Home page of Gil Bor

Mailing Address: CIMAT, A.P. 402, Guanajuato 36000, Gto., Mexico.
Office: I-307, CIMAT. (52)-473-7327155, ext. 4500.
E-mail: gil@cimat.mx
Research | Lecture notes and talks | Gallery (images and animations) | Education | Vita | Amusement | Links
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Research

  1. SO(3)-invariant Yang-Mills fields which are not self-dual (with R Montegomery)
    In: Hamiltonian systems, transformation groups and spectral transform methods (Montreal, PQ, 1989), 191--198, Univ. of Montréal, Montréal QC, 1990. Harnad, J., Marsden, J.E. (eds.). Montréal: Les publications CRM 1990.
  2. Yang-Mills Fields which are not Self-Dual
    Commun. Math. Phys. 145 (1992), 393-410.
  3. Symmetric Instantons and the ADHM Construction (with J Segert)
    Commun. Math. Phys. 183 (1997), 183-203.
  4. The cannonical bundle of an hermitian manifold (with L Hernández)
    Bol. Soc. Mat. Mexicana (3) 5.1 (1999), 187-198.
  5. Bochner formulae for orthogonal G-structures on compact manifolds (with L Hernández)
    Diff. Geom. Appl. 15 (2001), 265-286.
  6. A Bochner formula for almost-quaternionic-Hermitian structures (with L Hernández)
    Diff. Geom. Appl. 21.1 (2004), 79-92.
  7. Orthogonal almost complex structures of minimal energy (with L Hernández, M Salvai)
    Geom. Dedicata 127.1 (2007), 75-85.
  8. G2 and the 'rolling distribution' (with R Montgomery)
    l'Enseign. Math. 55 (2009), 157-196.
  9. Poincaré y el problema de N-cuerpos (with R Montgomery)
    Miscelanea Mat. 58 (2014), 83-102.
  10. The dancing metric, G2-symmetry and projective rolling (with L Hernández, P Nurowski)
    Trans. Amer. Math. Soc. 370(6) (2018), 4433-4481.
  11. Tire track geometry and integrable curve evolution (with M Levi, R Perline, S Tabachnikov)
    Int. Math. Res. Notices (2018), DOI
  12. Testing the Domino Theory of Gene Loss in Buchnera aphidicola: The Relevance of Epistatic Interactions (with D Martínez-Cano, A Moya, L Delaye)
    Life 8.2 (2018), 17.
  13. Hill's equation, tire tracks and rolling cones (with M Levi)
    Nonlinearity, 33.4 (2020), 1424.
  14. La geometría de trayectorias de bicicletas (with S Tabachnikov)
    Ciencias 135 (2020).
  15. On the isometric conjecture of Banach (with L Hernández, V Jimenez de Santiago, L Montejano)
    Geom. Topol. 25.5 (2021), 2621-2642. DOI
  16. Bicycle paths, elasticae and sub-Riemannian geometry (with A Ardentov, E Le Donne, R Montgomery, Y Sachkov)
    Nonlinearity 34.7 (2021), 4661-4683. DOI
  17. Left-invariant CR structures on 3-dimensional Lie groups (with H Jacobowitz)
    Complex Anal. Synerg. 7, 23 (2021).
  18. Variations on the Tait-Kneser theorem (with C Jackman and S Tabachnikov)
    Math Intelligencer (2021). DOI
  19. Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions (with O Makhmali, P Nurowski)
    Geometriae Dedicata 216, 9 (2022). DOI
  20. Revisiting Kepler: new symmetries of an old problem (with C Jackman)
    Arnold J. of Math., 12 Sept 2022 (online).
  21. Self-Backlund curves in centroaffine geometry and Lamé's equation (with M Bialy and S Tabachnikov)
    Comm. AMS 2 (2022), 232-282
  22. On cusps of caustics by reflection: a billiard variation on Jacobi's Last Geometric Statement (with S Tabachnikov)
    Am. Math. Monthly (21 March, 2023, online). DOI.
  23. Bicycling geodesics are Kirchhoff rods (with C Jackman and S Tabachnikov)
    Nonlinearity 36 (2023), 3572-3602. DOI
  24. Dancing polygons, rolling balls and the Cartan-Engel distribution (with L Hernández)
    New York J. Math. 29 (2023) 981-1015.
  25. Chains of path geometries on surfaces: theory and examples (with T Willse)
    Israel J Math, TBD (2024), 1-39. DOI
  26. Cusps of caustics by reflection in ellipses (with M Spivakovsky and S Tabachnikov)
    Preprint (2024).

Lecture notes and talks (mine and others)

Gallery of images and animations

Education

Vita

  • Short:
    • 1957: born, Israel.
    • 1983: B.A., Math+Physics, Hebrew U., Jerusalem.
    • 1985: M.A, Math, Hebrew U., Jerusalem.
    • 1991: Ph.D. , Univ. of California, Berkeley ("Yang Mills Fields which are not self-dual").
    • 1991-4: Post-doc, Univ. of Arizona, Tucson.
    • 1994-present: CIMAT, Guanajuato, Mexico.
    • Citizenship: Mexico, Israel.
    • Math interests: differential geometry, mathematical physics (mostly).
    • Other interests: woodworking, music, ...
  • Full

Amusement (my kind)

Some Links I like

Bye :-)