Sergei Tabachnikov

Sergei Tabachnikov's AcademicInfluence.com Rankings

Sergei Tabachnikov

Mathematics

#1777

World Rank

#2845

Historical Rank

#725

USA Rank

Measure Theory

#2599

World Rank

#3113

Historical Rank

#744

USA Rank

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Mathematics

Sergei Tabachnikov's Degrees

PhD Mathematics Moscow State University

Why Is Sergei Tabachnikov Influential?

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According to Wikipedia, Sergei Tabachnikov, also spelled Serge, is an American mathematician who works in geometry and dynamical systems. He is currently a Professor of Mathematics at Pennsylvania State University. Biography He earned his Ph.D. from Moscow State University in 1987 under the supervision of Dmitry Fuchs and Anatoly Fomenko. He has been living and working in the USA since 1990.

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Sergei Tabachnikov's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Geometry and billiards (2005) (365)
Rational billiards and flat structures (2002) (349)
Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups (2004) (186)
Invariants of Legendrian and transverse knots in the standard contact space (1997) (176)
Arnold's Problems (2006) (133)
The Pentagram Map: A Discrete Integrable System (2008) (123)
Chapter 13 Rational billiards and flat structures (2002) (108)
Topological robotics: motion planning in projective spaces (2002) (106)
Arithmetical properties of binomial coefficients (2007) (94)
On the Dual Billiard Problem (1995) (93)
Pseudo-Riemannian geodesics and billiards (2006) (78)
MORE ON PAPERFOLDING (1999) (67)
Liouville–Arnold integrability of the pentagram map on closed polygons (2011) (61)
The Poncelet Grid and Billiards in Ellipses (2007) (56)
Dual Billiards (2005) (54)
2-frieze patterns and the cluster structure of the space of polygons (2010) (52)
Dan Reznik’s identities and more (2020) (51)
Higher pentagram maps, weighted directed networks, and cluster dynamics (2011) (50)
Projectively equivalent metrics, exact transverse line fields and the geodesic flow on the ellipsoid (1999) (48)
Mathematical Omnibus: Thirty Lectures on Classic Mathematics (2007) (47)
Billiards in ellipses revisited (2020) (46)
Billiards in Finsler and Minkowski geometries (2002) (45)
Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture (2012) (45)
Linear difference equations, frieze patterns, and the combinatorial Gale transform (2013) (44)
Topology of cyclic configuration spaces and periodic trajectories of multi-dimensional billiards (1999) (42)
INTEGRABLE CLUSTER DYNAMICS OF DIRECTED NETWORKS AND PENTAGRAM MAPS (2014) (40)
Tire track geometry: Variations on a theme (2004) (39)
Geodesics on an ellipsoid in Minkowski space (2007) (39)
Centers of Mass of Poncelet Polygons, 200 Years After (2016) (30)
ESTIMATES FOR THE BENNEQUIN NUMBER OF LEGENDRIAN LINKS FROM STATE MODELS FOR KNOT POLYNOMIALS (1997) (30)
Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem (2003) (29)
Elementary Surprises in Projective Geometry (2009) (29)
ELLIPSOIDS, COMPLETE INTEGRABILITY AND HYPERBOLIC GEOMETRY (2002) (28)
The Four-Vertex Theorem Revisited—Two Variations on the Old Theme (1995) (28)
Ivory's Theorem revisited (2016) (28)
Sturm theory, Ghys theorem on zeroes of the Schwarzian derivative and flattening of legendrian curves (1995) (28)
Introducing projective billiards (1997) (28)
Osculating Curves: Around the Tait-Kneser Theorem (2012) (27)
A unified approach to the four vertex theorems II. (1999) (27)
Totally skew embeddings of manifolds (2003) (27)
Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards (2004) (27)
