Rodes and Canigou

Christian Rosendal
Assistant Professor of Mathematics
University of Illinois at Chicago

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

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.

Courses:

• Mathematical Logic, MA 430, Fall 2009.
• Descriptive set theory, MA 512, Spring 2009.
• Abstract algebra, MA 330, fall 2008, UIC.
• Linear algebra, MA 415, spring 2008, UIUC.
• Recursive function theory, MA 573, spring 2008, UIUC.
• Descriptive set theory, MA 595, fall 2007, UIUC.
• Banach spaces and Ramsey theory, MA 595, spring 2007, UIUC.
• Linear algebra, MA 415, spring 2007, UIUC.

Papers:

• Descriptive Classification Theory and Separable Banach Spaces, pdf. To appear in Notices of the American Mathematical Society.
• $\alpha$-minimality, pdf.
• Banach spaces without minimal subspaces - Examples (Part II). (joint with V. Ferenczi) pdf.
• Universally measurable subgroups of countable index To appear in Journal of Symbolic Logic. pdf.
• Automatic continuity of group homomorphisms. Bull. Symbolic Logic Volume 15, Issue 2 (2009), 184-214, pdf.
• An exact Ramsey principle for block sequences. Collectanea Mathematica, Vol. 61, no. 10 (2010) Pages 25-36, pdf.
• Banach spaces without minimal subspaces (Part I). (joint with V. Ferenczi) Journal of Functional Analysis, Volume 257, Issue 1, 1 July 2009, Pages 149-193, pdf.
• The generic isometry and measure preserving homeomorphism are conjugate to their powers. Fundamenta Mathematicae 205, No. 1, 1-27 (2009), pdf.
• 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, Volume 12, Issue 1 (2010), Pages 179-219. pdf
• The complexity of classifying separable Banach spaces up to isomorphism. (joint with V. Ferenczi and A. Louveau) J. London Math. Soc. 2009 79: 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 no. 4 (2009), p. 1323-1348, 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, pdf, Israel Journal of Math. 166 (2008), 349-367.
• A topological version of the Bergman property. Forum Mathematicum 21:2 (March 2009), pp. 299-332., 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.

Various notes:

• Haar null sets. pdf
• The (very) small index property. pdf
• Ample generics. pdf

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

Department of Mathematics, Statistics, and Computer Science (M/C 249)
University of Illinois at Chicago
851 S. Morgan Street
Chicago, IL 60607-7045
Email address: rosendal@math.uic.edu

Math department homepage