Education

Ph.D. Mathematics, University of California Berkeley, Aug 2011–Jun 2016.

Dissertation: Fun with Fields. Advised by Tom Scanlon.

B.S. Mathematics and Computer Science, University of Washington, Sep 2007–Jun 2011.

Thesis: Combinatorial Game Theory, Well-Tempered Scoring Games, and a Knot Game. Advised by Jim Morrow.

Employment

Associate professor. Fudan University School of Philosophy, Dec 2022–present.

Young associate researcher. Fudan University School of Philosophy, Sep 2020–Dec 2022.

Postdoc. Fudan University School of Mathematical Sciences, Oct 2018–Aug 2020.

Software Engineer. Niantic, Inc., Jan 2016–Jul 2018.

Research Interests

Model theory of fields and valued fields

Neostability: strongly dependent theories, NTP2 theories, dp-rank, o-minimality

Pseudofinite fields and ACFA

Definable groups and tame topology

Applications of cohomology and category theory to model theory

Journal Articles

1. d’Elbée, C., and Halevi, Y., and Johnson, W. (2025). The classification of dp-minimal integral domains.

Model Theory 4(2): 131–162.

2. Johnson, W. and Yao, N. (2025). Abelian groups definable in p-adically closed fields. Journal of

Symbolic Logic 90(1): 460–481.

3. Johnson, W. and Ye, J. (2025). Curve-excluding fields. Journal of the European Mathematical Society

online first.

4. Andújar Guerrero, P. and Johnson, W. (2024). Around definable types in p-adically closed fields.

Annals of Pure and Applied Logic 175(10): 103484.

5. Johnson, W. and Yao, N. (2024). One-dimensional subgroups and connected components in nonabelian

p-adic definable groups. Journal of Symbolic Logic online first.

6. Johnson, W., Tran, C.-M., Walsberg, E., and Ye, J. (2024). The etale-open topology and the stable

fields conjecture. Journal of the European Mathematical Society 26(10): 4033-4070.

7. Johnson, W. (2023). Topologizing interpretable groups in p-adically closed fields. Notre Dame Journal

of Formal Logic 64(4): 571-609.

8. Johnson, W. and Ye, J. (2023). A note on geometric theories of fields. Model Theory 2(1): 121–132.

9. Johnson, W. (2023). Type-definable NIP fields are Artin-Schreier closed. Fundamenta Mathematicae

260: 251–261.

10. Johnson, W. (2023). A note on fsg groups in p-adically closed fields. Mathematical Logic Quarterly

69(1): 50–57.

11. Johnson, W., Walsberg, E., and Ye, J. (2023). The étale open topology over the fraction field of a

henselian local domain. Mathematische Nachrichten 296(5): 1928–1937.

12. Johnson, W. (2023). The classification of dp-minimal and dp-small fields. Journal of the European

Mathematical Society 25(2): 467–513.

13. Johnson, W. (2022). Henselianity in NIP Fp-algebras. Model Theory 1(1): 115–128.

14. Johnson, W. and Yao, N. (2022). On non-compact p-adic definable groups. Journal of Symbolic Logic

87(1): 188–213.

15. Johnson, W. (2022). A criterion for uniform finiteness in the imaginary sorts. Archive for Mathematical

Logic 61: 583–589.

16. Johnson, W. (2022). Forking and dividing in fields with several orderings and valuations. Journal of

Mathematical Logic 22(1): 2150025.

17. Johnson, W. (2022). Counting mod n in pseudofinite fields. Israel Journal of Mathematics 247: 697–739.

18. Johnson, W. (2021). Dp-finite fields I(B): positive characteristic. Annals of Pure and Applied Logic

172(6): 102949.

19. Johnson, W. (2021). Dp-finite fields I(A): the infinitesimals. Annals of Pure and Applied Logic 172(6):

102947.

20. Johnson, W. (2020). On the proof of elimination of imaginaries in algebraically closed valued fields.

Notre Dame Journal of Formal Logic 61(3): 363–381.

21. Johnson, W. (2018). The canonical topology on dp-minimal fields. J. Math. Logic 18(2): 1850007.

22. Johnson, W. (2018). Interpretable sets in dense o-minimal structures. J. Symbolic Logic 83(4): 1477–

1500.

23. Appendix to Freitag, J., Li, W., Scanlon, T. and Johnson, W. (2017). Differential Chow varieties exist.

J. London Math. Soc. 95: 128–156.

24. Johnson, W. (2014). The combinatorial game theory of well-tempered scoring games. International

Journal of Game Theory 43: 415–438.

