richard
1993
The projective heat map. Zbl 1444.37003
Schwartz, Richard Evan
2017
The pentagram integrals for Poncelet families. Zbl 1309.37068
Schwartz, Richard Evan
2015
Pentagram spirals. Zbl 1291.37040
Schwartz, Richard Evan
2013
Research announcement: unbounded orbits for outer billiards. Zbl 1139.37024
Schwartz, Richard Evan
2008
A trichotomy for rectangles inscribed in Jordan loops. Zbl 1448.51008
Schwartz, Richard Evan
2020
Five point energy minimization: a synopsis. Zbl 1435.31010
Schwartz, Richard Evan
2020
Really big numbers. Zbl 1341.00013
Schwartz, Richard Evan
2014
A conformal averaging process on the circle. Zbl 1092.52503
Schwartz, Richard Evan
2006
The density of shapes in three-dimensional barycentric subdivision. Zbl 1048.52005
Schwartz, Richard Evan
2003
Lucy and Lily: a game of geometry and number theory. Zbl 1081.00501
Schwartz, Richard Evan
2002
Circle quotients and string art. Zbl 1012.52027
Schwartz, Richard Evan
2002
On the integral curve of a linear third order O. D. E. Zbl 0946.34003
Schwartz, Richard
1997
A trichotomy for rectangles inscribed in Jordan loops. Zbl 1448.51008
Schwartz, Richard Evan
2020
Five point energy minimization: a synopsis. Zbl 1435.31010
Schwartz, Richard Evan
2020
The projective heat map. Zbl 1444.37003
Schwartz, Richard Evan
2017
Centers of mass of Poncelet polygons, 200 years after. Zbl 1351.01013
Schwartz, Richard; Tabachnikov, Sergei
2016
The pentagram integrals for Poncelet families. Zbl 1309.37068
Schwartz, Richard Evan
2015
Linear difference equations, frieze patterns, and the combinatorial Gale transform. Zbl 1297.39004
Morier-Genoud, Sophie; Ovsienko, Valentin; Schwartz, Richard Evan; Tabachnikov, Serge
2014
The octogonal PETs. Zbl 1308.37022
Schwartz, Richard Evan
2014
Really big numbers. Zbl 1341.00013
Schwartz, Richard Evan
2014
The five-electron case of Thomson’s problem. Zbl 1269.78003
Schwartz, Richard Evan
2013
Liouville-Arnold integrability of the pentagram map on closed polygons. Zbl 1315.37035
Ovsienko, Valentin; Schwartz, Richard Evan; Tabachnikov, Serge
2013
Pentagram spirals. Zbl 1291.37040
Schwartz, Richard Evan
2013
Outer billiards on the Penrose kite: compactification and renormalization. Zbl 1277.37070
Schwartz, Richard Evan
2011
The pentagram integrals on inscribed polygons. Zbl 1246.37091
Schwartz, Richard Evan; Tabachnikov, Serge
2011
Outer billiards and the pinwheel map. Zbl 1268.37056
Schwartz, Richard Evan
2011
Mostly surfaces. Zbl 1237.30002
Schwartz, Richard Evan
2011
The pentagram map: a discrete integrable system. Zbl 1209.37063
Ovsienko, Valentin; Schwartz, Richard; Tabachnikov, Serge
2010
Elementary surprises in projective geometry. Zbl 1204.51024
Schwartz, Richard Evan; Tabachnikov, Serge
2010
Outer billiards on kites. Zbl 1205.37001
Schwartz, Richard Evan
2009
Obtuse triangular billiards. II: One hundred degrees worth of periodic trajectories. Zbl 1417.37154
Schwartz, Richard Evan
2009
Quasiperiodic motion for the pentagram map. Zbl 1163.37019
Ovsienko, Valentin; Schwartz, Richard; Tabachnikov, Serge
2009
Billiards in nearly isosceles triangles. Zbl 1203.37073
Hooper, W. Patrick; Schwartz, Richard Evan
2009
Discrete monodromy, pentagrams, and the method of condensation. Zbl 1148.51001
Schwartz, Richard Evan
2008
Research announcement: unbounded orbits for outer billiards. Zbl 1139.37024
Schwartz, Richard Evan
2008
The Poncelet grid. Zbl 1123.51027
Schwartz, Richard Evan
2007
Spherical CR geometry and Dehn surgery. Zbl 1116.57016
Schwartz, Richard Evan
2007
Unbounded orbits for outer billiards. I. Zbl 1130.37021
Schwartz, Richard Evan
2007
Obtuse triangular billiards. I: Near the $$(2,3,6)$$ triangle. Zbl 1112.37030
Schwartz, Richard Evan
2006
A conformal averaging process on the circle. Zbl 1092.52503
Schwartz, Richard Evan
2006
A better proof of the Goldman-Parker conjecture. Zbl 1098.20034
Schwartz, Richard Evan
2005
Real hyperbolic on the outside, complex hyperbolic on the inside. Zbl 1039.32030
Schwartz, Richard Evan
2003
The density of shapes in three-dimensional barycentric subdivision. Zbl 1048.52005
Schwartz, Richard Evan
2003
Complex hyperbolic triangle groups. Zbl 1022.53034
Schwartz, Richard Evan
2002
Lucy and Lily: a game of geometry and number theory. Zbl 1081.00501
