**Su Gao's Publication List**

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here to get a listing of Su Gao's papers from the AMS MathSciNet
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**Recent Research Papers**

- (with S. Jackson)
*Countable abelian group actions and hyperfinite equivalence relations*, Inventiones Mathematicae 201 (2015), no. 1, 309-383. - (with Z. Yin)
*A note on equivalence relations l*, Mathematical Logic Quarterly 61 (2015), no. 6, 516-523._{p}(l_{q}) - (with A. Hill)
*Topological isomorphism for rank-1 systems*, Journal d′Analyse Mathematique 128 (2016), no. 1, 1-49. - (with S. Jackson and B. Seward)
*Group colorings and Bernoulli subflows*, Memoirs of the American Mathematical Society 241, no. 1141, 2016, vi+241pp. - (with A. Hill)
*Bounded rank-1 transformations*, Journal d′Analyse Mathematique 129 (2016), 341-365. - (with L. Ding)
*Non-archimedean abelian Polish groups and their actions*, Advances in Mathematics 307 (2017), 312-343. - (with C. Chang)
*The complexity of the classification problem of continua*, Proceedings of the American Mathematical Society 145 (2017), no. 3, 1329-1342. - (with C. Ziegler)
*On polynomial-time relation reducibility*, Notre Dame Journal of Formal Logic 58 (2017), no. 2, 271-285. - (with S. Jackson, E. Krohne, and B. Seward)
*Forcing constructions and countable Borel equivalence relations*, preprint, 2015. - (with A. Hill)
*Disjointness between bounded rank-one transformations*, preprint, 2016. - (with S. Jackson, E. Krohne, and B. Seward)
*Continuous combinatorics of abelian group actions*, preprint, 2018. - (with C. Ziegler)
*Topological mixing properties of rank-one subshifts,*preprint, 2018. - (with M. Foreman, A. Hill, C. Silva, and B. Weiss)
*Rank-1 transformations, odometers, and finite factors*, preprint, 2018.

**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**

*The degrees of conditional problems*, The Journal of Symbolic Logic 59 (1994), no. 1, 166-181.*On automorphism groups of countable structures*, The Journal of Symbolic Logic 63 (1998), no. 3, 891-896.*A dichotomy theorem for mono-unary algebras*, Fundamenta Mathematicae 163 (2000), no. 1, 25-37.*Coding subset shift by subgroup conjugacy*, The Bulletin of the London Mathematical Society 32 (2000), no. 6, 653-657.*A remark on Martin's conjecture*, The Journal of Symbolic Logic 66 (2001), no. 1, 401-406.- (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. *Some dichotomy theorems for isomorphism relations of countable models*, The Journal of Symbolic Logic 66 (2001), no. 2, 902-922.*The action of SL(2,Z) on the subsets of Z*, Proceedings of the American Mathematical Society 129 (2001), no. 5, 1507-1512.^{2}- (with P. Gerdes)
*Computably enumerable equivalence relations*, Studia Logica 67 (2001), no. 1, 27-59. - (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. *Some applications of the Adams-Kechris technique*, Proceedings of the American Mathematical Society 130 (2002), no. 3, 863-874.- (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. - (with V. Pestov)
*On a universality property of some abelian Polish groups*, Fundamenta Mathematicae 179 (2003), no. 1, 1-15. *The homeomorphism problem for countable topological spaces*, Topology and Its Applications 139 (2004), no. 1-3, 97-112.- (with G. E. Jan, K.-Y. Chang and I. Parberry)
*A**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. *Unitary group actions and Hilbertian Polish metric spaces*, Logic and Its Applications, 53-72. Contemporary Mathematics 380, American Mathematical Society, RI, 2005.- (with C. Shao)
*Random generations of the countable random graph*, Annals of Pure and Applied Logic 143 (2006), 79-86. - (with L. Ding)
*Diagonal actions and Borel equivalence relations*, The Journal of Symbolic Logic 71 (2006), no. 4, 1081-1096. *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.- (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. - (with L. Ding)
*New metrics on free groups*, Topology and Its Applications 154 (2007), 410-420. - (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. *Complexity ranks of countable models*, Notre Dame Journal of Formal Logic 48 (2007), no. 1, 33-48.- (with L. Ding)
*Graev**metric groups and Polishable subgroups*, Advances in Mathematics 213 (2007), 887-901. - (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. - (with Y. Zhang)
*Definable sets of generators in maximal cofinitary groups*, Advances in Mathematics 217 (2008), 814-832. - (with L. Ding)
*On separable Banach subspaces*, Journal of Mathematical Analysis and Applications 340 (2008), 746-751. - (with S. Jackson and V. Kieftenbeld)
*A classification of ordinals up to Borel isomorphism*, Fundamenta Mathematicae 198 (2008), 61-76. - (with M. Oliver)
*Borel**complexity of isomorphism between quotient Boolean algebras*, Journal of Symbolic Logic 73 (2008), no. 4, 1328-1340. - (with
L. van den Dries)
*A Polish group without Lie sums*, Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg 79 (2009), 135-147. - (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. - (with V. Kieftenbeld)
*Resolvable maps preserve complete metrizability*, Proceedings of the American Mathematical Society 138 (2010), no. 6, 2245-2252. - (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. - (with C. Shao)
*Polish ultrametric Urysohn spaces and their isometry groups*, Topology and Its Applications 158 (2011), 492-508. - (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. *Graev**ultrametrics and surjectively universal non-Archimedean Polish groups*, Topology and Its Applications 160 (2013), 862-870.*Faithful representations of Polishable ideals*, Proceedings of the 12^{th}Asian Logic Conference, 125-143. World Scientific, NJ, 2013.- (with L. Ding)
*On the Borelness of the intersection operation*, Israel Journal of Mathematics 195 (2013), no. 2, 783-800. - (with M. Xuan)
*On non-Archimedean Polish groups with two-sided invariant metrics*, Topology and Its Applications 161 (2014), 343-353. - (with A. Hill)
*A model for rank one measure preserving transformations*, Topology and Its Applications 174 (2014), 25-40. - (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.