Sergei Tabachnikov

Sergei Tabachnikov
University Park, PA 16802, USA
Pennsylvania State University


Ph.D., Moscow State University, 1987.

Positions held

1978-1980: Mathematics Teacher, Specialized High School for Mathematics and Physics No 2, Moscow.
1979-1988: Curriculum developer and Program Coordinator, School of Mathematics by Correspondence (``Gelfand's School"), Moscow State University.
1988-1990: Managing Editor for Mathematics, \Kvant" magazine, USSR Academy of Sciences, Moscow.
1990-2000: Assistant, Associate, Full Professor of Mathematics, University of Arkansas.
2000-2018: Associate, Full Professor of Mathematics and MASS Director, Penn State.
2013-2015: Deputy Director, Institute for Computational and Experimental Mathematics (ICERM), Brown University.


2012: Fellow of American Mathematical Society (inaugural class)
2013: Teresa Cohen Service Award in Mathematics, Penn State
2021-2024: Mercator Fellowship, Heidelberg University

Editorial boards

1989-1990: Kvant magazine
2001-2020: American Mathematical Monthly
2011-2016: Notes, Editor
2012-2020: Student Mathematics Library Editorial Committee, AMS
2016-2020: Pure and Applied Undergraduate Texts Editorial Committee, AMS
Mathematical Intelligencer, Mathematical Gems and Curiosities:
2013-2020 – Editor;
2016-2020 – Associate Editor;
Since 2021 – co-Editor-in-Chief
Experimental Mathematics:
2013-2019 – Editor-in-Chief;
2019-2022 – associate editor
Matematicki Vesnik:
Since 2016 – associate editor
Arnold Mathematical Journal:
2018-2022 – associate editor;
Since 2023 – Editor-in-Chief
European Journal of Mathematics:
Since 2022 – associate editor
Journal of Experimental Mathematics:
Since 2023 – associate editor
Regular and Chaotic Dynamics:
Since 2024 – associate editor


2007-2010: Young Scholars (Epsilon) Awards Committee, AMS, member (Chair, 2009-2010)
2010-2013: Frank and Bennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student Committee, AMS-MAA-SIAM, member
2010-2017: International Mathematical Summer School for Students, Scientific Committee, Chair
2011-2013: Illustrative Mathematics Project Advisory Board, AMS representative
since 2013: Heidelberg Laureate Forum Selection Committee (Chair, since 2022)
2014-2016: AMS-MAA Mathfest Joint Lecture Committee (Chair, 2014-2015)
2014-2017: London Mathematical Society Undergraduate Summer School, Scientific Committee
2015-2019: ICERM Education Advisory Board, Chair, member
2016-2019: AMS Levi L. Conant Prize Committee, member
Since 2021: Association for Mathematical Research, Board of Directors member
Since 2022: Heidelberg Laureate Forum, Scientific Committee


Tabachnikov S.
Remarks on Rigidity Properties of Conics
2022, vol. 27, no. 1, pp.  18-23
Inspired by the recent results toward Birkhoff conjecture (a rigidity property of billiards in ellipses), we discuss two rigidity properties of conics. The first one concerns symmetries of an analog of polar duality associated with an oval, and the second concerns properties of the circle map associated with an oval and two pencils of lines.
Keywords: conics, polar duality, rigidity, circle maps, chess billiards
Citation: Tabachnikov S.,  Remarks on Rigidity Properties of Conics, Regular and Chaotic Dynamics, 2022, vol. 27, no. 1, pp. 18-23
Tabachnikov S.
Two Variations on the Periscope Theorem
2020, vol. 25, no. 1, pp.  11-17
A (multidimensional) spherical periscope is a system of two ideal mirrors that reflect every ray of light emanating from some point back to this point. A spherical periscope defines a local diffeomorphism of the space of rays through this point, and we describe such diffeomorphisms. We also solve a similar problem for (multidimensional) reversed periscopes, the systems of two mirrors that reverse the direction of a parallel beam of light.
Keywords: periscope, optical reflection, projectively gradient vector field
Citation: Tabachnikov S.,  Two Variations on the Periscope Theorem, Regular and Chaotic Dynamics, 2020, vol. 25, no. 1, pp. 11-17
Khesin B. A., Tabachnikov S.
Contact complete integrability
2010, vol. 15, nos. 4-5, pp.  504-520
Complete integrability in a symplectic setting means the existence of a Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we describe complete integrability in a contact set-up as a more subtle structure: a flag of two foliations, Legendrian and co-Legendrian, and a holonomy-invariant transverse measure of the former in the latter. This turns out to be equivalent to the existence of a canonical $\mathbb{R} \times \mathbb{R}^{n−1}$ structure on the leaves of the co-Legendrian foliation. Further, the above structure implies the existence of n commuting contact fields preserving a special contact 1-form, thus providing the geometric framework and establishing equivalence with previously known definitions of contact integrability. We also show that contact completely integrable systems are solvable in quadratures.
We present an example of contact complete integrability: the billiard system inside an ellipsoid in pseudo-Euclidean space, restricted to the space of oriented null geodesics. We describe a surprising acceleration mechanism for closed light-like billiard trajectories.
Keywords: complete integrability, contact structure, Legendrian foliation, pseudo-Euclidean geometry, billiard map
Citation: Khesin B. A., Tabachnikov S.,  Contact complete integrability, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 4-5, pp. 504-520
Dogru F., Tabachnikov S.
On Polygonal Dual Billiard in the Hyperbolic Plane
2003, vol. 8, no. 1, pp.  67-81
We study the polygonal dual billiard map in the hyperbolic plane. We show that for a class of convex polygons called large all orbits of the dual billiard map escape to infinity. We also analyse the dynamics of the dual billiard map when the dual billiard table is a regular polygon with all right angles.
Citation: Dogru F., Tabachnikov S.,  On Polygonal Dual Billiard in the Hyperbolic Plane, Regular and Chaotic Dynamics, 2003, vol. 8, no. 1, pp. 67-81

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