Su Gao's Publication List

 

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Recent Research Papers

  1. Graev ultrametrics and surjectively universal non-Archimedean Polish groups, Topology and Its Applications 160 (2013), 862-870.
  2. Faithful representations of Polishable ideals, Proceedings of the 12th Asian Logic Conference, 125-143. World Scientific, NJ, 2013.
  3. (with L. Ding) On the Borelness of the intersection operation, Israel Journal of Mathematics 195 (2013), no. 2, 783-800.
  4. (with M. Xuan) On non-Archimedean Polish groups with two-sided invariant metrics, Topology and Its Applications 161 (2014), 343-353.
  5. (with A. Hill) A model for rank one measure preserving transformations, Topology and Its Applications 174 (2014), 25-40.
  6. (with L. Ding) Is there a Spectral Theory for all bounded linear operators? Notices of the American Mathematical Society 61 (2014), no. 7, 730-735.
  7. (with S. Jackson) Countable abelian group actions and hyperfinite equivalence relations, Inventiones Mathematicae 201 (2015), no. 1, 309-383.
  8. (with Z. Yin) A note on equivalence relations lp(lq), Mathematical Logic Quarterly 61 (2015), no. 6, 516-523.
  9. (with A. Hill) Topological isomorphism for rank-1 systems, Journal d′Analyse Mathematique 128 (2016), no. 1, 1-49.
  10. (with S. Jackson and B. Seward) Group colorings and Bernoulli subflows, Memoirs of the American Mathematical Society 241, no. 1141, 2016, vi+241pp.
  11. (with A. Hill) Bounded rank-1 transformations, Journal d′Analyse Mathematique 129 (2016), 341-365.
  12. (with L. Ding) Non-archimedean abelian Polish groups and their actions, Advances in Mathematics 307 (2017), 312-343.
  13. (with C. Chang) The complexity of the classification problem of continua, Proceedings of the American Mathematical Society 145 (2017), no. 3, 1329-1342.
  14. (with C. Ziegler) On polynomial-time relation reducibility, to appear in the Notre Dame Journal of Formal Logic.
  15. (with S. Jackson, E. Krohne, an B. Seward) Forcing constructions and countable Borel equivalence relations, preprint, 2015.
  16. (with A. Hill) Disjointness between bounded rank-one transformations, preprint, 2016.

Survey Articles

1.      Equivalence relations, classification problems, and descriptive set theory (Chinese), to appear in 2015 Mathematics Institute Lectures, Chinese Academy of Sciences.

 

Editorial Work

1.      Special issue: International Meeting on Logic, Algebra and Geometry. Held in St. Petersburg, June 1-7, 2004. Annals of Pure and Applied Logic 143 (2006), no. 1-3. (coeditors: A. M. Vershik and Y. Zhang)

2.      Advances in Logic. The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton. Contemporary Mathematics 425, American Mathematical Society, RI, 2007. (coeditors: S. Jackson and Y. Zhang)

3.      Special issue: Methods of Logic in Mathematics. Annals of Pure and Applied Logic 158 (2009), no. 3. (coeditors: A. Blass and Y. Zhang)

Book

Invariant Descriptive Set Theory. Pure and Applied Mathematics, A Series of Monographs and Textbooks, 293. Taylor & Francis Group, 2009. ISBN-13: 978-1-58488-793-5.

