Research works

• On the expansiveness of coarse maps between Banach spaces and geometry preservation , (with B. de Mendonça Braga). Preprint arxiv : https://arxiv.org/pdf/2310.05684

• Asymptotic coarse Lipschitz equivalence , (with B. de Mendonça Braga). Preprint arxiv : https://arxiv.org/abs/2302.12016

• An asymptotic analog of a local-to-global phenomenon for uniformly convex renormings , (with F. Baudier). To appear in Pure and Applied Functional Analysis. Preprint arxiv : https://arxiv.org/pdf/2401.17465

• Universality, complexity and asymptotically uniformly smooth Banach spaces, (with R.M. Causey), Commentationes Mathematicae Universitatis Carolinae, vol. 64, no. 1 (2023), 1—17. Preprint arxiv : https://arxiv.org/abs/2203.13128

• Asymptotic smoothness and universality in Banach spaces , (with R.M. Causey), Colloquium Mathematicum, 172 (2023), no. 2, 281-324. Preprint arxiv : https://arxiv.org/abs/2207.02555

• Asymptotic smoothness in Banach spaces, three space properties and applications, (with R.M. Causey et A. Fovelle), Transactions of the American Mathematical Society 376 (2023), no. 3, 1895-1928. DOI : https://doi.org/10.1090/tran/8818 (electronic). Preprint arxiv : https://arxiv.org/abs/2110.06710

• On Kalton’s interlaced graphs and nonlinear embeddings into dual Banach spaces, (with B. de Mendonça Braga, C. Petitjean et A. Prochazka), Journal of Topology and Analysis 15 (2023), no. 2, 467-494. DOI : https://dx.doi.org/10.1142/S1793525321500345.

• Nonlinear aspects of super weakly compact sets, (with M. Raja), Annales de l’Institut Fourier 72 (2022), no. 3, 1305-1328. https://aif.centre-mersenne.org/articles/10.5802/aif.3488/

• The geometry of Hamming-type metrics and their embeddings into Banach spaces, (with F. Baudier, P. Motakis et Th. Schlumprecht), Israel Journal of Math. 244 (2021), 681-725.

• Coarse and Lipschitz universality, (avec F. Baudier, P. Motakis et Th. Schlumprecht). Fundamenta Mathematicae 254 (2021) , 181-214.

• A new coarsely rigid class of Banach spaces, (with F. Baudier, P. Motakis et Th Schlumprecht), Journal of the Institute of Mathematics of Jussieu 20 (2021) no 5, 1729-1747.

• On the coarse geometry of James spaces, (with C. Petitjean et A. Prochazka). Canad. Math. Bull. 63 (2020), no. 1, 77-93.

• Prescribed Szlenk index of separable Banach spaces, (with R.M. Causey). Studia Mathematica 248 (2019), no 2, 109-127.

• Asymptotic and coarse Lipschitz structures of quasi-reflexive Banach spaces, (with M. Raja). Houston J. of Math 44 (2018) no 3, 927-940.

• The coarse geometry of Tsirelson’s space and application, (with F. Baudier and Th. Schlumprecht). J. Amer. Math. Soc. 31 (2018), no. 3, 699–717.

• Some properties of coarse Lipschitz maps between Banach spaces, (with A. Dalet), North-Western European Journal of Mathematics, 3 (2017), 41-62.

• Szlenk indices of convex hulls, (with A. Prochazka and M. Raja ), Journal of Functional Analysis 272 (2017), 498-521. DOI : 10.1016/j.jfa.2016.10.013 available online on October 17, 2016.

• Equivalent norms with the property $\beta$ of Rolewicz, (with S. Dilworth, D. Kutzarova et L. Randrianarivony), Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111 (2017), no. 1, 101-113.

• Approximation and Schur properties for Lipschitz free spaces over compact metric spaces, (with P. Hájek and E. Pernecká). Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 1, 63–72.

• Tight embeddability of proper and stable metric spaces, (with F. Baudier), Anal. Geom. Metr. Spaces 3, 2015, 140–156.

