Rodes and Canigou

Christian Rosendal
Professor of Mathematics
University of Illinois at Chicago

Research:

• Infinite-dimensional Ramsey theory and infinite games of perfect information [16,21,22,31,32,36]
• Model theory, structural Ramsey theory, exact and approximate homogeneity of Fraisse classes [11,27,28]
• Decision procedures and finite approximations of monoids with connections to Computer Science [20,27,28]
• Small and large scale geometrisation of topological groups [13,35,41,43,45,48]
• Geometric group theory [26,38,44]
• Harmonic analysis of isometry groups [33,34,38,39,46]
• Ergodic theory and dynamical systems [10,11,19,20]
• Banach space geometry [3,5,7,21,30,46]
• Geometric non-linear functional analysis [42,48]
• Descriptive Classification Theory [1,6,8,25,40]
• Classification problems in Functional Analysis, C*-algebra and Topology [2,4,18,25,37]
• Topological rigidity of transformation groups [12,15,23]
• Automorphism groups of model theoretical structures [11,20,28,45]
• Geometric topology [14,41]

Courses:

Current and former students:

• Jake Herndon.
• Bruno de Mendonça Braga.
• Kostya Slutsky.
• Phillip Wesolek.
• Joseph Zielinski.

Papers:

1. Geometries of topological groups, pdf.
2. Continuity of universally measurable homomorphisms, Forum of Mathematics, Pi (2019), Vol. 7, e5, 20 pages, pdf.
3. Light groups of isomorphisms of Banach spaces and invariant LUR renormings, (joint with L. Antunes, V. Ferenczi and S. Grivaux), to appear in Pacific J. Math .pdf.
4. Coarse Geometry of Topological Groups, (book manuscript, version of March 2018) pdf.
5. Coarse equivalence and topological couplings of locally compact groups (joint with U. Bader), Geometriae Dedicata 196 (2018), 1-9, pdf file; online published version.
6. Lipschitz structure and minimal metrics on topological groups, Arkiv för matematik, Vol. 56, No. 1 (2018), pp. 185-206, pdf.
7. Equivariant geometry of Banach spaces and topological groups, Forum of Mathematics, Sigma, (2017), Vol. 5, e22, 62 pages pdf.
8. Large scale geometry of homeomorphism groups (joint with K. Mann), Ergodic Theory and Dynamical Systems 38 (2018), no. 7, 2748-2779, pdf.
9. Compact metrizable structures and classification problems (joint with J. Zielinski), J. Symb. Logic 83 (2018), no. 1, 165–186, pdf.
10. Non-unitarisable representations and maximal symmetry (joint with V. Ferenczi), J. Inst. Math. Jussieu, Volume 16, Issue 2 April 2017, pp. 421-445 pdf .
11. On the cohomology of weakly almost periodic group representations, (joint with U. Bader and R. Sauer), J. Topology and Analysis 6 (2014), no. 2, 153–165 pdf. (An earlier version in a more geometric language can be found here.)
12. The isomorphism relation for separable C*-algebras, (joint with G. A. Elliott, I. Farah, V. I. Paulsen, A. S. Toms and A. Törnquist), Math. Res. Lett. 20 (2013), no. 6, 1071-1080. pdf.
13. Determinacy of adversarial Gowers games, Fund. Math. 227 (2014), no. 2, 163-178 pdf.
14. Global and local boundedness of Polish groups, Indiana Univ. Math. J. 62 (2013), no. 5, 1621-1678 pdf.
15. On isometry groups and maximal symmetry, (joint with V. Ferenczi) Duke Math. J. 162 (2013), no. 10, 1771-1831. pdf.
16. Displaying Polish groups on separable Banach spaces, (joint with V. Ferenczi) Extracta Mathematicae 26 (2011), no. 2, 195-233, pdf.
17. Characterising subspaces of Banach spaces with a Schauder basis having the shift property, Studia Mathematica 207 (2011), no. 1, 59-73, pdf.
18. Alpha-minimal Banach spaces, J. Functional Analysis 262 (2012), no. 8, 3638-3664, pdf.
19. Banach spaces without minimal subspaces - Examples, (joint with V. Ferenczi) Annales de l'Institut Fourier 62 (2012), no. 2, 439-475, pdf.