Contact complete integrability (2009) (27)
Differential and Symplectic Topology of Knots and Curves (1999) (27)
Tire tracks and integrable curve evolution (2017) (26)
On Bicycle Tire Tracks Geometry, Hatchet Planimeter, Menzin's Conjecture, and Oscillation of Unicycle Tracks (2008) (25)
Around four vertices (1990) (25)
Open problems, questions and challenges in finite- dimensional integrable systems (2018) (24)
Periodic trajectories in the regular pentagon (2011) (22)
The rules are simple-but, as we all know, simple rules may give scope for wonderfully intricate combinations (2005) (22)
On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards (2006) (21)
ON ALGEBRAICALLY INTEGRABLE OUTER BILLIARDS (2007) (21)
Geometry of Lagrangian and Legendrian 2-web (1993) (21)
Asymptotic dynamics of the dual billiard transformation (1996) (20)
Exact Transverse Line Fields and Projective Billiards in a Ball (1997) (19)
Dual billiards in the hyperbolic plane (2002) (19)
Differential Topology, Infinite-Dimensional Lie Algebras, and Applications (1999) (19)
Parameterized Plane Curves, Minkowski Caustics, Minkowski Vertices and Conservative Line Fields (19)
Commuting dual billiard maps (1994) (18)
On fibrations with flat fibres (2012) (17)
Dragon Curves Revisited (2014) (16)
A proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards (2007) (15)
Circumcenter of Mass and Generalized Euler Line (2013) (15)
Computation of the Bennequin invariant of a Legendre curve from the geometry of its front (1988) (15)
Cross-ratio Dynamics on Ideal Polygons (2018) (14)
Introducing supersymmetric frieze patterns and linear difference operators (2015) (14)
Iterating Evolutes and Involutes (2015) (14)
On skew loops, skew branes and quadratic hypersurfaces (2003) (14)
Billiard transformations of parallel flows: A periscope theorem (2016) (13)
A Four Vertex Theorem for Polygons (2000) (13)
INVARIANTS OF SMOOTH TRIPLE POINT FREE PLANE CURVES (1996) (13)
The Pentagram Integrals on Inscribed Polygons (2010) (13)
Quasiperiodic Motion for the Pentagram Map (2009) (13)
Periodic trajectories in 3-dimensional convex billiards (2001) (12)
THE TALE OF A GEOMETRIC INEQUALITY (1999) (12)
Self-dual polygons and self-dual curves (2007) (12)
Hopf Fibrations and Hurwitz-Radon Numbers (2016) (12)
On the discrete bicycle transformation (2012) (12)
Two remarks on the asymptotic Hopf invariant (1990) (11)
ON POLYGONAL DUAL BILLIARD IN THE HYPERBOLIC PLANE (2003) (11)
Periodic trajectories in the regular pentagon, II (2011) (11)
Going in Circles: Variations on the Money-Coutts Theorem (2000) (11)
Non-existence of n-dimensional T-embedded discs in R 2n (2005) (11)
On the bicycle transformation and the filament equation: Results and conjectures (2016) (11)
Introducing symplectic billiards (2017) (10)
$SL_2(\mathbb{Z})$-tilings of the torus, Coxeter-Conway friezes and Farey triangulations (2014) (10)
On Zeroes of the Schwarzian Derivative (1997) (9)
Dual Numbers, Weighted Quivers, and Extended Somos and Gale-Robinson Sequences (2017) (9)
Projective geometry of polygons and discrete 4-vertex and 6-vertex theorems (1999) (9)
Fagnano Orbits of Polygonal Dual Billiards (1999) (9)
Remarks on the Circumcenter of Mass (2014) (8)
Coxeter's frieze patterns and discretization of the Virasoro orbit (2013) (8)
On three-periodic trajectories of multi-dimensional dual billiards (2003) (8)
Topological aspects of the Dvoretzky Theorem (2009) (8)
Birkhoff billiards are insecure (2007) (8)
Variations on the Tait–Kneser Theorem (2006) (8)
Projective Configuration Theorems: Old Wine into New Wineskins (2016) (8)
Projective connections , group Vey cocycle and deformation quantization (1996) (8)
