Sergei Tabachnikov
Professor of Mathematics, Penn State
tabachni@math.psu.edu
Papers
Characteristic classes of parabolic foliations and symmetric functions. Serdica, 11 (1985), 86-95Characteristic classes of parabolic foliations of series B, C, and D and degrees of isotropic Grassmannians. (Russian) Funktsional. Anal. i Prilozhen. 20 (1986), no. 2, 84-85
Characteristic classes of Lagrangian foliations. Func. Anal. Appl., 23, No 2 (1989), 90-91
Around four vertices. Russ. Math. Surv., 45, No 1 (1990), 191-192
Two remarks on the asymptotic Hopf invariant. Func. Anal. Appl., 24, No 1 (1990), 84-85
Geometry of Lagrangian and Legendrian 2-webs. Diff. Geom. Appl., 3 (1993) 265--284
Poncelet's theorem and dual billiards. L'Enseign. Math., 39 (1993), 189-194
Outer billiards. Russ. Math. Surv., 48, No 6 (1993), 75-102
Commuting dual billiard maps. Geom. Dedicata, 53 (1994), 57--68
A cone eversion. Amer. Math. Monthly, 102 (1995), 52-56
On the dual billiard problem. Adv. in Math. 115 (1995), 221-249
Asymptotic dynamics of the dual billiard transformation. J. Stat. Phys., 83 (1996), 27-38
Introducing projective billiards. Ergod. Theory and Dynam. Syst., 17 (1997), 957-976
On functions with zero mean over a finite group. Func. Anal. Appl., 31, No 1 (1997), 93-94
Fagnano orbits of polygonal dual billiards. Geom. Dedicata, 77 (1999), 279-286
More on paper folding, with D. Fuchs. Amer. Math. Monthly, 106 (1999), 27-35
Going in circles: variations on the Money-Coutts theorem. Geom. Dedicata, 80 (2000), 201-209
A four vertex theorem for polygons. Amer. Math. Monthly, 107 (2000), 830-833
Ellipsoids, complete integrability and hyperbolic geometry. Moscow Math. J., 2 (2002), 185-198
Dual billiards in the hyperbolic plane. Nonlinearity, 15 (2002), 1051-1072
On skew loops, skew branes and quadratic hypersurfaces. Moscow Math. J., 3 (2003), 681-690
A tale of a geometric inequality. MASS Selecta, AMS, 2003, 257-262
Dual billiards, with F. Dogru. Math. Intelligencer, 27, No 4 (2005), 18-25
Tire track geometry: variations on a theme. Israel J. Math., 151 (2006), 1-28
Book review of Arnold's Problems. Math. Intelligencer, 29, No 1 (2007), 49-52
Hyperbolic Caratheodory conjecture, with V. Ovsienko. Proc. of Steklov Inst., 258 (2007), 178-193
Totally skew embeddings of manifolds, with M. Ghomi. Math. Z., 258 (2008), 499-512
On algebraically integrable outer billiards. Pacific J. Math., 235 (2008), 89-92
Birkhoff billiards are insecure. Discr. Cont. Dyn. Syst., 23 (2009), 1035-1040
What is ... the Schwarzian derivative? with V. Ovsienko. Notices of AMS, 56 (2009), 34-36
Sylvester's problem (in Russian), with V. Timorin. Kvant 2009, No 5, 2-6, No 6, 6-10
Existence and non-existence of skew branes. J. Fixed Point Theory Appl., 7 (2010), 419-431
Variations on the Tait-Kneser theorem, with V. Timorin. Preprint
Contact complete integrability, with B. Khesin. Reg. Chaotic Dynamics, 15 (2010), 504-520
The pentagram integrals on inscribed polygons, with R. Schwartz. Electr. J. Comb., 18 (2011), P171
The (un)equal tangents problem. Amer. Math. Monthly, 119 (2012), 398-405
Periodic trajectories in the regular pentagon, II, with D. Fuchs. Moscow Math. J., 13 (2013), 19-32
On fibrations with flat fibers, with V. Ovsienko. Bull. London Math. Soc., 45 (2013), 625-632
Dragon curves revisited. Math. Intelligencer, 36, No 1 (2014), 13-17
Proofs (not) from The Book. Math. Intelligencer, 36, No 2 (2014), 9-14
A Baker's dozen of problems. Arnold Math. J., 1 (2015), 59-67
Remarks on the circumcenter of mass, with E. Tsukerman. Arnold Math. J., 1 (2015), 101-112
The Six Circles Theorem revisited, with D. Ivanov. Amer. Math. Monthly, 123 (2016), 689-698
Skewers. Arnold Math. J., 2 (2016), 171-193
Polynomials as polygons. Math. Intelligencer, v. 39, No 1 (2017), 41-43
Ivory's Theorem revisited, with I. Izmestiev. J. Integrable Systems, 2 (2017), 1-36
Vladimir Igorevich Arnold, with B. Khesin. Biogr. Mems Fell. Royal Soc., publ. online 08/30/17
Introducing symplectic billiards, with P. Albers. Advances in Math., 333 (2018), 822-867
A four vertex theorem for frieze patterns? Math. Intelligencer, v. 40, No 4 (2018), 14-18
Kasner meets Poncelet. Math. Intelligencer, v. 41, No 4 (2019), 56-59
Fun problems in geometry and beyond, with B. Khesin. SIGMA 15 (2019), 097, 21 pages
Two variations on the periscope theorem. Reg. Chaotic Dynamics, 25 (2020), 11-17
Dan Reznik's identities and more, with M. Bialy. European J. Math., 8 (2022), 1341-1354
Loewner's "forgotten" theorem, with P. Albers. Math. Intelligencer, v. 44, No 1 (2022), 7-11
Remarks on rigidity properties of conics. Reg. Chaotic Dynamics, 27 (2022), 18-23
On projective evolutes of polygons, with M. Arnold and R. Schwartz. Experimental Math., online first
Differential geometry of space curves: forgotten chapters, with D. Fuchs, I. Izmestiev, M. Raffaelli, and G. Szewieczek. Math Intelligencer, v. 46, No 1 (2024), 9-21
Iterating skew evolutes and skew involutes: a linear analog of the bicycle kinematics. Moscow Math. J. (Ilyashenko Festschrift), 23 (2023), 625-640
Monotone twist maps and Dowker-type theorems (with P. Albers). Preprint
Geometry of integrable linkages (with R. Perline). Preprint
A family of maps and a vector field on plane polygons (with A. Arnold and L. Costa). Preprint