Frédéric Bihan


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Coordinates:

Frédéric Bihan, Maître de Conférences,
Département de Mathématiques LAMA,
Université de Savoie, Campus Scientifique,
73376 Le Bourget-du-Lac Cedex, France

Téléphone : (+33/0) 4 79 75 86 79
Bureau : 19
Email : prénom.nom@univ-savoie.fr

News

  • En juin 2016, je donnerai à l'université de Buenos Aires un cours de niveau Master intitulé

    "Real Solutions of Polynomial Equations".

  • Boulos El Hilany a débuté en novembre 2013 une thèse sous ma direction

    Sujet "Géométrie tropicale et systèmes polynomiaux".

  • J'ai soutenu mon HDR le 09 décembre 2011

    Titre du mémoire "Topologie des variétés creuses".

  • Responsable du séminaire de géométrie du LAMA (jusqu'à Mars 2014).

  • Ancien membre du conseil de l'UFR SFA.



  • Research Interests

    Topology of Real Algebraic Varieties - Toric Varieties - Fewnomial Theory - Tropical Geometry


    Some Events


  • Combinatorial Algebraic Geometry , Thematic semester at the Fields Institute for Research in Mathematics, Toronto, july-december 2016.

  • 7th European Congress of Mathematics , July 18 - 22, 2016, TU Berlin.

  • MEGA 2015 , Effective Methods in Algebraic Geometry, 15-19 juin 2015, Trento, Italie.

  • Solving Polynomial Equations 13--17 October 2014 at the Simons Institute for the Theory of Computing,
    Semester-long programme on Algorithms and Complexity in Algebraic Geometry, Berkeley.

  • Around Moduli Spaces, Thematic Semester 2014, janvier-juin 2014, Centre de Mathématiques Henri Lebesgue.
    I will participate to the conference Moduli spaces of real and complex varieties, Angers (France), from June 2nd to June 6th, 2014
    (Organisation board: Frédéric Mangolte, Jean-Philippe Monnier, Daniel Naie).

  • Tropical geometry in its complex and symplectic aspects, janvier-juin 2014, Centre Interfacultaire Bernoulli, Lausanne, Suisse
    (organisateurs :  I. Itenberg, G. Mikhalkin). I gave a talk at the conference Complex-algebraic aspects of tropical geometry, Mon 17 March 2014 - Fri 21 March 2014.

  • MEGA2013, Effective Methods in Algebraic Geometry, Goethe-Universität Frankfurt am Main, June 3-7, 2013.

  • Algebra and Geometry, International Conference dedicated to the 65-th anniversary of Askold G. Khovanskii June 4 - 9, 2012, Moscow, Russie.

  • Tropical Geometry Workshop, 12-16 décembre 2011,CIEM (International Centre for Mathematical meetings), Castro Urdiales, Espagne.

  • Real algebraic Geometry, (en l'honneur de Michel Coste, Louis Mahé et Marie-Francoise Roy), 20-24 juin 2011, Université de Rennes 1, France.
    (organisateurs :  K. Bekka, G. Fichou, J.-P. Monnier, R. Quarez ).

  • MEGA 2011 , Effective Methods in Algebraic Geometry, 30 Mai-03 juin 2011, Stockholm, Suède.

  • Séminaire triangulaire Genève-Paris-Strasbourg Géométrie tropicale ,31 mars 2011, Institut de mathématiques de Jussieu.

  • "Solving polynomial equations", 21-25 février 2011, CIAM, KTH, Conférence du semestre "Algebraic Geometry with a view towards applications", Mittag-Leffler, Stockholm

  • Structures réelles sur les variétés complexes : résultats et perspectives (dédiée au 60ème anniversaire de Viatcheslav Kharlamov), 14-18 juin 2010 Centre International de Rencontres Mathématiques (C.I.R.M.), Luminy, France. (organisateurs :  Ilia Itenberg, J.-Y. Welschinger ).


    Papers

    They are listed in reverse chronological order. The more recent are available on the preprint server ArXiv. You can also ask for offprints.
    1. [PDF] Descartes' rule of signs for polynomials systems supported on circuits,
      with Alicia Dickenstein, 22 pages, 2016.

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

    3. [PDF] A sharp bound on the number of real intersection points of a sparse plane curve with a line,
      with Boulos El Hilany, 10 pages, 2015.

    4. [PDF] Irrational mixed decomposition and sharp fewnomial bounds for tropical polynomial systems,
      26 pages, 2014

    5. [PDF] Maximally positive polynomial systems supported on circuits, 15 pages, accepted
      for publication in Journal of Symbolic Computation, 2014.

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

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

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

    9. [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.

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

    11. [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.

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

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

    14. [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.

    15. [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).

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

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

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

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

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

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

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

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

    24. 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.

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

    26. 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: january 2010