Publications and Preprints

1. "Non-trivial higher homotopy of first-order theories", with Tim Campion, preprint.

2. "Curve-excluding fields", with Will Johnson, submitted.

3. "Tropical functions on a skeleton", with Antoine Ducros, Ehud Hrushovski, and François Loeser, submitted.

4. "When is the étale open topology a field topology?", with Philip Dittmann and Erik Walsberg, to appear in Israel J. Math.

5. "A note on geometric theories of fields", with Will Johnson, Model Theory Vol. 2 (2023), No. 1, 121–132. [DOI]

6. "An invitation to extension domination", with Kyle Gannon, to appear in Notre Dame J. Form. Log.

7. "Beautiful pairs", with Pablo Cubides Kovacsics and Martin Hils, submitted. 

8. "The étale open topology over the fraction field of a henselian local domain", with Will Johnson and Erik Walsberg, Math. Nachr. 296 (2023), no. 5, 1928-1937. [DOI]

9. "Éz fields", with Erik Walsberg,  J. Algebra. 614 (2023), 611–649. [DOI]

10. "The étale open topology and the stable fields conjecture", with Will Jonhson, Chieu-Minh Tran, and Erik Walsberg, to appear in J. Eur. Math. Soc. [DOI]

11. "Cohomology of algebraic varieties over non-archimedean fields", with Pablo Cubides Kovacsics and Mário Edmundo, Forum Math. Sigma 10 (2022), Paper No. e94, 72 pp. [DOI]

12. "Stable formulas in ordered structures", with Daniel Hoffmann and Chieu-Minh Tran, Israel J. Math. 254 (2023), no. 1, 293–312. [DOI]

13. "A note on μ-stabilizers in ACVF", Ann. Pure Appl. Logic 174 (2023), no. 3, Paper No. 103210, 14 pp. [DOI]

14. "Peterzil-Steinhorn subgroups and μ-stabilizers in ACF", with Moshe Kamensky and Sergei Starchenko, J. Inst. Math. Jussieu 22 (2023), no. 3, 1003-1022. [DOI]

15. "Homotopy types of abstract elementary classes", with Tim Campion, J. Pure Appl. Algebra. 225 (2021), no. 5, Paper No. 106461, 9 pp. [DOI]

16. "Pro-definability of spaces of definable types", with Pablo Cubides Kovacsics, Proc. Amer. Math. Soc. Ser. B. 8 (2021), 173-188.  [DOI]

17. "Classifying spaces and the Lascar group", with Tim Campion and Greg Cousins, J. Symb. Log. 86 (2021), no 4, 1396 - 1431. [DOI]

Ongoing Projects

Here is a fairly incomplete list of things that I have advertised at some point (and I am trying to get rid of this list). Feel free to contact me if you are interested in the topics and want to know some updates. 

1. "A model-theoretic study of adic spaces", with Pablo Cubides Kovacsics and Martin Hils.

2. "The finite closed topology and pseudo finite fields", with Will Jonhson, Chieu-Minh Tran, and Erik Walsberg.

3. "Stable theories have trivial second homotopy groups", with Tim Campion and Greg Cousins.