个人简介
现任南开大学讲席教授。1985-1989年，北京大学数学系，攻读学士学位；1989-1992年，陈省身数学研究所，攻读硕士学位；1992-1998年，加州大学洛杉矶分校，攻读博士学位。1998-2001年，加州理工学院，从事博士后研究。2001-2021年就职于北得克萨斯大学，历任助理教授，副教授，教授，校董讲席教授，数学系主任，理学院院长。研究领域主要为数理逻辑与数学基础，在拓扑群，符号与拓扑动力系统，及遍历论方面也有建树。他在描述集合论领域的研究工作中取得一系列突破性研究成果，解决了描述集合论领域中多个处于核心地位的公开问题，相关成果发表在Inventiones Mathematicae，Advances in Mathematics, Memoirs of the American Mathematical Society，Transactions of the American Mathematical Society等核心数学期刊以及Journal of Symbolic Logic, Bulletin of Symbolic Logic, Annals of Pure and Applied Logic等逻辑类权威杂志上。他担任杂志Notre Dame Journal of Formal Logic, Mathematical Logic Quarterly, 以及Perspectives in Logic丛书的编委，是两个美国数学会American Mathematical Society和Mathematical Association of America的终身会员，符号逻辑协会（Association for Symbolic Logic），美国科学促进会（American Association for the Advancement of Science）和科学研究荣誉组织Sigma Xi会员。
教育经历
1992-1998加利福尼亚大学洛杉矶分校数学系博士
1989-1992南开大学数学研究所研究生, 导师：胡国定教授
1985-1989北京大学数学系本科
工作经历
2021-至今南开大学讲席教授
2018-2021北得州大学校董讲席教授
2017-2021北得州大学理学院院长
2011-2016北得州大学数学系主任
2010-2016北得州大学项目主任
2008-2021北得州大学数学系教授
2005-2008北得州大学数学系副教授
2001-2005 北得州大学数学系助理教授
科研项目
U.S. National Science Foundation DMS-1800323
Title: Descriptive Dynamics and Borel Combinatorics of Group Actions
Role: PI
Award Amount: $270,000
Award Period: 2018-2021
U.S. National Science Foundation DMS-1259803
Title: Fostering Outstanding Cohorts in Undergraduate Science II
Role: Co-PI
Award Amount: $625,235
Award Period: 2013-2019
U.S. National Science Foundation DMS-1201290
Title: Equivalence Relations, Symbolic Dynamics, and Descriptive Set Theory Role: PI
Award Amount: $240,026
Award Period: 2012-2016
U.S. National Science Foundation DMS-0943870
Title: EMSW-21-RTG: Research Training Group in Logic and Dynamics
Role: PI
Award Amount: $1,507,481
Award Period: 2010-2016
U.S. National Science Foundation DMS-0901853
Title: Invariant Descriptive Set Theory and Its Applications
Role: PI
Award Amount: $260,417
Award Period: 2009-2013
John Templeton Foundation
Title: Classifying Infinity
Role: PI
Award Amount: $37,873
ward Period: 2008-2010
U.S. National Science Foundation DMS-0501039
Title: Orbit Equivalence Relations and Classification Problems
Role: PI
Award Amount: $91,345
Award Period: 2005-2009
U.S. National Science Foundation DMS-0444019
Title: Conference in Mathematical Logic At UNT
Role: Co-PI
Award Amount: $16,000
Award Period: 2004
U.S. National Science Foundation DMS-0100439
Title: Complex Definable Equivalence Relations and Applications
Role: PI
Award Amount: $67,491
Award Period: 2001-2005
University of North Texas. Faculty Research Grants, 2001-2002, 2002-2003, 2003-2004 and 2005-2006.
University of North Texas. Junior Faculty Summer Research Fellowship, 2001-2002.
Alfred Sloan Foundation. Alfred Sloan Dissertation Fellowship, 1997-1998.