Four equivalent properties of integrable billiards (2019) (8)
Wire billiards, the first steps (2019) (8)
More on paper folding (2007) (7)
The Poncelet grid and the billiard in an ellipse (2005) (7)
The (Un)equal Tangents Problem (2012) (7)
Open Questions in Tiling (2000) (7)
A cone eversion (1995) (6)
Projective Differential Geometry Old and New: Multi-dimensional Schwarzian derivatives and differential operators (2004) (6)
On curves and polygons with the equiangular chord property (2013) (6)
Billiard ball map and integral geometry (2005) (6)
Hyperbolic Carathéodory conjecture (2007) (6)
The equal tangents property (2012) (5)
Existence and non-existence of skew branes (2005) (5)
On Centro-Affine Curves and Bäcklund Transformations of the KdV Equation (2018) (5)
Geometry of exact transverse line fields and projective billiards (5)
Variations on R. Schwartz’s Inequality for the Schwarzian Derivative (2010) (5)
Mathematical Omnibus: Thirty Lectures on Classic (2010) (5)
Kvant Selecta: Algebra and Analysis, II (1999) (4)
Counting Periodic Trajectories of Finsler Billiards (2017) (4)
COMMUNICATIONS OF THE MOSCOW MATHEMATICAL SOCIETY: An invariant of a submanifold transversal to a distribution (1988) (4)
Tribute to Vladimir Arnold (2012) (4)
Spaces of pseudo-Riemannian geodesics and pseudo-Euclidean billiards (2006) (4)
Projective Differential Geometry Old and New: References (2004) (4)
The Six Circles Theorem Revisited (2013) (4)
Arnold: Swimming Against the Tide (2014) (4)
Iterating evolutes of spatial polygons and of spatial curves (2016) (3)
Segments of equal areas (2007) (3)
On characteristic classes of homogeneous foliations (1984) (3)
New Whitney-type formulae for plane curves. (1999) (3)
Self-Bäcklund curves in centroaffine geometry and Lamé’s equation (2022) (3)
Polynomials as Polygons (2017) (3)
Polygonal symplectic billiards (2019) (3)
Fun Problems in Geometry and Beyond (2019) (3)
Characteristic classes of Grassmanian bundles (1985) (3)
Mathematics Advanced Study Semesters (2005) (3)
Kasner Meets Poncelet (2017) (3)
Descartes Circle Theorem, Steiner Porism, and Spherical Designs (2018) (3)
Iterating Evolutes of Spacial Polygons and of Spacial Curves (2016) (3)
Discrete spherical means of directional derivatives and Veronese maps (2011) (3)
A Baker’s Dozen of Problems (2015) (2)
Proofs (Not) from The Book (2014) (2)
MASS program at penn state (2002) (2)
Projective Differential Geometry Old and New: Introduction (2004) (2)
Two Variations on the Periscope Theorem (2019) (2)
Characteristic classes of Lagrangian foliations (1989) (2)
Remarks on Joachimsthal Integral and Poritsky Property (2020) (2)
Skewers (2016) (2)
Contact complete integrability (2010) (2)
Configuration Spaces of Plane Polygons and a sub-Riemannian Approach to the Equitangent Problem (2014) (2)
The Scottish Book. Mathematics from the Scottish Café, with Selected Problems from the New Scottish Book, second edition Edited by R. Daniel Mauldin (2019) (2)
Remarks on the geometry of exact transverse line fields. Differential topology, infinite-dimensional Lie algebras, and applications. (1999) (2)
Kvant Selecta: Combinatorics, I (2001) (1)
Chases and Escapes. The Mathematics of Pursuit and Evasion by Paul J. Nahin (2009) (1)
On functions with zero mean over a finite group (1997) (1)
Alexander’s horned sphere (2007) (1)
On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities (2007) (1)
The Institute for Computational and Experimental Research in Mathematics (ICERM) (2016) (1)
Tire track geometry and integrable curve evolution (2017) (1)
Remarks on Rigidity Properties of Conics (2021) (1)
