Banach Spaces

Abstract Embeddability Ranks, (joint with F. Baudier), to appear in Expositiones Mathematicae, arxiv.

Separation ratios of maps between Banach spaces, C. R. Math. Acad. Sci. Paris 361 (2023), 1663–1673, arxiv.

Amenability, Optimal Transport and General Mean Ergodic Theorems, pdf.

Geometries of topological groups,  Bull. Amer. Math. Soc. (N.S.) 60 (2023), no. 4, 539–568, pdf.

On uniform and coarse rigidity  of L^p([0,1]), Studia Math. 268 (2023), no. 2, 235–240, pdf.

Light groups of isomorphisms of Banach spaces and invariant LUR renormings, (joint with L. Antunes, V. Ferenczi and S. Grivaux), Pacific J. Math., Vol. 301 (2019), No. 1, 31–54, pdf. 

Equivariant geometry of Banach spaces and topological groups, Forum of Mathematics, Sigma, (2017), Vol. 5, e22, 62 pages, pdf.

Non-unitarisable representations and maximal symmetry (joint with V. Ferenczi), J. Inst. Math. Jussieu, Volume 16, Issue 2 April 2017, pp. 421-445 pdf .

Determinacy of adversarial Gowers games, Fund. Math. 227 (2014), no. 2, 163-178, pdf.

On isometry groups and maximal symmetry, (joint with V. Ferenczi) Duke Math. J. 162 (2013), no. 10, 1771-1831, pdf.

Displaying Polish groups on separable Banach spaces, (joint with V. Ferenczi) Extracta Mathematicae 26 (2011), no. 2, 195-233, pdf.

Characterising subspaces of Banach spaces with a Schauder basis having the shift property, Studia Mathematica 207 (2011), no. 1, 59-73, pdf.

Alpha-minimal Banach spaces, J. Functional Analysis 262 (2012), no. 8, 3638-3664, pdf.

Banach spaces without minimal subspaces - Examples, (joint with V. Ferenczi) Annales de l'Institut Fourier 62 (2012), no. 2, 439-475, pdf.

Subspace structure of some operator and Banach spaces, (joint with T. Oikhberg) J. Logic and Analysis 3 (2011), no. 2, 1-31, pdf.

Descriptive Classification Theory and Separable Banach Spaces, Notices of the American Mathematical Society, October 2011, 1251-1262, pdf.

An exact Ramsey principle for block sequences. Collectanea Mathematica 61 (2010), no. 10, 25-36, pdf. A subsequent slicker version is available here.

Banach spaces without minimal subspaces, (joint with V. Ferenczi) J. Functional Analysis 257 (2009), no. 1, 149-193, pdf.

The complexity of classifying separable Banach spaces up to isomorphism, (joint with V. Ferenczi and A. Louveau) J. London Math. Soc. 79 (2009), no. 2, 323-345, pdf.

Complexity and homogeneity in Banach spaces, (joint with V. Ferenczi) Banach Spaces and their Applications in Mathematics, Ed. Beata Randrianantoanina and Narcisse Randrianantoanina, Walter de Gruyter, Berlin, p. 83-110, pdf.

Infinite asymptotic games. Annales de l'Institut Fourier 59 (2009), no. 4, 1323-1348, pdf.

On the algebraic structure of the unitary group, (joint with E. Ricard) Collect. Math. 58 (2007), no. 2, 181-192, pdf.

Incomparable, non-isomorphic and minimal Banach spaces. Fundamenta Mathematicae, 183 (2004), no. 3, 253-274, pdf.

Ergodic Banach spaces, (joint with V. Ferenczi) Advances in Mathematics 195 (2005), no. 1, 259-282, pdf.

On a problem of H. P. Rosenthal concerning a characterization of c0 and lp, (joint with V. Ferenczi and A. M. Pelczar) Bull. London Math. Soc. 36 (2004), no. 3, 396-406, pdf.

On the number of non-isomorphic subspaces of a Banach space, (joint with V. Ferenczi), Studia Mathematica 168 (2005), no. 3, 203-216, pdf.