Florent Balacheff

Researcher Ramon y Cajal


Address :

Departament de Matemàtiques
Facultat de Ciències
Universitat Autònoma de Barcelona
08193 Bellaterra (Barcelona), Spain


Email :

fbalacheff(AT)mat(Punt)uab(Punt)cat


Research interests:

Quantitative topology in Riemannian and Finsler geometry, including systolic geometry and topology and its links with contact geometry, symplectic geometry, convex geometry, dynamical systems, graph theory, geometry of numbers theory, lattices in Euclidean spaces, metric geometry, Teichmueller and moduli spaces.


Preprints

  • [24] With Teo Gil Moreno de Mora, Optimal isosystolic inequalities on two-dimensional Finsler tori.
    Preprint arXiv (2022). [Pdf]

  • Publications

  • [23] With Gil Solanes and Kroum Tzanev, The Santaló point for the Holmes-Thompson boundary area.
    Advances in Mathematics, Vol. 397 (2022), Paper No. 108118. [Journal] [Pdf]
  • [22] With Vincent Despré and Hugo Parlier, Systoles and diameters of hyperbolic surfaces.
    Kyoto Journal of Mathematics. Accepted for publication (2021). [Pdf]
  • [21] With Steve Karam and Hugo Parlier, The minimal length product over homology bases of manifolds.
    Mathematische Annalen, Vol. 380 (2021), 825-854. [Journal] [Pdf]
  • [20] With Louis Merlin, A curvature-free Log(2k-1) Theorem.
    Proceedings of the American Mathematical Society. Accepted for publication (2020), DOI 10.1090/proc/15280. [Journal] [Pdf]
  • [19] With Steve Karam, Macroscopic Schoen conjecture for manifolds with non-zero simplicial volume.
    Transactions of the American Mathematical Society, Vol. 372 (2019), 7071-7086. [Journal] [Pdf]
  • [18] With Ivan Babenko et Guillaume Bulteau, Systolic geometry and simplicial complexity for groups.
    Journal für die reine und angewandte Mathematik, Vol. 757 (2019), 247-277. [Journal] [Pdf]
  • [17] With Juan-Carlos Alvarez Paiva et Kroum Tzanev, Isosystolic inequalities for optical hypersurfaces.
    Advances in Mathematics, Vol. 301 (2016), 934-972. [Journal] [Pdf]
  • [16] With Steve Karam, Length product of homologically independent loops for tori.
    Journal of Topology and Analysis, Vol. 8 (2016), No 3, 497-500. [Journal] [Pdf]
  • [15] Measurements of Riemannian two-disks and two-spheres.
    Pacific Journal of Mathematics, Vol. 275 (2015), No 1, 167-181. [Journal] [Pdf]
  • [14] With Ivan Babenko, Systolic volume of homology classes.
    Algebraic and Geometric Topology, Vol. 15 (2015), No 2, 733-767. [Journal] [Pdf]
  • [13] With Juan-Carlos Alvarez Paiva, Contact geometry and isosystolic inequalities.
    Geometric And Functional Analysis, Vol. 24 (2014), No 2, 648-669. [Journal] [Pdf]
  • [12] With Eran Makover et Hugo Parlier, Systole growth for finite area hyperbolic surfaces.
    Annales de la Faculté des Sciences de Toulouse, Vol. 23 (2014), No 1, 175-180. [Journal] [Pdf]
  • [11] With Hugo Parlier, Bers' constants for punctured spheres and hyperelliptic surfaces.
    Journal of Topology and Analysis, Vol. 4 (2012), No 3, 271-296. [Journal] [Pdf]
  • [10] With Hugo Parlier et Stéphane Sabourau, Short loop decompositions of surfaces and the geometry of Jacobians.
    Geometric And Functional Analysis, Vol. 22 (2012), No 1 , 37-73. [Journal] [Pdf]
  • [9] A local optimal diastolic inequality on the two-sphere.
    Journal of Topology and Analysis, Vol. 2 (2010), No 1, 109-121. [Journal] [Pdf]
  • [8] With Stéphane Sabourau, Diastolic and isoperimetric inequalities on surfaces.
    Annales Scientifiques de l'École Normale Supérieure, Vol. 43 (2010), No 4, 579-605. [Journal] [Pdf].
  • [7] With Christopher Croke et Mikhail G. Katz, A Zoll counterexample to a geodesic length conjecture.
    Geometric And Functional Analysis, Vol. 19 (2009), No 1 , 1-10. [Journal] [Pdf]
  • [6] With Daniel Massart, Stable norms of non-orientable surfaces.
    Annales de l'Institut Fourier, Vol. 58 (2008), No 4 , 1337-1369. [Journal] [Pdf]
  • [5] Volume entropy, weighted girths and stable balls on graphs.
    Journal of Graph Theory, Vol. 55 (2007), No 4, 291-305. [Journal] [Pdf]
  • [4] Invariant d'Hermite du réseau des flots entiers d'un graphe pondéré.
    L'Enseignement Mathématique, Vol. 52 (2006), No 3-4, 255-266. [Journal] [Pdf]
  • [3] Sur la systole de la sphère au voisinage de la métrique standard.
    Geometriae Dedicata, Vol. 121 (2006), No 1, 61-71. [Journal] [Pdf]
  • [2] With Ivan Babenko, Sur la forme de la boule unité de la norme stable unidimensionnelle.
    Manuscripta Mathematica, Vol. 119 (2006), No 3, 347-358. [Journal] [Pdf]
  • [1] With Ivan Babenko, Géométrie systolique des sommes connexes et des revêtements cycliques.
    Mathematische Annalen, Vol. 333 (2005), No 1, 157-180. [Journal] [Pdf]

  • Publications in Proceedings

  • [2] With Juan-Carlos Alvarez Paiva, Optimalité systolique infinitésimale de l'oscillateur harmonique.
    Séminaire Théorie Spectrale et Géométrie (Institut Fourier, Grenoble), vol. 27 (2009), 11-16. [Pdf]
  • [1] Sur des problèmes de la géométrie systolique.
    Séminaire Théorie Spectrale et Géométrie (Institut Fourier, Grenoble), vol. 22 (2004), 71-82. [Pdf]

  • Supervision

    PhD student

    David Fisac Camara: 2020-present (co-tutelle with Hugo Parlier)

    Teo Gil Moreno de Mora: 2022-present (co-tutelle with Stéphane Sabourau)

    Postdoctoral student

    Steve Karam: 2014-2016.


    Curriculum Vitae

    [ Pdf ]


    Habilitation Thesis (Habilitation à diriger des recherches)

    Contributions à la géométrie systolique locale et globale. [ Pdf ]

    Defended on December 11th, December, 2012 at Lille University.


    PhD thesis

    Inégalités isopérimétriques sur les graphes et applications en géométrie différentielle. [ Pdf ]

    Defended on July 11th, 2005 at Montpellier University.


    Course (in French) of Differential Geometry and Equations

    Cours. [ Pdf ]

    DM 1. [ Pdf ]

    DM 2. [ Pdf ]

    TD 1. [ Pdf ]

    TD 2. [ Pdf ]

    TD 3. [ Pdf ]

    TD 4. [ Pdf ]

    TD 5. [ Pdf ]