The equal tangents problem (2011) (1)
Existence and nonexistence of skew branes (2010) (1)
Affine Hopf fibration (2015) (1)
The Ice Cube Proof (2014) (1)
A family of integrable transformations of centroaffine polygons: geometrical aspects (2021) (1)
Converse Sturm–Hurwitz–Kellogg theorem and related results (2007) (0)
Algebra and analysis (1999) (0)
Invariant differential operators of general position (1982) (0)
Preface: why projective? (2004) (0)
. 12 June 1937 (2017) (0)
Geometry and Dynamics of the Pentagram Map (2009) (0)
Self-B\"acklund curves in centroaffine geometry and Lam\'e's equation (2020) (0)
On Projective Evolutes of Polygons (2022) (0)
Bicycling geodesics are Kirchhoff rods (2022) (0)
Memories of Vladimir Arnold [contributions by various authors] (2012) (0)
Special Issue : Valery Vasilievich Kozlov – 60 Contact Complete Integrability (2009) (0)
Appendix. Personal notes. Differential topology, infinite-dimensional Lie algebras, and applications (1999) (0)
On Lagrangian tangent sweeps and Lagrangian outer billiards (2015) (0)
On Cusps of Caustics by Reflection: Billiard Variations on the Four Vertex Theorem and on Jacobi’s Last Geometric Statement (2023) (0)
Contribution to ‘Tribute to Vladimir Arnold’ (2017) (0)
Centers of Mass of Poncelet Polygons, 200 Years After (2016) (0)
On Centro-Affine Curves and Bäcklund Transformations of the KdV Equation (2018) (0)
Curvature and polyhedra (2007) (0)
Variations on A. Kneser's theorem (2006) (0)
1 Polygonal billiards , rational billiards 1 . 1 Polygonal billiards (2006) (0)
A Baker’s Dozen of Problems (2014) (0)
Introducing supersymmetric frieze patterns and linear difference operators (2015) (0)
GEOMETRY OF POLYNOMIALS (2010) (0)
Hyperbolic Carath\'{e}odory conjecture (2006) (0)
Paper Möbius band (2007) (0)
Configuration Spaces of Plane Polygons and a sub-Riemannian Approach to the Equitangent Problem (2015) (0)
Remarks on Rigidity Properties of Conics (2022) (0)
Can one make a tetrahedron out of a cube (2007) (0)
Dual Numbers, Weighted Quivers, and Extended Somos and Gale-Robinson Sequences (2018) (0)
Equations of degree five (2007) (0)
Kiselyov's geometry: Planimetry (2018) (0)
Non-inscribable polyhedra (2007) (0)
Gravitational attraction of ellipsoids (2007) (0)
Remarks on skew evolutes and skew involutes (2023) (0)
Tribute to Vladimir Arnold Boris Khesin (2011) (0)
Remarks on Joachimsthal Integral and Poritsky Property (2021) (0)
Discrete integrable systems in projective geometry (2008) (0)
Motivation: Mechanics and optics (2005) (0)
On the 80th Birthday of Dmitry Borisovich Fuchs (2020) (0)
Memories of Vladimir Arnold (2012) (0)
You Failed Your Math Test, Comrade Einstein: Adventures and Misadventures of Young Mathematicians, or Test Your Skills in Almost Recreational Mathematics by M. Shifman (2020) (0)
Billiards in polygons (2005) (0)
Projective Differential Geometry Old and New: Projective structures on smooth manifolds (2004) (0)
Hopf Fibrations and Hurwitz-Radon Numbers (2016) (0)
Billiard in the circle and the square (2005) (0)
Can a number be approximately rational (2007) (0)
On cusps of caustics by reflection: a billiard variation on Jacobi's Last Geometric Statement (2021) (0)
Characteristic classes of parabolic fiberings of the series B, C, and D, and the degrees of isotropic Grassmanians (1986) (0)
Kasner Meets Poncelet (2019) (0)
The Crofton formula (2007) (0)
Discrete spherical means of directional derivatives and their applications (2010) (0)
Projective invariants of submanifolds (2004) (0)
Projective Differential Geometry Old and New: The algebra of the projective line and cohomology of Diff( S 1) (2004) (0)
