Florent Balacheff

Professor Titular

Address :

Departament de Matemàtiques
Facultat de Ciències
Universitat Autònoma de Barcelona
and
Centre de Recerca Matemātica
08193 Bellaterra (Barcelona), Spain

Email :

florent.balacheff(AT)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

  • [28] Complete 3-manifolds of positive scalar curvature with quadratic decay.
    With Teo Gil Moreno de Mora Sarda and Stéphane Sabourau.
    Preprint arXiv (2024). [Pdf]

  • [27] A Basmajian-type inequality for Riemannian surfaces.
    With David Fisac.
    Preprint arXiv (2023). [Pdf]

    • Publications

  • [26] Short incompressible graphs and 2-free groups.
    With Wolfgang Pitsch.
    Revista Matemática Iberoamericana, Vol. 40 (2024), 1691-1700. [Journal] [Pdf]

  • [25] Isosystolic inequalities on two-dimensional Finsler tori.
    With Teo Gil Moreno de Mora Sarda.
    EMS Surveys of Mathematical Sciences, Vol. 11 (2024), 205-233. [Journal] [Pdf]

  • [24] Projective transformations of convex bodies and volume product.
    With Gil Solanes and Kroum Tzanev.
    International Mathematics Research Notices, Issue 11 (2024), 9054-9065. [Journal] [Pdf]

  • [23] A curvature-free Log(2k-1) Theorem.
    With Louis Merlin.
    Proceedings of the American Mathematical Society, Vol. 151 (2023), 2429-2434. [Journal] [Pdf]

  • [22] Systoles and diameters of hyperbolic surfaces.
    With Vincent Despré and Hugo Parlier.
    Kyoto Journal of Mathematics, Vol. 63 (2023), 211-222. [Journal] [Pdf]

  • [21] The Santaló point for the Holmes-Thompson boundary area.
    With Gil Solanes and Kroum Tzanev.
    Advances in Mathematics, Vol. 397 (2022), Paper No. 108118. [Journal] [Pdf]

  • [20] The minimal length product over homology bases of manifolds.
    With Steve Karam and Hugo Parlier,.
    Mathematische Annalen, Vol. 380 (2021), 825-854. [Journal] [Pdf]

  • [19] Macroscopic Schoen conjecture for manifolds with non-zero simplicial volume.
    With Steve Karam.
    Transactions of the American Mathematical Society, Vol. 372 (2019), 7071-7086. [Journal] [Pdf]

  • [18] Systolic geometry and simplicial complexity for groups.
    With Ivan Babenko et Guillaume Bulteau.
    Journal für die reine und angewandte Mathematik, Vol. 757 (2019), 247-277. [Journal] [Pdf]

  • [17] Isosystolic inequalities for optical hypersurfaces.
    With Juan-Carlos Alvarez Paiva et Kroum Tzanev.
    Advances in Mathematics, Vol. 301 (2016), 934-972. [Journal] [Pdf]

  • [16] Length product of homologically independent loops for tori.
    With Steve Karam.
    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] Systolic volume of homology classes.
    With Ivan Babenko.
    Algebraic and Geometric Topology, Vol. 15 (2015), No 2, 733-767. [Journal] [Pdf]

  • [13] Contact geometry and isosystolic inequalities.
    With Juan-Carlos Alvarez Paiva.
    Geometric And Functional Analysis, Vol. 24 (2014), No 2, 648-669. [Journal] [Pdf]

  • [12] Systole growth for finite area hyperbolic surfaces.
    With Eran Makover et Hugo Parlier.
    Annales de la Faculté des Sciences de Toulouse, Vol. 23 (2014), No 1, 175-180. [Journal] [Pdf]

  • [11] Bers' constants for punctured spheres and hyperelliptic surfaces.
    With Hugo Parlier.
    Journal of Topology and Analysis, Vol. 4 (2012), No 3, 271-296. [Journal] [Pdf]

  • [10] Short loop decompositions of surfaces and the geometry of Jacobians.
    With Hugo Parlier et Stéphane Sabourau.
    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] Diastolic and isoperimetric inequalities on surfaces.
    With Stéphane Sabourau.
    Annales Scientifiques de l'École Normale Supérieure, Vol. 43 (2010), No 4, 579-605. [Journal] [Pdf].

  • [7] A Zoll counterexample to a geodesic length conjecture.
    With Christopher Croke et Mikhail G. Katz.
    Geometric And Functional Analysis, Vol. 19 (2009), No 1 , 1-10. [Journal] [Pdf]

  • [6] Stable norms of non-orientable surfaces.
    With Daniel Massart.
    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] Sur la forme de la boule unité de la norme stable unidimensionnelle.
    With Ivan Babenko.
    Manuscripta Mathematica, Vol. 119 (2006), No 3, 347-358. [Journal] [Pdf]

  • [1] Géométrie systolique des sommes connexes et des revêtements cycliques.
    With Ivan Babenko.
    Mathematische Annalen, Vol. 333 (2005), No 1, 157-180. [Journal] [Pdf]

    • Publications in Proceedings

  • [2] Optimalité systolique infinitésimale de l'oscillateur harmonique.
    With Juan-Carlos Alvarez Paiva.
    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 students

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

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

    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 ]