学术交流
1. Invited talk (online) in the BIRS Workshop on Interactions between Descriptive Set Theory and Smooth Dynamics, March 27-April 1, 2022.
2. Invited talk (online) in the College Colloquium of Chongqing University, April 29, 2022.
Editorial Work
1. S. Gao, A. M. Vershik and Y. Zhang, eds., 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.
2. S. Gao, S. Jackson and Y. Zhang, eds., 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.
3. A. Blass, S. Gao and Y. Zhang, eds., Special issue: Methods of Logic in Mathematics. Annals of Pure and Applied Logic 158 (2009), no. 3. 开讲席教授
近期论文
查看导师最新文章
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47. L. Ding and S. Gao, Non-archimedean abelian Polish groups and their actions, Advances in Mathematics 307 (2017), 312-343.
DOI:10.1016/j.aim.2016.11.019
48. C. Chang and S. Gao, The complexity of the classification problem of continua, Proceedings of the American Mathematical Society 145 (2017), no. 3, 1329-1342.
DOI: 10.1090/proc/13288
49. S. Gao and C. Ziegler, On polynomial-time relation reducibility, Notre Dame Journal of Formal Logic 58 (2017), no. 2, 271-285.
DOI:10.1215/00294527-3867118
50. S. Gao, Equivalence relations, classification problems, and descriptive set theory (Chinese), 2015 Mathematics Institute Lectures, 91-109. Chinese Academy of Sciences, 2017.
51. S. Gao and C. Ziegler, Topological mixing properties of rank-one subshifts, Transactions of the London Mathematical Society 6 (2019), no. 1, 1-21.
DOI:10.1112/tlm3.12016
52. C. Chang and S. Gao, The complexity of the classification problems of finite-dimensional continua, Topology and Its Applications 267 (2019), 106876.
DOI: 10.1016/j.topol.2019.106876
53. S. Gao and C. Ziegler, Topological factors of rank-one subshifts, Proceedings of the American Mathematical Society, Series B 7 (2020), 118-126.
DOI:10.1090/bproc/55
54. S. Gao and A. Hill, Disjointness between bounded rank-one transformations, Colloquium Mathematicum 164 (2021), no. 1, 91-121.
DOI:10.4064/cm8081-2-2020
55. M. Etedadialiabadi, S. Gao, F. Le Maître, and J. Melleray, Dense locally finite subgroups of automorphism groups of ultraextensive spaces, Advances in Mathematics 391 (2021), 107966.
DOI:10.1016/j.aim.2021.107966
56.M. Etedadialiabadi and S. Gao, On extensions of partial isomorphisms, The Journal of Symbolic Logic 87 (2022), no. 1, 416-435.
DOI: 10.1017/jsl.2020.19
57. S. Gao, S. Jackson, E. Krohne, and B. Seward, Forcing constructions and countable Borel equivalence relations, The Journal of Symbolic Logic, published online.
DOI: 10.1017/jsl.2022.23
Older Research Papers
1. S. Gao, The degrees of conditional problems, The Journal of Symbolic Logic 59 (1994), no. 1, 166- 181.
DOI: 10.2307/2275258
2. S. Gao, On automorphism groups of countable structures, The Journal of Symbolic Logic 63 (1998), no. 3, 891-896.
DOI: 10.2307/2586718
3. S. Gao, A dichotomy theorem for mono-unary algebras, Fundamenta Mathematicae 163 (2000), no. 1, 25-37.
DOI:10.4064/fm-163-1-25-37
4. S. Gao, Coding subset shift by subgroup conjugacy, The Bulletin of the London Mathematical Society 32 (2000), no. 6, 653-657.
DOI: 10.1112/S0024609300007463
5. S. Gao, A remark on Martin's conjecture, The Journal of Symbolic Logic 66 (2001), no. 1,401-406.
DOI:10.2307/2694929
6. R. Camerlo and S. Gao, The completeness of the isomorphism relation for countable Boolean algebras, Transactions of the American Mathematical Society 353 (2001), no. 2,491-518.