Rigidity of polyhedra (2007) (0)
Billiards in Bounded Convex Domains (2006) (0)
Loewner’s “Forgotten” Theorem (2021) (0)
Straight lines on curved surfaces (2007) (0)
A Singular Mathematical Promenade by Étienne Ghys (2018) (0)
Billiards inside conics and quadrics (2005) (0)
CHARACTERISTIC CLASSES OF LAGRANGIAN (2004) (0)
Solutions to selected exercises (2007) (0)
Iterating evolutes of spatial curves and of spatial polygons (2016) (0)
Iterating skew evolutes and skew involutes: a linear analog of the bicycle kinematics (2023) (0)
Proofs (Not) from The Book (2013) (0)
Billard in Polygonen (2013) (0)
INTEGRABILITY AND NEAR-INTEGRABILITY IN MECHANICS AND GEOMETRY (16w5017) (2016) (0)
Photo Section III: 2000s (2014) (0)
Geometry of equations (2007) (0)
Loewner’s “Forgotten” Theorem (2022) (0)
Projective Differential Geometry Old and New: Appendices (2004) (0)
Nikolay Konstantinov, 01.02.1932–07.03.2021, a Mathematical Educator Par Excellence (2022) (0)
Book Review: Exterior billiards: systems with impacts outside bounded domains (2014) (0)
Polynomials as Polygons (2017) (0)
A Singular Mathematical Promenade by Étienne Ghys (2018) (0)
Memories of Vladimir Arnold Boris Khesin (2011) (0)
On Lagrangian tangent sweeps and Lagrangian outer billiards (2015) (0)
Two Variations on the Periscope Theorem (2020) (0)
Projective Differential Geometry Old and New: Vertices of projective curves (2004) (0)
Billiards in ellipses and geodesics on ellipsoids (2007) (0)
A Four-Vertex Theorem for Frieze Patterns? (2018) (0)
On plane curves (2007) (0)
Polyhedron Covered Twice by Lines: 10724 (2001) (0)
A PROBLEM WHICH ARCHIMEDES WOULD PROBABLY LIKE (1995) (0)
A Four-Vertex Theorem for Frieze Patterns? (2018) (0)
How many roots does a polynomial have (2007) (0)
Symplectically convex and symplectically star-shaped curves: a variational problem (2020) (0)
Existence and non-existence of caustics (2005) (0)
Book Review: Outer billiards on kites (2011) (0)
Circumcenter of Mass and Generalized Euler Line (2014) (0)
Iterating Evolutes and Involutes (2017) (0)
Hamiltonian Systems, from Topology to Applications through Analysis (2018) (0)
The geometry of the projective line (2004) (0)
Billard in Ellipsen und Geodäten an Ellipsoiden (2011) (0)
The Ice Cube Proof (2014) (0)
Equations of degree three and four (2007) (0)
Letter from the Guest Editors (2013) (0)
Motivation: Mechanik und Optik (2013) (0)
Differential geometry of space curves: Forgotten chapters (2022) (0)
Dual billiard Filiz Dogru and (2005) (0)
Osculating Curves: Around the Tait-Kneser Theorem (2012) (0)
Vladimir Igorevich Arnold. 12 June 1937—3 June 2010 (2018) (0)
PATTERNS , AND THE COMBINATORIAL GALE TRANSFORM (2014) (0)
Comments on “A Mathematical Trivium” (2014) (0)
Sturm T heory, G hys T heorem o n Z eroes o f t he S chwarzian Derivative a nd F lattening o f L egendrian C urves (1996) (0)
Remarks on the Circumcenter of Mass (2015) (0)
Editors’ foreword for the special issue “New Developments in Integrable Systems” (2022) (0)
Open Problems on Billiards and Geometric Optics (2021) (0)
On conformal points of area preserving maps and related topics (2022) (0)
Proofs ( not ) from The Book S . Tabachnikov (2013) (0)
Polar Bear or Penguin? Musings on Earth Cartography and Chebyshev Nets (2020) (0)
V.I.Arnold, as I have seen him (2012) (0)
Paper sheet geometry (2007) (0)
Dragon Curves Revisited (2013) (0)
Photo Section I: 1940s-1970s (2014) (0)
Photo Section II: 1980s–1990s (2014) (0)
Fe b 20 06 Variations on the Tait – Kneser theorem (2006) (0)
Twenty-seven lines (2007) (0)
The Poncelet porism and other closure theorems (2007) (0)

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