• Comments on Hölder free spaces, Nigel J. Selecta, Birkhaüser Mathematics 2015, Contemporary Mathematicians, F. Gesztesy, G. Godefroy, L. Grafakos, I. Verbitsky, I. (Eds.)

• Comments on maximal regularity, Nigel J. Selecta, Birkhaüser Mathematics 2015, Contemporary Mathematicians, F. Gesztesy, G. Godefroy, L. Grafakos, I. Verbitsky, I. (Eds.)

• The non-linear geometry of Banach spaces after Nigel Kalton, (with G. Godefroy and V. Zizler), Rocky Mountain J. of Math., 44, 2014, no 5, 1529 - 1583.

• Asymptotic geometry of Banach spaces and non linear quotients, (with S. Dilworth, D. Kutzarova and L. Randrianarivony), Proc. Amer. Math. Soc., 142, 2014, 2747-2762.

• Approximation properties and Schauder decompositions in Lipschitz-free spaces, (with E. Pernecka), Journal of Functional Analysis, 264, 2013, 2323-2334.

• Three space properties and asymptotic structure of Banach spaces, (with P.H. Brooker), J. Math. Anal. Appl. 398(2), 2013, 867-871.

• A short course in non linear geometry of Banach spaces in Topics in Functional and Harmonic Analysis, 77-102, Theta Series in Advanced Mathematics, Bucharest 2012, Ed. by C. Badea, D. Li and V. Petkova.

• A new metric invariant for Banach spaces, (with F. Baudier and N. Kalton), Studia
  Mathematica, 199, 2010, 73-94.

• Weak* dentability index of spaces (with P. Hájek and A. Procházka), J. Math. Anal. Appl. 353, 2009, 239-243.

• The spectral type of sums of operators on non-hilbertian Banach lattices, (with I. Doust), J. Australian Math. Soc., 84(2), 2008, 193-198.

• Isometric embeddings of compact sets into Banach spaces, (with Y. Dutrieux) Journal of Functional Analysis, 255, 2008, 494-501.

• Best constants for Lipschitz embeddings of metric spaces into c0, (with N. Kalton), Fundamenta Mathematicae, 199, 2008, 249-272.

• Embeddings of locally finite metric spaces into Banach spaces, (with F. Baudier), Proc. Amer. Math. Soc., 136, 2008, 1029-1033.

• Various slicing indices on Banach spaces, (with P. Hájek), Med. J. of Math., 4, 2007, 179-190.

• Spectral theory for linear operators on C(K) or L1 spaces, (with I. Doust and F. Lancien), Proc. C.M.A. Australian Nat. Univ., 42, 2007, 1-10.

• Universality of Asplund spaces, (with P. Hájek and V. Montesinos), Proc. Amer. Math. Soc., 135, 2007, 2031-2035.

• A survey on the Szlenk index and some of its applications, Rev. R. Acad. Cien. Serie A Mat., 100(1-2), 2006, 209-235.

• On the extension of Holder maps with values in spaces of continuous functions, (with B. Randrianantoanina), Israel J. of Math., 147, 2005, 75-92.

• On the extensions of Holder-Lipschitz maps, (with B. Randrianantoanina), Extracta Mathematicae, special volume “Some open problems on Functional Analysis and Function Theory" dedicated to the memory of Hans Hahn, 2005.

• On the composition of differentiable functions, (with M. Bachir), Canadian Bull. of Math., 46(4), 2003, 481-494.

• Lp-maximal regularity on Banach spaces with a Schauder basis, (with N. Kalton), Archiv der Math., 78, 2002, 397-408.

• Szlenk indices and uniform homeomorphisms, (with G. Godefroy and N. Kalton), Transactions of the A.M.S., 353, Number 10, 2001, 3895-3918.

• A solution to the problem of Lp-maximal regularity, (with N. Kalton), Mathematishe Zeitschrift, 235, 2000, 559-568.

• Subspaces of c_0 and Lipschitz isomorphisms, (with G. Godefroy and N. Kalton), Geometric And Functional Analysis, 10, 2000, 798-820.

• Lp maximal regularity in Banach spaces with a Schauder basis, (with N. Kalton), Ulmer Seminare, Heft 4, 1999, 293-303.