DOI: 10.1090/S0002-9947-00-02659-3
7. S. Gao, Some dichotomy theorems for isomorphism relations of countable models, The Journal of Symbolic Logic 66 (2001), no. 2, 902-922.
DOI: 10.2307/2695052
8. S. Gao, The action of SL(2,Z) on the subsets of Z2, Proceedings of the American Mathematical Society 129 (2001), no. 5, 1507-1512.
DOI: 10.1090/S0002-9939-00-05721-X
9. S. Gao and P. Gerdes, Computably enumerable equivalence relations, Studia Logica 67(2001), no. 1, 27-59.
DOI:10.1023/A:1010521410739
10. J. Clemens, S. Gao and A. S. Kechris, Polish metric spaces: their classification and isometry groups, The Bulletin of Symbolic Logic 7 (2001), no. 3, 361-375.
DOI: 10.2307/2687754
11. S. Gao, Some applications of the Adams-Kechris technique, Proceedings of the American Mathematical Society 130 (2002), no. 3, 863-874.
DOI: 10.1090/S0002-9939-01-06082-8
12. S. Gao and 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.
DOI: 10.1090/memo/0766
13. S. Gao and V. Pestov, On a universality property of some abelian Polish groups, Fundamenta Mathematicae 179 (2003), no. 1, 1-15.
DOI:10.4064/fm179-1-1
14. S. Gao, The homeomorphism problem for countable topological spaces, Topology and Its Applications 139 (2004), no. 1-3, 97-112.
DOI:10.1016/j.topol.2003.09.005
15. G. E. Jan, K.-Y. Chang, S. Gao 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.
DOI:10.1145/1044111.1044118
16. S. Gao, Unitary group actions and Hilbertian Polish metric spaces, Logic and Its Applications, 53-72. Contemporary Mathematics 380, American Mathematical Society, RI, 2005.
DOI:10.1090/conm/380/07107
17. S. Gao and C. Shao, Random generations of the countable random graph, Annals of Pure and Applied Logic 143 (2006), 79-86.
DOI:10.1016/j.apal.2005.12.016
18. L. Ding and S. Gao, Diagonal actions and Borel equivalence relations, The Journal of Symbolic Logic 71 (2006), no. 4, 1081-1096.
DOI: 10.2178/jsl/1164060445
19. S. Gao, 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.
DOI:10.1142/9789812772749_0007
20. L. Ding and S. Gao, On generalizations of Lavrentieff's theorem for Polish group actions, Transactions of the American Mathematical Society 359 (2007), no. 1, 417-426.
DOI: 10.1090/S0002-9947-06-03991-2
21. L. Ding and S. Gao, New metrics on free groups, Topology and Its Applications 154 (2007), 410- 420.
DOI:10.1016/j.topol.2006.05.006
22. S. Gao, 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.
DOI:10.1090/conm/425/08122
23. S. Gao, Complexity ranks of countable models, Notre Dame Journal of Formal Logic 48 (2007), no. 1, 33-48.
DOI:10.1305/ndjfl/1172787543
24. L. Ding and S. Gao, Graev metric groups and Polishable subgroups, Advances in Mathematics 213 (2007), 887-901.
DOI:10.1016/j.aim.2007.01.014
25. S. Gao, S. Jackson, M. Laczkovich and R. D. Mauldin, On the unique representationof families of sets, Transactions of the American Mathematical Society 360 (2008),939- 958.
DOI: 10.1090/S0002-9947-07-04243-2
26. S. Gao and Y. Zhang, Definable sets of generators in maximal cofinitary groups, Advances in Mathematics 217 (2008), 814-832.
DOI:10.1016/j.aim.2007.09.005
27. L. Ding and S. Gao, On separable Banach subspaces, Journal of Mathematical Analysis and Applications 340 (2008), 746-751.