Schwartz, Richard Evan
2002
Circle quotients and string art. Zbl 1012.52027
Schwartz, Richard Evan
2002
Ideal triangle groups, dented tori, and numerical analysis. Zbl 1055.20040
Schwartz, Richard Evan
2001
The pentagram map is recurrent. Zbl 1013.52003
Schwartz, Richard Evan
2001
Degenerating the complex hyperbolic ideal triangle groups. Zbl 0998.53050
Schwartz, Richard Evan
2001
Desargues theorem, dynamics, and hyperplane arrangements. Zbl 0996.51002
Schwartz, Richard Evan
2001
Symmetric patterns of geodesics and automorphisms of surface groups. Zbl 0884.58021
Schwartz, Richard Evan
1997
On the integral curve of a linear third order O. D. E. Zbl 0946.34003
Schwartz, Richard
1997
The large-scale geometry of Hilbert modular groups. Zbl 0871.11035
Farb, Benson; Schwartz, Richard
1996
Quasi-isometric rigidity and Diophantine approximation. Zbl 1029.11038
Schwartz, Richard Evan
1996
The quasi-isometry classification of rank one lattices. Zbl 0852.22010
Schwartz, Richard Evan
1995
Pappus’s theorem and the modular group. Zbl 0806.57004
Schwartz, Richard
1993
The correlation of length spectra of two hyperbolic surfaces. Zbl 0772.58045
Schwartz, Richard; Sharp, Richard
1993
The pentagram map. Zbl 0765.52004
Schwartz, Richard
1992
A projectively natural flow for circle diffeomorphisms. Zbl 0773.58022
Schwartz, Richard
1992
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#### Cited by 278 Authors

 20 Tabachnikov, Serge L. 16 Schwartz, Richard Evan 9 Ovsienko, Valentin Yu. 7 Falbel, Elisha 7 Morier-Genoud, Sophie 6 Parker, John R. 5 Will, Pierre 4 Behrstock, Jason A. 4 Deraux, Martin 4 Eskin, Alex 4 Glick, Max 4 Hooper, W. Patrick 4 Khesin, Boris A. 4 Kleiner, Bruce 4 Mosher, Lee 4 Soloviev, Fedor 3 Akopyan, Arseniy V. 3 Brauchart, Johann S. 3 Dragović, Vladimir 3 Long, Darren D. 3 Marí Beffa, Gloria 3 Mj, Mahan 3 Paupert, Julien 3 Radnović, Milena 3 Reid, Alan W. 3 Saff, Edward Barry 3 Steinerberger, Stefan 3 Vivaldi, Franco 3 Walsh, Genevieve S. 3 Xie, Baohua 2 Artigue, Alfonso 2 Ashwin, Peter 2 Barbot, Thierry 2 Bedaride, Nicolas 2 Bobenko, Alexander Ivanovich 2 Boileau, Michel Charles 2 Boyer, Steven 2 Cashen, Christopher H. 2 Cebanu, Radu 2 Cieślak, Waldemar 2 Cunha, Heleno 2 Exner, Pavel 2 Farb, Benson 2 Fisher, David Michael 2 Gaivão, José Pedro 2 Garcia, Ronaldo A. 2 Goetz, Arek 2 Gongopadhyay, Krishnendu 2 Gusevskii, Nikolay 2 Gutkin, Eugene 2 Jeong, In-Jee 2 Kamiya, Shigeyasu 2 Kapovich, Ilya 2 Kapovich, Michael 2 Kim, YoungJu 2 Krichever, Igor’ Moiseevich 2 Malyshev, Vadim Aleksandrovich 2 Marshakov, Andrey 2 Mozgawa, Witold 2 Neumann, Walter David 2 Nguyen, Hoang Thanh 2 Papasoglu, Panos 2 Pardini Valério, Viviane 2 Pratoussevitch, Anna 2 Pylyavskyy, Pavlo 2 Rukhovich, Filipp Dmitrievich 2 Whyte, Kevin 2 Wortman, Kevin A. 1 Acosta, Miguel 1 Albers, Peter 1 Al’kin, Ruslan Valer’evich 1 Allcock, Daniel Jonathan 1 Alvarez, Sébastien 1 Alwani, Fairuz 1 Antolín, Yago 1 Arnold, Maxim 1 Arredondo, John Alexander 1 Bader, Uri 1 Badt, Oded 1 Balitskiy, Alexey 1 Baralić, Đorđe 1 Barrera, Waldemar 1 Berger, Marcel 1 Bertazzon, Jean-Francois 1 Bilyk, Dmitry 1 Birtea, Petre 1 Biswas, Kingshook 1 Bolsinov, Alexey V. 1 Bondarenko, Andriy V. 1 Calegari, Danny Matthew Cornelius 1 Cano Cordero, Angel 1 Cao, Wensheng 1 Carbone, Lisa J. 1 Ceccherini-Silberstein, Tullio G. 1 Charette, Virginie 1 Chen, Xuemei 1 Cheng, Jih-Hsin 1 Chervov, Alexander Viktorovich 1 Chiu, Hung-Lin 1 Comănescu, Dan ...and 178 more Authors
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#### Cited in 107 Serials

 18 Geometriae Dedicata 14 Geometry & Topology 7 Advances in Mathematics 6 Journal of Geometry and Physics 6 The Mathematical Intelligencer 5 Communications in Mathematical Physics 5 Acta Mathematica 5 Duke Mathematical Journal 5 Proceedings of the American Mathematical Society 5 Transactions of the American Mathematical Society 5 Experimental Mathematics 4 Journal of Mathematical Physics 4 Annales de l’Institut Fourier 4 Journal für die Reine und Angewandte Mathematik 4 Ergodic Theory and Dynamical Systems 4 Discrete & Computational Geometry 4 Bulletin of the American Mathematical Society. New Series 4 Conformal Geometry and Dynamics 3 Inventiones