Research interests: Multifractal analysis of functions, stochastic processes and signals; geometric measure theory; Diophantine approximation.

Seminar organization: Harmonic analysis seminar at Université Paris-Sud

Project memberships:

Coauthors: Ery Arias-Castro, Julien Barral, Yann Bugeaud, Emmanuel Candès, Stéphane Jaffard, Stéphane Seuret.

Papers:

  • Metric Diophantine approximation on the middle-third Cantor set, with Y. Bugeaud, J. Eur. Math. Soc. 18(6):1233-1272, 2016. [doi|arXiv|hal]
  • Describability via ubiquity and eutaxy in Diophantine approximation, Ann. Math. Blaise Pascal 22(S2):1-149, 2015. [cedram|arXiv|hal]
  • Local multifractal analysis, with J. Barral, S. Jaffard and S. Seuret, in: D. Carfi, M.L. Lapidus, E.P.J. Pearse, and M. van Frankenhuijsen, editors, Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics, Contemporary Mathematics, vol. 601, Amer. Math. Soc., Providence, pages 31-64, 2013. [doi|arXiv|hal]
  • Multivariate Davenport series, with S. Jaffard, in: J. Barral and S. Seuret, editors, Further Developments in Fractals and Related Fields: Mathematical Foundations and Connections, Trends in Mathematics, Birkhäuser, Boston, pages 63-113, 2013. [doi|arXiv|hal]
  • Multifractal analysis of Lévy fields, with S. Jaffard, Probab. Theory Relat. Fields 153(1-2):45-96, 2012. [doi|arXiv]
  • Detection of an anomalous cluster in a network, with E. Arias-Castro and E.J. Candès, Ann. Statist. 39(1):278-304, 2011. [doi|arXiv]
  • Supplement to “Detection of an anomalous cluster in a network”, with E. Arias-Castro and E.J. Candès, Ann. Statist. (online), 22 pages, 2010. [doi]
  • On randomly placed arcs on the circle, in: J. Barral and S. Seuret, editors, Recent Developments in Fractals and Related Fields, Applied and Numerical Harmonic Analysis, vol. 67, Birkhäuser, Boston, pages 343-351, 2010. [doi|arXiv]
  • Detection of an abnormal cluster in a network, with E. Arias-Castro and E.J. Candès, in: Proceedings of the 57th session of the International Statistical Institute, Durban, South Africa, August 16-22, 2009, Bull. Int. Stat. Inst., 8 pages, 2009. [pdf]
  • Large intersection properties in Diophantine approximation and dynamical systems, J. London Math. Soc. (2) 79(2):377-398, 2009. [doi|arXiv]
  • Random fractals and tree-indexed Markov chains, Rev. Mat. Iberoamericana 25(3):1089-1126, 2009. [Euclid|arXiv]
  • Singularity sets of Lévy processes, Probab. Theory Relat. Fields 143(3-4):517-544, 2009. [doi|arXiv]
  • Random wavelet series based on a tree-indexed Markov chain, Comm. Math. Phys. 283(2):451-477, 2008. [doi|arXiv]
  • Sets with large intersection and ubiquity, Math. Proc. Cambridge Philos. Soc. 144(1):119-144, 2008. [doi|pdf]
  • Ubiquitous systems and metric number theory, Adv. Math. 218(2):368-394, 2008. [doi|arXiv]
  • Propriétés d'ubiquité en analyse multifractale et séries aléatoires d'ondelettes à coefficients corrélés, PhD thesis, Université Paris 12, 240 pages, June 2007. [tel]
  • Ensembles à grande intersection et ubiquité, C. R. Acad. Sci. Paris, Ser. I 343(7):447-452, 2006. [doi]

Lecture notes:

  • Topics in metric number theory, 217 pages, version of May 2015. [pdf]
  • These notes served as a basis for the master's course Metric number theory and multifractal analysis that I gave at Université Paris-Saclay. Comments are welcome!

Contact:

  • Université Paris-Sud, Laboratoire de Mathématiques (Bâtiment 425), 91405 Orsay Cedex, France
  • Phone: +33 1 69 15 79 53
  • Email:
  • Office: 218 B