Older Research Papers

  1. The degrees of conditional problems, The Journal of Symbolic Logic 59 (1994), no. 1, 166-181.
  2. On automorphism groups of countable structures, The Journal of Symbolic Logic 63 (1998), no. 3, 891-896.
  3. A dichotomy theorem for mono-unary algebras, Fundamenta Mathematicae 163 (2000), no. 1, 25-37.
  4. Coding subset shift by subgroup conjugacy, The Bulletin of the London Mathematical Society 32 (2000), no. 6, 653-657.
  5. A remark on Martin's conjecture, The Journal of Symbolic Logic 66 (2001), no. 1, 401-406.
  6. (with R. Camerlo) The completeness of the isomorphism relation for countable Boolean algebras, Transactions of the American Mathematical Society 353 (2001), no. 2, 491-518.
  7. Some dichotomy theorems for isomorphism relations of countable models, The Journal of Symbolic Logic 66 (2001), no. 2, 902-922.
  8. The action of SL(2,Z) on the subsets of Z2, Proceedings of the American Mathematical Society 129 (2001), no. 5, 1507-1512.
  9. (with P. Gerdes) Computably enumerable equivalence relations, Studia Logica 67 (2001), no. 1, 27-59.
  10. (with J. Clemens and A. S. Kechris) Polish metric spaces: their classification and isometry groups, The Bulletin of Symbolic Logic 7 (2001), no. 3, 361-375.
  11. Some applications of the Adams-Kechris technique, Proceedings of the American Mathematical Society 130 (2002), no. 3, 863-874.
  12. (with A. S. Kechris) On the classification of Polish metric spaces up to isometry, Memoirs of the American Mathematical Society 161, no. 766, 2003, viii+78pp.
  13. (with V. Pestov) On a universality property of some abelian Polish groups, Fundamenta Mathematicae 179 (2003), no. 1, 1-15.
  14. The homeomorphism problem for countable topological spaces, Topology and Its Applications 139 (2004), no. 1-3, 97-112.
  15. (with G. E. Jan, K.-Y. Chang and I. ParberryA 4-geometry maze router and its application on multi-terminal nets, ACM Transactions on Design Automation of Electronic Systems (TODAES) 10 (2005), no. 1, 116-135.
  16. Unitary group actions and Hilbertian Polish metric spaces, Logic and Its Applications, 53-72. Contemporary Mathematics 380, American Mathematical Society, RI, 2005.
  17. (with C. Shao) Random generations of the countable random graph,  Annals of Pure and Applied Logic 143 (2006), 79-86.
  18. (with L. Ding) Diagonal actions and Borel equivalence relations, The Journal of Symbolic Logic 71 (2006), no. 4, 1081-1096.
  19. Equivalence relations and classical Banach spaces, Mathematical Logic in Asia, 70-89, Proceedings of the 9th Asian Logic Conference, Novosibirsk, Russia, 16-19 August 2005,  S.S. Goncharov, R Downey, and H. Ono, eds., World Scientific, 2006.
  20. (with L. Ding) On generalizations of Lavrentieff's theorem for Polish group actions, Transactions of the American Mathematical Society 359 (2007), no. 1, 417-426.
  21. (with L. Ding) New metrics on free groups, Topology and Its Applications 154 (2007), 410-420.
  22. (with A. W. Miller and W. A. R. Weiss) Steinhaus sets and Jackson sets, Advances in Logic, 127-145. Contemporary Mathematics 425, American Mathematical Society, RI, 2007.
  23. Complexity ranks of countable models, Notre Dame Journal of Formal Logic 48 (2007), no. 1, 33-48.
  24. (with L. Ding) Graev metric groups and Polishable subgroups, Advances in Mathematics 213 (2007), 887-901.
  25. (with S. Jackson, M. Laczkovich and R. D. Mauldin) On the unique representation of families of sets, Transactions of the American Mathematical Society 360 (2008), 939-958.
  26. (with Y. Zhang) Definable sets of generators in maximal cofinitary groups, Advances in Mathematics 217 (2008), 814-832.
  27. (with L. Ding) On separable Banach subspaces, Journal of Mathematical Analysis and Applications 340 (2008), 746-751.
  28. (with S. Jackson and V. Kieftenbeld) A classification of ordinals up to Borel isomorphism, Fundamenta Mathematicae 198 (2008), 61-76.
  29. (with M. Oliver) Borel complexity of isomorphism between quotient Boolean algebras, Journal of Symbolic Logic 73 (2008), no. 4, 1328-1340.
  30. (with L. van den Dries) A Polish group without Lie sums, Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg 79 (2009), 135-147.
  31. (with S. Jackson and B. Seward) A coloring property for countable groups, Mathematical Proceedings of the Cambridge Philosophical Society 147 (2009), no. 3, 579-592.
  32. (with V. Kieftenbeld) Resolvable maps preserve complete metrizability, Proceedings of the American Mathematical Society 138 (2010), no. 6, 2245-2252.
  33. (with S. Jackson and V. Kieftenbeld) The Laczkovich-Komjath property for coanalytic equivalence relations, The Journal of Symbolic Logic 75 (2010), no. 3, 1091-1101.
  34. (with C. Shao) Polish ultrametric Urysohn spaces and their isometry groups, Topology and Its Applications 158 (2011), 492-508.
  35. (with S. Jackson and B. Sari) On the complexity of the uniform homeomorphism relation between separable Banach spaces, Transactions of the American Mathematical Society 363 (2011), no. 6, 3071-3099.