Preprints

25. A note on one-variable theorems for NSOP (2025). arXiv:2504.12746.

26. Translating between NIP integral domains and topological fields (2025). arXiv:2504.10927.

27. Generic differentiability and P-minimal groups (2024). arXiv:2404.17234.

28. Visceral theories without assumptions (2024). arXiv:2404.11453.

29. C-minimal fields have the exchange property (2024). arXiv:2403.17478.

30. Dp-finite and Noetherian NIP integral domains (2023). arXiv:2302.03315.

31. Dp-finite fields VI: the dp-finite Shelah conjecture (2020). arXiv:2005.13989.

32. Dp-finite fields V: topological fields of finite weight (2020). arXiv:2004.14732.

33. Dp-finite fields IV: the rank 2 picture (2020). arXiv:2003.09130.

34. Dp-finite fields III: inflators and directories (2019). arXiv:1911.04727.

35. Dp-finite fields II: the canonical topology and its relation to henselianity (2019). arXiv:1910.05932.

36. Finite burden in multivalued algebraically closed fields (2019). arXiv:1905.04991.

37. Circular planar resistor networks with nonlinear and signed conductors (2012). arXiv:1203.4045.

38. The knotting-unknotting game played on sums of rational shadows (2011). arXiv:1107.2635.

Conference Talks

39. A classification of dp-minimal integral domains. 2024 Beijing Model Theory Conference, China.

40. C-minimal fields are geometric. 2023 Asian Logic Conference, Tianjin, China.

41. Generic differentiability and the P-minimal group conjectures of Onshuus and Pillay. 2023 Beijing Logic

Meeting, China.

42. Around NIP Noetherian domains. 2023 conference “Model theory of valued fields” at CIRM, Marseille,

France.

43. Dolich and Goodrick’s visceral theories. 2021 Δ15 Logic Workshop, Nanjing, China.

44. On non-compact p-adic definable groups. 2021 Workshop on Trends in Pure and Applied Model Theory,

Fields institute, Toronto, Canada.

45. V-topologies and beyond. 2020 Chinese Mathematical Society Annual Conference, Shijiazhuang, China.

46. An update on dp-finite fields. 2019 Chinese Annual Conference on Mathematical Logic, Chongqing,

China.

47. From modular lattices to valuation rings. 2019 conference “Model Theory of Valued fields and Applications”,

University of Münster, Germany.

48. Multi-valued algebraically closed fields are NTP2. 2018 workshop “Model Theory of Valued Fields”, IHP,

Paris, France.

49. When does Teq eliminate ∃∞? 2016 North American meeting of the Association for Symbolic Logic,

Storrs, US.

50. On dp-minimal fields. 2015 Neostability Theory meeting in Oaxaca, Mexico.

51. Interpretable sets in o-minimal structures. 2015 North American meeting of the ASL, Urbana-Champaign,

US.

Miscellaneous

52. Fun with Fields (2016). PhD dissertation, UC Berkeley.

53. Combinatorial Game Theory, Well-Tempered Scoring Games, and a Knot Game (2011). Undergraduate

Senior Thesis, University of Washington.

Fellowships and Awards

2022 National Natural Science Foundation of China Young Science Fund Project

2018 NSF Mathematical Sciences Postdoctoral Research Fellowship

2016 Sacks Prize for outstanding dissertation in mathematical logic (Association for Symbolic Logic)

2016 Herb Alexander Prize for an outstanding dissertation in pure mathematics (UC Berkeley)

2011 NSF Graduate Research Fellow

2009 Putnam Fellow

2008, 2010 honorable mention in Putnam contest

2011 Dean’s Medalist in the Natural Sciences (University of Washington)

Teaching

Fudan University

Taught introductory model theory in Fall 2020-2024

Taught advanced model theory in Spring 2021-2025

Currently advising four master’s students.

UC Berkeley

Graduate Student Instructor, Fall 2014–Spring 2015, first year calculus. Led weekly discussion sections,

held office hours, helped grade exams. Worked for Ole Hald in 2014 and Alexander Coward in 2015.

Directed Reading Program Mentor, Fall 2014. Guided an undergraduate mathematics major through

van den Dries’ Tame Topology and O-minimal Structures, and helped her prepare a short talk on the book.

University of Washington

Undergraduate Teaching Assistant, Fall 2010–Spring 2011, second year honors calculus and complex

analysis (proof-based). Led weekly discussion sections, held office hours, graded homework.