20. Subspace structure of some operator and Banach spaces, (joint with T. Oikhberg) J. Logic and Analysis 3 (2011), no. 2, 1-31, pdf.
21. Finitely approximable groups and actions. Part 2: Generic representations, J. Symbolic Logic 76 (2011), no. 4, 1307-1321, pdf.
22. Finitely approximable groups and actions. Part 1: The Ribes-Zalesskii property, J. Symbolic Logic 76 (2011), no. 4, 1297-1306, pdf.
23. Completely metrisable groups acting on trees, J. Symbolic Logic 76 (2011), no. 3, 1005-1022, pdf.
24. Descriptive Classification Theory and Separable Banach Spaces, Notices of the American Mathematical Society, October 2011, 1251-1262, pdf.
25. Universally measurable subgroups of countable index J. Symbolic Logic 75 (2010), no. 3, 1081-1086, pdf.
26. Automatic continuity of group homomorphisms. Bull. Symbolic Logic 15 (2009), no. 2, 184-214, pdf.
27. An exact Ramsey principle for block sequences. Collectanea Mathematica 61 (2010), no. 10, 25-36, pdf. A subsequent slicker version is available here.
28. Banach spaces without minimal subspaces, (joint with V. Ferenczi) J. Functional Analysis 257 (2009), no. 1, 149-193, pdf.
29. The generic isometry and measure preserving homeomorphism are conjugate to their powers. Fundamenta Mathematicae 205 (2009), no. 1, 1-27, pdf.
30. Descriptive Kakutani equivalence, (joint with B. D. Miller) Journal of the European Mathematical Society 12 (2010), no. 1, 179-219, pdf
31. 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.
32. 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
33. Infinite asymptotic games. Annales de l'Institut Fourier 59 (2009), no. 4, 1323-1348, pdf
34. On the algebraic structure of the unitary group, (joint with E. Ricard) Collect. Math. 58 (2007), no. 2, 181-192, pdf.
35. Automatic continuity in homeomorphism groups of compact 2-manifolds, Israel Journal of Math. 166 (2008), 349-367, pdf.
36. A topological version of the Bergman property. Forum Mathematicum 21 (2009), no. 2, 299-332, pdf.
37. Automatic continuity of homomorphisms and fixed points on metric compacta, (joint with S. Solecki), Israel Journal of Math. 162 (2007), 349-371, pdf.
38. Turbulence, amalgamation and generic automorphisms of homogeneous structures, (joint with A. S. Kechris), Proc. London Math. Soc. 94 (2007), no. 2, 302-350, pdf.
39. Isomorphisms of Borel full groups, (joint with B. D. Miller) Proc. Amer. Math. Soc. 135 (2007), no. 2, 517-522, pdf.
40. On the non-existence of certain group topologies. Fundamenta Mathematicae 187 (2005), 213-228, pdf.
41. Complete analytic equivalence relations, (joint with A. Louveau) Trans. Amer. Math. Soc. 357 (2005), no. 12, 4839-4866, pdf.
42. Incomparable, non-isomorphic and minimal Banach spaces. Fundamenta Mathematicae, 183 (2004), no. 3, 253-274, pdf.
43. Cofinal families of Borel equivalence relations and quasiorders. J. Symbolic Logic 70 (2005), no. 4, 1325-1340, pdf.
44. Ergodic Banach spaces, (joint with V. Ferenczi) Advances in Mathematics 195 (2005), no. 1, 259-282, pdf.
45. The complexity of continuous embeddability between dendrites, (joint with A. Marcone) J. Symbolic Logic 69 (2004), no. 3, 663-673, pdf.
46. 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.
47. On the number of non-isomorphic subspaces of a Banach space, (joint with V. Ferenczi), Studia Mathematica 168 (2005), no. 3, 203-216, pdf.
48. Relations d'equivalence analytiques completes, (joint with A. Louveau), C. R. Acad. Sci. Paris Ser. I Math. 333 (2001), no. 10, 903-906, pdf.

Department of Mathematics, Statistics, and Computer Science (M/C 249)
University of Illinois at Chicago
851 S. Morgan Street
Chicago, IL 60607-7045

Math department homepage