Mathematicae 3 Mathematische Annalen 3 Constructive Approximation 3 The Journal of Geometric Analysis 3 Geometric and Functional Analysis. GAFA 3 Dynamical Systems 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Israel Journal of Mathematics 2 Journal of Statistical Physics 2 Letters in Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Commentarii Mathematici Helvetici 2 Functional Analysis and its Applications 2 Journal of Computational and Applied Mathematics 2 Mathematische Zeitschrift 2 Topology and its Applications 2 Acta Mathematica Hungarica 2 Journal of the American Mathematical Society 2 International Journal of Mathematics 2 International Journal of Algebra and Computation 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Doklady Mathematics 2 Advances in Geometry 2 Algebraic & Geometric Topology 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal of Modern Dynamics 2 Arnold Mathematical Journal 1 International Journal of Modern Physics A 1 American Mathematical Monthly 1 Indian Journal of Pure & Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 The Mathematical Gazette 1 Problems of Information Transmission 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Bulletin of the London Mathematical Society 1 Indiana University Mathematics Journal 1 Publications Mathématiques 1 Journal of Differential Equations 1 Journal of Number Theory 1 Journal of Optimization Theory and Applications 1 Journal of Pure and Applied Algebra 1 Memoirs of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Results in Mathematics 1 Advances in Applied Mathematics 1 Physica D 1 Graphs and Combinatorics 1 Journal of Complexity 1 L’Enseignement Mathématique. 2e Série 1 International Journal of Computer Mathematics 1 Linear Algebra and its Applications 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 International Journal of Robust and Nonlinear Control 1 Journal of Nonlinear Science 1 Journal of Algebraic Combinatorics 1 Potential Analysis 1 Journal of Mathematical Sciences (New York) 1 Bulletin des Sciences Mathématiques 1 Journal of Difference Equations and Applications 1 The Journal of Fourier Analysis and Applications 1 Documenta Mathematica 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Chaos 1 Annals of Mathematics. Second Series 1 Regular and Chaotic Dynamics 1 Journal of the European Mathematical Society (JEMS) 1 Foundations of Computational Mathematics 1 Forum Geometricorum 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Functional Analysis and Other Mathematics 1 Groups, Geometry, and Dynamics 1 Operators and Matrices 1 Electronic Research Announcements in Mathematical Sciences 1 Journal of Topology and Analysis 1 Advances in Mathematical Physics 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika ...and 7 more Serials
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#### Cited in 46 Fields

 78 Dynamical systems and ergodic theory (37-XX) 59 Geometry (51-XX) 52 Group theory and generalizations (20-XX) 48 Manifolds and cell complexes (57-XX) 38 Topological groups, Lie groups (22-XX) 34 Differential geometry (53-XX) 33 Several complex variables and analytic spaces (32-XX) 23 Convex and discrete geometry (52-XX) 22 Algebraic geometry (14-XX) 19 Functions of a complex variable (30-XX) 16 Number theory (11-XX) 14 Combinatorics (05-XX) 14 Commutative algebra (13-XX) 7 Nonassociative rings and algebras (17-XX) 7 Numerical analysis (65-XX) 6 History and biography (01-XX) 6 Partial differential equations (35-XX) 6 Quantum theory (81-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 General and overarching topics; collections (00-XX) 5 Potential theory (31-XX) 5 Computer science (68-XX) 4 Difference and functional equations (39-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Mechanics of particles and systems (70-XX) 4 Operations research, mathematical programming (90-XX) 3 Associative rings and algebras (16-XX) 3 Measure and integration (28-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Mathematical logic and foundations (03-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 General topology (54-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)

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