Frédéric Bihan

me Welcome to my homepage


Frédéric Bihan, Maître de Conférences Hdr,
Responsable de l'équipe de géométrie
Laboratoire de Mathématiques LAMA,
Université Savoie Mont Blanc, Campus Scientifique,
73376 Le Bourget-du-Lac Cedex, France

Téléphone : (+33/0) 4 79 75 86 79
Bureau : 19
Email : pré


  • Mon étudiant Tristan Humbert co-encadré par Sébastien Tavenas a soutenu sa thèse en décembre 2022,

  • Organisateur avec E. Brugallé, A. Dickenstein et N. Dutertre de la conférence Géométrie Algébrique Réelle, CIRM, Luminy, Octobre 2022.

  • Membre du comité scientifique de la série de Conférences MEGA depuis juin 2019.

  • Responsable de la Licence Miash de l'USMB basée à l'IAE (Annecy) depuis fin 2017.

  • Research Interests

    Real algebraic geometry - Toric varieties - Fewnomial theory - Tropical geometry - Convex polytopes


    Most of my papers are on the preprint server ArXiv.
    1. [PDF] Sparse systems with high local multiplicity"
      with Alicia Dickenstein and Jens Forsgard, 22 pages, 2023.

    2. [PDF] New bounds for the number of connected components of fewnomial hypersurfaces"
      with Sébastien Tavenas and Tristan Humbert, 45 pages, August 2022.

    3. [PDF] Optimal Descartes' rule of signs for systems supported on circuits",
      with Alicia Dickenstein and Jens Forsgard, Math. Ann. 381 (2021), no 3-4, 1283-1307.

    4. [PDF] Sign conditions for the existence of at least one positive solution of a sparse polynomial system,
      with Alicia Dickenstein and Magali Giaroli, Adv. Math. 375 (2020), 107412, 28 pages.

    5. [PDF] Regions of multistationarity in cascades of Goldbeter-Koshland loops,
      with Alicia Dickenstein and Magali Giaroli, J. Math. Biol. (2019) Vol. 78(4), 1115-1145.

    6. [PDF] Lower bounds for positive roots and regions of multistationarity in chemical reaction networks,
      with Alicia Dickenstein and Magali Giaroli, J. Algebra (2020), Vol. 542, 367-411.

    7. [PDF] A polyhedral method for Sparse systems with many positive solutions,
      with Francisco Santos and Pierre-Jean Spaenlehauer, SIAM J. Appl. Algebra Geometry, 2(4) (2018), 620-645.
      (Based on the paper 25 below but with many more results and some sections removed).

    8. [PDF] Criteria for strict monotonicity of the mixed volume of convex polytopes,
      with Ivan Soprunov, Advances in Geometry, Vol. 19, Issue 4, 527-540 (2019).

    9. [PDF] Descartes' rule of signs for polynomials systems supported on circuits,
      with Alicia Dickenstein, Int. Math. Res. Not. 2017, no. 22, 6867-6893.

    10. [PDF] Sparse polynomial systems with many positive solutions from bipartite simplicial complexes,
      with Pierre-Jean Spaenlehauer, 25 pages, 2015.

    11. [PDF] A sharp bound on the number of real intersection points of a sparse plane curve with a line,
      with Boulos El Hilany, J. Symbolic Comput. 81 (2017), 88-96.

    12. [PDF] Irrational mixed decomposition and sharp fewnomial bounds for tropical polynomial systems,
      Discrete Comput. Geom. 55 (2016), no. 4, 907-933.

    13. [PDF] Maximally positive polynomial systems supported on circuits, J. Symbolic Comput. 68 (2015), part 2, 61-74.

    14. [PDF] Intersection multiplicity numbers between tropical hypersurfaces,
      with Benoît Bertrand, 17 pages, Contemporary Mathematics book series, vol. 589, 2013.

    15. [PDF] Mémoire de HDR "Topologie des variétés creuses", december 2011.

    16. [PDF] Fewnomial bounds for completely mixed polynomial systems,
      with Frank Sottile, Advances in Geometry, 11 (2011), no. 3, 541-556.

    17. [PDF] Faster Real Feasibility via Circuit Discriminants,
      with J. Maurice Rojas and Casey Stella, proceedings of ISSAC 2009 (July 28-31, Seoul, Korea), pp. 39-46, ACM Press, 2009.

    18. [PDF] Betti number bounds for fewnomial hypersurfaces via stratified Morse theory,
      with Frank Sottile, Proceedings of the American Mathematical Society, 137 (2009), 2825--2833.

    19. [PDF] Bounds on the number of real solutions to polynomial equations,
      with Dan Bates and Frank Sottile, International Mathematical Research Notices, 2007, no. 23, 7 pp.

    20. [PDF] Gale duality for complete intersection,
      with Frank Sottile, 10 pages, Annales de l'Institut Fourier, 58 (2008), no. 3, 877--891.

    21. [PDF] Euler characteristic of real non degenerate tropical complete intersections,
      with Benoît Bertrand, 30 pages, April 2007, revised on october 2007.

    22. [PDF] On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces,
      with J. Maurice Rojas and Frank Sottile, IMA Volume 146 "Algorithms in Algebraic Geometry" edited by Alicia Dickenstein, Frank-Olaf Schreyer, and Andrew J. Sommese, 15-20, Springer, New York, 2007.

    23. [PDF] New fewnomial upper bounds from Gale dual polynomial systems,
      with Frank Sottile, Moscow Mathematical Journal, volume 7, Number 3, (2007), 387-407.
      (special volume dedicated to Askold Khovanskii for his 60th birthday).

    24. [PDF] Topological types of real regular elliptic surfaces,
      with Frédéric Mangolte, Geometriae Dedicata, volume 127, (2007), 57-73.

    25. [PDF] First steps in algorithmic real fewnomial theory,
      with J. Maurice Rojas and Casey Stella, 25 pages, submitted, january 2006.

    26. [PDF] Polynomial systems supported on circuits and dessins d'enfants,
      J. London Math. Soc. 75 (2007), no. 1, 116-132.

    27. [PDF] Is every toric variety an M-variety ?,
      with Matthias Franz, Clint McCrory and Joost Van Hamel,
      Manuscripta Mathematica 120 (2006), 217-232.

    28. [PDF] Polynomial systems with few real zeroes,
      with Benoît Bertrand and Frank Sottile,
      Math. Zeitschrift 253 (2006), 361-385.

    29. [PDF] Asymptotiques de nombres de Betti d'hypersurfaces projectives réelles,
      Preprint in french, 2003, 28 pages.

    30. Asymptotic behaviour of Betti numbers of real algebraic surfaces,
      Commentarii Mathematici Helvetici 78 (2003), 227-244.

    31. Viro method for the construction of real complete intersections,
      Advances in Mathematics 169 no 2, (2002), 177-186.

    32. Betti numbers of real numerical quintic surfaces,
      "Topology, Ergodic Theory, Real Algebraic Geometry. Rokhlin's Memorial''
      Amer. Math. Soc. Transl. ser. 2 202
      ed. V. Turaev and A. Vershik, (2001), 31-38.

    33. Une sextique de l'espace projectif réel avec un grand nombre d'anses,
      Revista Matematica Complutense 14 no 2, (2001), 439-461.

    34. Une quintique numérique réelle dont le premier nombre de Betti est maximal
      C. R. Acad. Sci. Paris Ser. 1 Math 329 no 2, (1999), 135-140.

      Last updated: september 2019