research


CV

Research





Research interests: Analysis, Geometric measure theory, Calculus of variations

I worked mainly on Plateau's problem, especially on the local structure, global behavior and classification of singularities of minimal sets. I am also interested in related problems in Geometric measure theory and Calculus of variation.



Ph.D. Thesis

Ensembles et cnes minimaux de dimension 2 dans les espaces euclidiens,  Orsay, December 7th 2010



Publications and preprints:

  1. Almgren-minimality of unions of two almost orthogonal planes in ℝ4,

    [arXiv:1103.1468], Proc. Lond. Math. Soc. (3) 106 (2013), no. 5, 1005-1059. 

  2. Topological minimal sets and their applications,

    [arXiv:1103.3871], Calc. Var. Partial Differential Equations 47 (2013), no. 3-4, 523-546. 

  3. Global regularity for minimal sets near a T set and counterexamples,

     [arXiv:1112.3565], Revista Matemtica Iberoamericana 30 (2014), no. 1, 203236.

  4. Regularity for minimal sets near a On union of two planes, [arXiv:1203.0560], to appear in Annales de L'Institut Fourier.

  5. Almgren and topological minimality for the set YY, Journal of Functional Analysis, 266 (2014), no. 10, 60076054. [arXiv:1203.0564].

  6. On the topological minimality of unions of planes of arbitrary dimension, International Mathematics Research Notices 2015; doi: 10.1093/imrn/rnv059, [arXiv:1312.3489]

  7. Limits of topological minimal sets with finitely generated coefficient group,  [arXiv:1403.3838]





Talks given at seminars and conferences


Dec 2009   The seminar of analysis of Fourier Institute, Grenoble,
        "Ensembles et cnes minimaux de dimension 2 dans $\R^4$".

Dec 2009   The seminar of harmonic analysis of University Paris-Sud XI (Orsay),
        "Ensembles et cnes minimaux de dimension 2 dans $\R^4$".

Dec 2009   Ph.D students seminar at University Paris-Sud XI,
        "Ensembles minimaux".

Aug 2010   International conference on fractals and dynamic system, East China normal university, Shanghai,
         "Minimal sets".

Mar 2011   The seminar of geometry and analysis of University of Nice,
         "Ensembles et Cnes minimaux de dimension 2 dans $\R^4$".

May 2011   The seminar of analysis of University of Toulouse,
         "Ensembles minimaux".
Oct 2011    The seminar of ergodic theory and dynamical systems of University of Picardy, Amien,
         "Probleme de Plateau, ensemble minimal et la classification des singularites de di- mension 2".

Nov 2011   The seminar of analysis of Fourier Institute, Grenoble,
         "Ensembles minimaux et topologie".

May 2012   The seminar of calculus of variations at Université Paris Sud, Orsay,
         "Ensembles minimaux".

Sept 2012  The Birmingham-Warwick analysis seminar at University of Warwick,
         "Minimal sets".

Dec 2012   International conference on advances on Fractals and related topics, Hong Kong,
        "An introduction to the theory of minimal sets and their local structure".

Dec 2012  Tsinghua University, department of mathematical science, Beijing,
         "An introduction to the theory of minimal sets and their local structure".

Jul 2013    International Congress of Chinese Mathematicians, Taipei,
          "Minimal sets and classification of singularities".

Aug 2013  Morningside Centre of Mathematics, Chinese Academy of Sciences, Beijing,
        "stationary varifold and uniqueness of tangent behavior".

Oct 2013   ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis, Centro De Giorgi, Scuola Normale Superiore Pisa,
        "Minimal sets and classification of singularities".

Jan 2014   series lecture given during the visit to Chinese University of Hong Kong, Hong Kong,
        "An introduction to the theory of minimal sets".

Mar 2014    Max Planck Institute, Golm, Germany,
        "Comparison surfaces".

Apr 2014     Max Planck Institute, Golm, Germany,
        "Topological minimal sets".

Apr 2014      University of Helsinki, Finland,
        "Minimal sets and classification of singularities".

Apr 2014 University of Jyväskylä, Finland,
        "Minimal sets and classification of singularities".

July- August 2014 series of lectures given during the visit to the Mathematical Science Centre at Tsinghua University.
        "An introduction to the theory of minimal sets".

Oct 2014 Université Lyon 1, Lyon, France.
        "Plateaus problem, minimal sets and classification of singularities".

Nov 2014  Ecole centrale Lyon, Lyon, France.
        "Plateaus problem, minimal sets and classification of singularities"

Nov 2014  Toulouse, France.
        "Plateaus problem, minimal sets and classification of singularities"

Dec 2014  University of Tsinghua, Beijing, China.
        "Unique tangent behavior of stationary varifolds"

Juin 2015  Invited talk at the international conference "Geometric measure theory: Theory and applications", Grenoble, France.

July- August 2015 series of lectures given during the visit to the Mathematical Science Centre at Tsinghua University.
        "An introduction to Plateau's problem in arbitrary dimension".




Participations to national and international conferences

Jul 2008 Harmonic analysis conference at Orsay, in honor of Noël Lohoué, Orsay.

Oct 2008 Optimal transportation, geometry and functional inequalities, Pisa, Italy.

Nov 2008 Optimal transportation and applications, Pisa, Italy.

Jun 2009  Harmonic analysis, geometric measure theory and quasiconformal mappings, CRM, Bellaterra, Espagne.

May 2010 CODY Fourth Year Conference : Conformal Methods in Analysis and Dynamics, Seillac, France.

Jun 2010  GNAMPA - ERC SUMMER SCHOOL (Analytic Techniques for Geometric and Functional Inequalities), Ischia, Italy.

Aug 2010  International conference on fractals and dynamic system, East China normal uni- versity, Shanghai, China

Jun 2011  Fractal and related fields II, Porquerolles, France.

Jun-Jul 2011  SMS 2011 Summer School "Metric Measure Spaces : Geometric and Analysis Aspects", Montréal, Canada.

Jul 2012 AEI workshop "Geometric measure theory", Golm, Germany.

Oct 2012 First meeting of the ANR project "GEOMETRYA", Lyon, France.

Dec 2012 International conference on advances on Fractals and related topics, Hong Kong.

Jul 2013 International Congress of Chinese Mathematicians, Taipei.

Sep 2013 Metric and variational structures in singular varieties, Chambéry.

Oct 2013 ERC School on Geometric Measure Theory and Real Analysis, Pisa.

Oct 2013 ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis, Pisa.

June 2015 International conference "Geometric measure theory: Theory and applications", Grenoble, France.





Academic visits
Apr 2013   Université Paris Sud, Orsay, France, 1 week.

Dec 2013- Jan 2014  Chinese University of Hong Kong, Hong Kong, 6 weeks.

Mar-Apr 2014  Max Planck Institute, Golm, Germany, 3 weeks.

Apr 2014  University of Helsinki and University of Jyväskylä, Finland, 1 week.

July-Aug 2014 Mathematical Science Centre at Tsinghua University, Beijing, China, 2 months

Nov 2014 University of Toulouse III, Toulouse, France, 3 days.

Dec 2014 Tsinghua University, Beijing, China, 3 weeks.

Feb 2015 University of Paris Sud, Orsay, France, 1 week.

Mar 2015 University of Warwick, Coventry, UK, 1 week.

July-Aug 2015 Mathematical Science Centre at Tsinghua University, Beijing, China, 1 month.