PhD thesis


Etude des espaces Lipschiz-libres, Université de Franche-Comté.

Research stay


Center for Mathematical Modeling , Santiago, Chile, with Prof. Daniilidis, April 2016.

Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague, with Prof. Hajek, December 2013.

Publications


Free Spaces Over Ultrametric Spaces Are Never Isometric to l_1 , with P. Kaufmann and A. Prochazka, Bull. Bel. Math. Soc.


Free Spaces Over Some proper Metric Spaces, Mediterr. J.Math.


Free Spaces Over Countable Compact Metric Spaces, Proc. Amer. Math. Soc.

Presentations during conferences


  • Rencontres d'Analyse Fonctionnelle Besançon-Neuchâtel, LMB, Besançon, May 2016. Talk named Free spaces and l_1.

  • Function Theory on Infinite Dimensional Spaces XIV, Universidad Complutense de Madrid, February 2016. Talk named Free spaces and l_1.

  • Journées du GdR CNRS AFHP 2015, CIRM, Marseille, December 2015. Talk named Free spaces and l_1.

  • International Workshop on Optimal Transport and Geometry, IMAG, Montpellier, June 2015. Talk named Lipschitz-free spaces.

  • Fall School "Metric Embeddings: Constructions and Obstructions", IHP, Paris, October 2014. Talk and survey named "Obstruction to uniform or coarse embeddability into reflexive Banach spaces", based on Coarse and uniform embeddings into reflexive spaces from N.Kalton (2007).

  • Conference on Geometric Functional Analysis and its Applications, Besançon, October 2014. Talk named "Free spaces over proper ultrametric spaces".

  • Journées de l'école doctorale Carnot-Pasteur, Besançon, May 2014. Talk named "Sur les espaces Lipschitz-libres".

  • Journées Cortenaises d'Analyse Mathématiques 2014, Corte, Corse, May 2014. Talk named "Sur l'espace libre des ultramétriques propres".

  • Function Theory on Infinite Dimensional Spaces XIII, ICMAT-Campus de Cantoblanco, Madrid, Spain, February 2014. Talk named "On Lipschitz free space over countable compact metric space".

  • Functional analysis meeting 60e birthday of Gilles Godefroy, University of Mons, Belgique, November 2013. Poster named "Lipschitz free space over countable compact metric space ".

  • Journées du GdR CNRS AFHP 2013, University of Lyon 1-Institut Camille Jordan, October 2013. Talk named "Sur l'espace Lipschitz-libre des compact dénombrables".

    Poster


  • Functional analysis meeting 60e birthday of Gilles Godefroy, University of Mons, Belgique, November 2013. Poster named "Lipschitz free space over countable compact metric space ".

    Presentations during seminar


  • Mathematics seminar, Department of Mathematics of the Universidad Técnica Federico Santa María, Valparaiso, Chile, April 2016. Talk named "Lipschitz-free spaces".

  • Optimization and equilibrium seminar, Center for Mathematical Modeling, Santiago, Chile, April 2016. Talk named "Lipschitz-free spaces".

  • Séminaire d'analyse réelle, Insitut mathématiques de Toulouse, October 2015. Talk named "Lipschitz-free spaces".
  • Séminaire Groupes et Analyse, Institut de Mathématiques de Neuchatel, February 2015. Talk named "Obstruction to coarse and uniform embeddings into reflexive Banach spaces".

  • Séminaire d'analyse fonctionnelle, University Lille 1, February 2015. Talk named "Sur l'espace Lipschitz-libre des espaces ultramétriques".

  • Séminaire d'initiation à l'analyse, Institut de Mathématiques de Jussieu, February 2015. Talk named "Sur l'espace Lipschitz-libre des espaces ultramétriques".

  • Séminaire des doctorants du Laboratoire de Mathématiques de Besançon, University of Besançon, January 2015. Talk named "Sur les espaces Lipschitz-libres".

  • Séminaire des doctorants du Laboratoire Paul Painlevé, University of Lille 1, April 2014. Talk named "Sur les espaces Lipschitz-libres".

  • Séminaire d'Analyse et Géométrie, University of Aix-Marseille, March 2014. Talk named "Sur l'espace Lipschitz-libre des compact dénombrables".

  • Séminaire des doctorants du Laboratoire de Mathématiques de Clermont-Ferrand, Blaise Pascal University, February 2014. Talk named "Sur les espaces Lipschitz-libres".

  • Functional Analysis seminar, Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague, December 2013. Talk named "On Lipschitz free space over countable compact metric space".

  • Séminaire d'analyse fonctionnelle, Laboratoire de Mathématiques de Besançon, September 2013. Talk named "Sur l'espace Lipschitz-libre des compact dénombrables".

    Participations to school and conferences


  • Autumn School on Nonlinear Geometry of Banach Spaces and Applications, Métabief, France, October 2014

  • Journées du GdR CNRS AFHP 2014, Lille, October 2014

  • Rencontres d'Analyse Fonctionnelle Besançon-Neuchâtel, Laboratoire de Mathématiques de Besançon, may 2014

  • Banach Spaces: Geometry and Analysis, Memorial conference for Joram Lindenstrauss, Jerusalem, Israel, may 2013

  • 41st Winter School in Abstract Analysis, Kacov, Czech republic, january 2013

  • Journées du GdR CNRS AFHP 2012, Université Paris-Est, Marne-La-Vallée, october 2012

  • Géométrie des Espaces de Banach, CIRM, Marseille, august 2012

  • Rencontres d'Analyse Fonctionnelle Besançon-Neuchâtel, Institut Mathématiques de Neuchâtel, june 2012

    Presentations during "Groupe de travail" in non-linear Geometry of Banach Spaces, LMB


  • Free spaces over ultametric spaces, based on M. Cuth and M. Doucha paper Free spaces over ultrametric spaces, 2015, preprint

  • Super-reflexive space has metric Markov cotype, based on M. Mendel and A. Naor paper Nonlinear spectral calculus and super-expanders

  • There exist no uniform or coarse embedding of the Lipschitz-free space over [0,1]² on L², based on A. Naor and G. Schechtman paper Planar Earthmover is not in L¹, 2008

    Master thesis


  • Counter examples for the non-linear classification of Banach spaces, under the supervision of Gilles Lancien

  • Linear and non linear isometries, under the supervision of Gilles Lancien