Su Gao's Publication List
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Recent Research Papers
- (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 C. Ziegler) Topological
mixing properties of rank-one subshifts,
Transactions of the London Mathematical Society 6 (2019), no. 1, 1-21.
- (with C. Chang) The
complexity of the classification problems of finite-dimensional continua,
Topology and Its Applications 267 (2019) 106876.
- (with C. Ziegler) Topological
factors of rank-one subshifts, Proceedings
of the American Mathematical Society, Series B 7 (2020), 118-126.
- (with A. Hill) Disjointness
between bounded rank-one transformations, Colloquium Mathematicum 164 (2021), no. 1, 91-121.
- (with M. Etedadialiabadi) On extensions of partial isomorphisms,
to appear in The Journal of Symbolic Logic.
- (with M. Etedadialiabadi, F. Le Maître, and J.
Melleray) Dense
locally finite subgroups of automorphism groups
of ultraextensive spaces, to appear in Advances in Mathematics.
- (with S. Jackson, E. Krohne, and B. Seward) Forcing
constructions and countable Borel equivalence
relations, preprint, 2nd version, 2019.
- (with M. Etedadialiabadi) On extensions of partial isometries,
preprint, 2nd version, 2021.
- (with M. Foreman, A. Hill, C. E. Silva, and B. Weiss) Rank-1
transformations, odometers, and finite factors, preprint, 2nd version, 2021.
- (with S. Jackson, E. Krohne, and B. Seward) Continuous
combinatorics of abelian group actions, preprint,
2nd version, 2021.
Survey Articles
1. Equivalence relations, classification problems, and
descriptive set theory
(Chinese), in 2015 Mathematics Institute Lectures, 91-109, Chinese Academy of
Sciences, 2017.
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 Z2, Proceedings of the American Mathematical Society 129
(2001), no. 5, 1507-1512.
- (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 12th
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.
- (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 lp(lq),
Mathematical Logic Quarterly 61 (2015), no. 6, 516-523.
- (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.