• L’espace de Banach c_0 est déterminé par sa métrique, (with G. Godefroy and N. Kalton), Note aux C.R.A.S., 327-I, 1998, 817-822.

• Counterexamples concerning sectorial operators, Archiv der Math., 71, 1998, 388-398.

• A generalized functional calculus for operators on subspaces of Lp and application to maximal regularity, (with C. Le Merdy), Illinois J. of Math., 42, 1998, 470-480.

• A joint functional calculus for sectorial operators with commuting resolvents, (with F. Lancien and C. Le Merdy), Proc. London Math. Soc., 77, 1998, 387-414.

• Un calcul fonctionnel joint pour des opérateurs sectoriels, (with F. Lancien and C. Le Merdy), Note aux C.R.A.S., 323-I, 1996, 263-268.

• On the Szlenk index and the weak* dentability index, Quarterly J. Math. Oxford, 47, 1996, 59-71.

• On uniformly convex and uniformly Kadec-Klee renormings, Serdica J. of Math., 21, 1995, 1-18.

• Réflexivité et normes duales possédant la propriété uniforme de Kadec-Klee, Publications Mathématiques de Besançon, 14, 1993/94.

• Dentability indices and locally uniformly convex renormings, Rocky Mountain J. of Math., 23-n 2, 1993, 635-647.

• Indices de dentabilité et indice de Szlenk, Note aux C.R.A.S., 314-I, 1992, 905-910.

• Théorie de l’indice et problèmes de renormage en géométrie des espaces de Banach, Thèse de doctorat de Mathématiques de l’Université Paris 6, janvier 1992.

• Indices de Szlenk et espaces de James, Publications Mathématiques de l’Université Paris 6, Séminaire d’initiation à l’Analyse, 1989/90, n 28.

Students

Pierre Portal. PhD thesis : « Harmonic analyis of Banach valued functions for the study of parabolic evolution equations » (co-supervised with N.J. Kalton). Defense in June 2004.
Present situation : Associate Professor at the Australian National University in Canberra. Maître de Conférences à l’Université de Lille (on leave).
Page personnelle : https://sites.google.com/view/pierre-portal/

Florent Baudier. PhD thesis : « Embeddings of metric spaces into Banach spaces ». Defense in January 2009.
Present situation : Associate Professor, Department of Mathematics, Texas A&M University, USA.
Web page : http://www.math.tamu.edu/~florent/

Aude Dalet PhD thesis : « The study of Lipschitz free spaces ». Defense in June 2015.
Present situation : PRAG (Lecturer) at the UFRST - University of Franche-Comté (Besançon).
Web page : http://adalet.perso.math.cnrs.fr/

Colin Petitjean PhD thesis : « A few aspects of the geometry of Lipschitz-free spaces » (co-supervised with A. Prochazka). Defense in June 2018.
Present situation : Maître de Conférences Université Gustave Eiffel (Marne-la-Vallée).
Web page : http://cpetit13.perso.math.cnrs.fr/index.html

François Nétillard PhD thesis : « Plongements grossièrement Lipschitz et presque Lipschitz dans les espaces de Banach ». Defense in October 2019.
Present situation : Professeur agrégé en CPGE.

Yoël Perreau PhD thesis : « On a few non-linear and isometric aspects of the asymptotic geometry of Banach spaces ». Defense in July 2022.
Present situation : Postdoc at the University of Tartu (Estonia).

Audrey Fovelle PhD thesis : « Linear and non-linear aspects in asymptotic geometry of Banach spaces ».
Present situation : Postdoc at the University of Granada (Spain).
Web page : https://lmb.univ-fcomte.fr/Fovelle-Audrey

Supervision of Erasmus PhD students

Eva Pernecka 2011-2012 - PhD obtained in 2014 at Charles University in Prague : « Analysis in Banach spaces ». Advisor Petr Hajek.
Present situation : Assistant Professor, Czech Technical University
Web page : https://fit.cvut.cz/en/faculty/people/5300-eva-pernecka

Michal Kraus 2011-2012 - PhD obtained in 2012 at Charles University in Prague : « Some results in convexity and in Banach space theory ». Advisor Jaroslav Lukes.