DOI:10.1016/j.jmaa.2007.08.057
28. S. Gao, S. Jackson and V. Kieftenbeld, A classification of ordinals up to Borel isomorphism, Fundamenta Mathematicae 198 (2008), 61-76.
DOI:10.4064/fm198-1-3
29. S. Gao and M. Oliver, Borel complexity of isomorphism between quotient Boolean algebras, The Journal of Symbolic Logic 73 (2008), no. 4, 1328-1340.
DOI:10.2178/jsl/1230396922
30. L. van den Dries and S. Gao, A Polish group without Lie sums, Abhandlungen aus dem Mathematischen Seminar der Universitaet Hamburg 79 (2009), 135-147.
DOI:10.1007/s12188-009-0019-y
31. S. Gao, S. Jackson and B. Seward, A coloring property for countable groups, Mathematical Proceedings of the Cambridge Philosophical Society 147 (2009), no. 3, 579- 592.
DOI:10.1017/S0305004109002655
32. S. Gao and V. Kieftenbeld, Resolvable maps preserve complete metrizability, Proceedings of the American Mathematical Society 138 (2010), no. 6, 2245-2252.
DOI: 10.1090/S0002-9939-10-10246-9
33. S. Gao, S. Jackson and V. Kieftenbeld, The Laczkovich-Komjath property for coanalytic equivalence relations, The Journal of Symbolic Logic 75 (2010), no. 3, 1091- 1101.
DOI: 10.2178/jsl/1278682218
34. S. Gao and C. Shao, Polish ultrametric Urysohn spaces and their isometry groups, Topology and Its Applications 158 (2011), 492-508.
DOI: 10.1016/j.topol.2010.12.003
35. S. Gao, 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.
DOI:10.1090/S0002-9947-2011-05075-0
36. S. Gao, Graev ultrametrics and surjectively universal non-Archimedean Polish groups, Topology and Its Applications 160 (2013), 862-870.
DOI:10.1016/j.topol.2013.02.009
37. S. Gao, Faithful representations of Polishable ideals, Proceedings of the 12th Asian Logic Conference, 125-143. World Scientific, NJ, 2013.
DOI:10.1142/9789814449274_0007
38. L. Ding and S. Gao, On the Borelness of the intersection operation, Israel Journal of Mathematics 195 (2013), no. 2, 783-800.
DOI:10.1007/s11856-012-0115-z
39. S. Gao and M. Xuan, On non-Archimedean Polish groups with two-sided invariant metrics, Topology and Its Applications 161 (2014), 343-353.
DOI:10.1016/j.topol.2013.10.034
40. S. Gao and A. Hill, A model for rank one measure preserving transformations, Topology and Its Applications 174 (2014), 25-40.
DOI: 10.1016/j.topol.2014.06.010
41. L. Ding and S. Gao, Is there a Spectral Theory for all bounded linear operators?, Notices of the American Mathematical Society 61 (2014), no. 7, 730-735.
DOI:10.1090/noti1146
42. S. Gao and S. Jackson, Countable abelian group actions and hyperfinite equivalence relations, Inventiones Mathematicae 201 (2015), no. 1, 309-383.
DOI:10.1007/s00222-015-0603-y
43. S. Gao and Z. Yin, A note on equivalence relations ℓp(ℓq), Mathematical Logic Quarterly 61(2015), no. 6, 516-523.
DOI:10.1002/malq.201500051
44. S. Gao and A. Hill, Topological isomorphism for rank-1 systems, Journal d′Analyse Mathematique, 128 (2016), no. 1, 1-49.
DOI:10.1007/s11854-016-0001-4
45. S. Gao and A. Hill, Bounded rank-one transformations, Journal d′Analyse Mathematique,129 (2016), 341-365.
DOI:10.1007/s11854-016-0024-x
46. S. Gao, S. Jackson and B. Seward, Group colorings and Bernoulli subflows, Memoirs of the American Mathematical Society 241, no. 1141, 2016, vi+241pp.
DOI:10.1090/memo/1141
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