高速

数学科学学院

个人简介

高速，南开大学讲席教授。本科毕业于北京大学数学系，硕士毕业于陈省身数学研究所，1998年获加州大学洛杉矶分校博士学位。1998-2001年，在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《中国科学：数学》及两个国际逻辑杂志编委，丛书Perspectivesin Logic主编，符号逻辑协会（Association for Symbolic Logic）理事会及执委会成员，中国数学会数理逻辑专业委员会主任等职。

科研项目

National Natural Science Foundation of China 12271263

Title: A Study of the Automorphism Groups of Ultraextensive Spaces

Role: PI

Award Amount: 470,000 yuan

Award Period: 2023-2026

National Natural Science Foundation of China 12250710128

Title: Borel Combinatorics of Countable Group Actions and Applications

Role: PI

Award Amount: 1,600,000 yuan

Award Period: 2023-2024

National Science Foundation DMS-1800323

Title: Descriptive Dynamics and Borel Combinatorics of Group Actions

Role: PI

Award Amount: $270,000

Award Period: 2018-2021

National Science Foundation DMS-1259803

Title: Fostering Outstanding Cohorts in Undergraduate Science II

Role: Co-PI

Award Amount: $625,235

Award Period: 2013-2019

National Science Foundation DMS-1201290

Title: Equivalence Relations, Symbolic Dynamics, and Descriptive Set Theory Role: PI

Award Amount: $240,026

Award Period: 2012-2016

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

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

Award Period: 2008-2010

National Science Foundation DMS-0501039

Title: Orbit Equivalence Relations and Classification Problems

Role: PI

Award Amount: $91,345

Award Period: 2005-2009

National Science Foundation DMS-0444019

Title: Conference in Mathematical Logic At UNT

Role: Co-PI

Award Amount: $16,000

Award Period: 2004

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.

论文著作

Monograph

S. Gao, 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

Recent Research Papers

59. M. Foreman, S. Gao, A. Hill, C. E. Silva, and B. Weiss, Rank-1 transformations, odometers, and finite factors, Israel Journal of Mathematics 255 (2023), 231-249.

DOI: 10.1007/s11856-022-2451-y

60. S. Gao, Descriptive combinatorics of countable abelian group actions (in Chinese), Scientia Sinica Mathematica 54 (2024), 575-592.

DOI: 10.1360/SSM-2023-0112

61. S. Gao, L. Jacoby, W. Johnson, J. Leng, R. Li, C. E. Silva, Y. Wu, On finite spacer rank for words and subshifts, Discrete and Continuous Dynamical Systems 45 (2025), no. 1, 248-285.

DOI: 10.3934/dcds.2024092

62. S. Gao, R. Li, Subshifts of finite symbolic rank, Ergodic Theory and Dynamical Systems45 (2025), no. 3, 807-848.

DOI: 10.1017/etds.2024.45

63. S. Gao and X. Ren, The amalgamation property and Urysohn structures in continuous logic, The Journal of Symbolic Logic, published online 4/12/2024.

DOI: 10.1017/jsl.2024.26

64. S. Gao, R. Wang and T. Wang, Continuous edge chromatic numbers of abelian group actions, to appear in Science China Mathematics, published online 1/3/2025.

DOI: 10.1007/s11425-024-2336-x

65. S. Gao and M. Xiao, An order analysis of hyperfinite Borel equivalence relations, The Journal of Symbolic Logic, published online 3/21/2025.

DOI: 10.1017/jsl.2024.82

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

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 (2017), 91-109. Chinese Academy of Sciences.

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 87(2022) ,no.3, 873-893.

DOI: 10.1017/jsl.2022.23

58. M. Etedadialiabadi and S. Gao, Sarnak's conjecture for a class of rank-one subshifts, Proceedings of the American Mathematical Society, Series B 9 (2022), 460-471.

DOI: 10.1090/bproc/148

学术交流

Research Talks

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.

3. Invited talk (online) in the Conference about Computing in Topological Structures, Sirius Mathematics Center, Sochi, Russia, June 27-July 1, 2022.

4. Invited talk in the Conference in Mathematical Logic, Harbin Institute of Technology, Harbin, China, August 8-9, 2022.

5. Invited talk (online) in the WDCM-2022: Fourth Workshop on Digitalization and Computable Models, Novosibirsk and Kazan, Russia, October 24-29, 2022.

6.Invited talk in Dyadisc 6 (Dynamics on the Cantor set and applications), Amiens, France, July 5-7, 2023.

7.Invited talk in Beijing Logic Meeting, Chinese Academy of Sciences, July 24-28, 2023.

8.Invited talk in the Conference on Descriptive Set Theory & Dynamics, University of Warsaw, Poland, August 21-25, 2023.

9.Invited talk in the Workshop on Mathematical Logic and Philosophy of Mathematics, Tsinghua University, Beijing, China, September 26-28, 2023.

10. Invited Departmental Seminars and Colloquium talks in 2023: Wuhan University (February), Wuhan University of Technology (February), Sichuan University (May), Tokyo Model Theory Seminar (June), Yonsei University (June), Beijing Jiaotong University (July).

11. Invited plenary talk in the Fourth International Conference on Topological Algebras and Their Applications, Nankai University, April 3-7, 2024.

12. Invited plenary talk in the First United Academic Meeting of the Mathematical Societies of Beijing, Tianjin, and Hebei, Hebei Normal University, Shijiazhuang, April 19-22, 2024.

13. Invited Departmental Seminars and Colloquium talks in 2024: Tsinghua Logic Salon (May), Shaanxi Normal University (May), Northwestern University (China, May), Harbin Institute of Technology (August, December), McGill University (September), Quebec Mathematical Sciences Colloquium (September), Rutgers University (September), University of Wisconsin-Madison (October), University of California Berkeley (October), Peking University (October), Beijing International Mathematical Research Center (November), Sichuan University (November), Southern University of Science and Technology (December), Hunan University (December), Hebei University of Technology (December)

14. Lecturer for the 2024 IMS Summer School in Mathematical Logic, National University of Singapore, July 1-19, 2024.

15. Invited plenary talk in the Forum on the Frontiers and Prospectives in Mathematics, Editorial Board meeting of Science China Mathematics, Enshi, July 20-21, 2024.

16. Invited talk in the Conference on Generalized Computability Theory, CIEM, Castro Urdiales, Cantabria, Spain, August 19-23, 2024.

17. Invited talk in the LPMC conference, Nankai University, November 23, 2024.

18. Invited Mini-course in the 2024 General Topology Symposium, Ehime University, Ehime, Japan, November 27-28, 2024.

19. Invited talk in the Conference on Limits on Computability, Definability, Provability--Celebrating the Mathematical and Professional Contributions of Chong Chi Tat, National University of Singapore, January 9-10, 2025.

20. Invited keynote talk in the 11th Indian Conference on Logic and its Applications, Indian Statistical Institute, Kolkata, India, February 3-5, 2025.

21. Invited keynote talk in theInternational Conference on Pure Mathematics and its Applications (ICPMA-2025), University of Culcutta, Kolkata, India, February 5-7, 2025.

22. Invited departmental seminars and colloquium talks in 2025: Ramakrishna Mission Vivekananda University(RKMVERI –Ramekrishna Mission Vivekananda Educational and Research Institute, February)

学位：博士

毕业院校： UCLA

邮件： logic@nankai.edu.cn

办公地点：数学科学学院237

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