Ascent to Sant Marti del Canigo.

Christian Rosendal
Assistant Professor of Mathematics
University of Illinois at Urbana-Champaign

• Ph.D., Mathematics, Paris 6, 2003.
• Cand. Scient., Mathematics, University of Oslo, 2002.
• DEA, Mathematical Logic, Paris 7, 2000.

Department of Mathematics
273 Altgeld Hall, MC 382
1409 West Green Street
Urbana, IL 61801
United States

Lecture notes for minicourse on Banach spaces in Castro-Urdiales:

Exact Ramsey principles for block sequences pdf
Strong asymptotic structure of infinite dimensional Banach spaces pdf
The 5th dichotomy pdf
The 3rd dichotomy pdf

Courses:

Linear algebra, MA 415, spring 2008.

Recursive function theory, MA 573, spring 2008.

Descriptive set theory, MA 595, fall 2007.

Banach spaces and Ramsey theory, MA 595, spring 2007.

Linear algebra, MA 415, spring 2007.

Research Interests:

Set theory and functional analysis. Mainly Descriptive set theory and its applications in and connections with Banach space theory, Ergodic theory, Topological dynamics, and Model theory.

Papers:

• Banach spaces without minimal subspaces. (joint with V. Ferenczi) preprint, pdf, arXiv:0711.1350.
• The generic isometry and measure preserving homeomorphism are conjugate to their powers. preprint, pdf, arXiv:0711.1351.
• Generic representations of finitely generated groups on Fraisse structures. preprint, pdf, arXiv:0711.1362.
• Descriptive Kakutani equivalence. (joint with B. D. Miller) to appear in Journal of the European Mathematical Society. pdf
• The complexity of classifying separable Banach spaces up to isomorphism. (joint with V. Ferenczi and A. Louveau) arXiv math.FA/0610289.
• 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. arXiv math.FA/0608616, revised version pdf
• On the algebraic structure of the unitary group. (joint with E. Ricard) Collect. Math. 58,2 (2007), 181-192, pdf.
• Automatic continuity in homeomorphism groups of compact 2-manifolds. Revised version with diagrams pdf, to appear in Israel Journal of Math.
• A topological version of the Bergman property. To appear in Forum Mathematicum, pdf.
• Automatic continuity of homomorphisms and fixed points on metric compacta. (joint with S. Solecki) Israel Journal of Math. 162 (2007), 349-371.
• Turbulence, amalgamation and generic automorphisms of homogeneous structures. (joint with A. S. Kechris), Proc. London Math. Soc., 94 (2007) no.2, 302-350, pdf.
• Isomorphisms of Borel full groups. (joint with B. D. Miller) Proc. Amer. Math. Soc. 135 (2007), 517-522.
• On the non-existence of certain group topologies. Fundamenta Mathematicae 187 (2005), 213-228.
• Complete analytic equivalence relations. (with A. Louveau) Trans. Amer. Math. Soc. 357 (2005), no. 12, 4839-4866.
• Incomparable, non-isomorphic and minimal Banach spaces. Fundamenta Mathematicae, 183 (2004), no. 3, 253-274.
• Cofinal families of Borel equivalence relations and quasiorders. J. Symbolic Logic 70 (2005), no. 4, 1325-1340.
• Ergodic Banach spaces. (with V. Ferenczi) Advances in Mathematics, Volume 195, Issue 1, (2005), 259-282.
• The complexity of continuous embeddability between dendrites. (with A. Marcone) J. Symbolic Logic 69 (2004), no. 3, 663-673.
• On a problem of H. P. Rosenthal concerning a characterization of c0 and lp. (with V. Ferenczi and A. M. Pelczar) Bull. London Math. Soc. 36 (2004), no. 3, 396-406.
• On the number of non-isomorphic subspaces of a Banach space. (with V. Ferenczi), Studia Mathematica 168 (2005), 203-216.
• Relations d'equivalence analytiques completes. (with A. Louveau), C. R. Acad. Sci. Paris Ser. I Math. 333 (2001), no. 10, 903-906.