Sylvy Anscombe
My research interests lie in Model Theory, a part of Mathematical Logic, including connections to algebra and number theory. I am supported by GeoMod.

publications

research articles
  1. Characterizing NIP henselian fields, with Franziska Jahnke.
    Journal of the London Mathematical Society, 109(3), 2024.
  2. Axiomatizing the existential theory of $\mathbb{F}_{q}(\!(t)\!)$, with Philip Dittmann and Arno Fehm.
    Algebra & Number Theory, 17-11 (2023), 2013--2032.
  3. The model theory of Cohen rings, with Franziska Jahnke.
    Confluentes Mathematici, 14, no. 2, 1–28, 2022.
  4. Denseness results in the theory of algebraic fields, with Philip Dittmann and Arno Fehm.
    Annals of Pure and Applied Logic, 172, 2021.
  5. A $p$-adic analogue of Siegel's theorem on sums of squares, with Philip Dittmann and Arno Fehm.
    Mathematische Nachrichten, 293:1434–1451, 2020.
  6. Approximation theorems for spaces of localities, with Philip Dittmann and Arno Fehm.
    Mathematische Zeitschrift, 296:1471–1499, 2020.
  7. Existentially generated subfields of large fields.
    Journal of Algebra, 517C:78–94, 2019.
  8. Henselianity in the language of rings, with Franziska Jahnke.
    Annals of Pure and Applied Logic, 169(9):872–895, 2018.
  9. Characterizing diophantine henselian valuation rings and valuation ideals, with Arno Fehm.
    Proceedings of the London Mathematical Society, 115:293–322, 2017.
  10. Notes on extremal and tame valued fields, with Franz-Viktor Kuhlmann.
    Journal of Symbolic Logic, 81:400–416, 2016.
  11. The existential theory of equicharacteristic henselian valued fields, with Arno Fehm.
    Algebra & Number Theory, 10-3:665–683, 2016.
  12. An existential $\emptyset$-definition of $\mathbb{F}_{q}[\![t]\!]$ in $\mathbb{F}_{q}(\!(t)\!)$, with Jochen Koenigsmann.
    Journal of Symbolic Logic, 79:1336–1343, 2014.
thesis
  1. Definability in Henselian Fields. DPhil Thesis, University of Oxford, 2013.
    Supervised by Prof. Jochen Koenigsmann.
submitted/notes
  1. Universal-existential theories of fields, with Arno Fehm.
    Manuscript, 2024. arXiv:2405.12771 [math.LO]
  2. One-dimensional $F$-definable sets in $F(\!(t)\!)$.
    Manuscript, 2024. arXiv:1503.05803 [math.LO]
  3. Interpretations of syntactic fragments of theories of fields, with Arno Fehm.
    Submitted, 2024. arXiv:2312.17616 [math.LO]
  4. Ax–Kochen–Ershov principles for finitely ramified henselian fields, with Philip Dittmann and Franziska Jahnke.
    Submitted, 2023. arXiv:2305.12145 [math.LO]
other publications
  1. A survey of local-global methods for Hilbert's Tenth Problem, with Valentijn Karemaker, Zeynep Kisakürek, Vlerë Mehmeti, Margherita Pagano, and Laura Paladino.
    To appear in Women in Numbers Europe IV, edited by Ramla Abdellatif, Valentijn Karemaker, and Lejla Smajlovic. arXiv:2309.14987 [math.NT]
  2. Imperfection in NIP fields, with Franziska Jahnke.
    Extended abstract, Oberwolfach Reports (20) 2023, pp. 125–127.
  3. Exposé Bourbaki 1186 : Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson].
    Séminaire Bourbaki, volume 2021/2022, exposés 1181-1196. Astérisque, no.438, p. 247–279, 2022.

talks

short courses
  1. Introduction to logic: first-order and categorical (slides, handout, questions), ALGAR 2022, Antwerp, September 2022.
  2. Shelah’s Conjecture and Johnson’s Theorem (slides), ECIMT-2022, Münster, March 2022.
  3. Les $p$-adiques via la théorie des modèles (slides, questions), École d'été 2021 du GDR JC2A, Paris, August 2021.
  4. Diophantine subsets of henselian fields (slides, questions), ALGAR 2020: Valuations, quadratic forms and definability, Antwerp, July 2020.
conference talks and seminars (a selection)
  1. Fragments of theories of fields and transfer of existential decidability, Model theory and related topics, Manchester, July 2023.
  2. Transfer of decidability for existential theories of (valued) fields, Definability and Computability over Arithmetically Significant Fields, online, June 2023.
  3. Interpretations of fragments of theories of fields, Géométrie et Théorie des Modèles, Jussieu, Paris, June, 2023.
  4. Interpretations of fragments of theories of fields, SEEMOD XV, Oxford, 13th June 2023.
  5. Transfer of decidability for existential theories of (valued) fields, (abstract, video), Théorie des modèles des corps valués, CIRM, Luminy, May, 2023.
  6. Hilbert's Tenth Problem - for the 21st century, MOSS 2023, Project Spiral, April, 2023.
  7. Le Xème problème de Hilbert - un problème pour le XXème et le XXIème siècle, (slides), «Des Mathématiques», ENS, Paris, February 2023.
  8. Hilbert's Tenth Problem: Between logic and number theory (slides), ASL Tutorial Lectures, JMM 2023, Boston, January 2023.
  9. Hilbert's Tenth Problem and henselian valuations (slides, abstract), TMD 2022, online, December 2022.
  10. Existential theories of classes of fields --- henselian and otherwise (abstract), Oberseminar Modelltheorie, Geometrie und Gruppentheorie, Münster, December 2022.
  11. Asymptotic classes of finite structures and their ultralimits (slides, abstract), DaLFI 2022, IRIF, Paris, November 2022.
  12. Cohen rings and existential AKE principles (abstract), Théorie des Modèles et Groupes, IMJ-PRG, Paris, November 2022.
  13. Generalized measurable structures (slides, handout), MWMT2022, Chicago, October 2022.
  14. Existential AKE principles for henselian valued fields (video), Decidability, definability and computability in number theory, Part 2, MSRI, July 2022.
  15. Henselian discretely valued fields and existential AKE principles (slides), Logic Colloquium 2022, Reykjavik, June 2022.
  16. Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson] (notes), Séminaire N. Bourbaki, IHP, Paris, November 2021.
  17. Diophantine subsets and subfields of large fields (slides), SMTH2, June 2021.
  18. Some existential theories of fields (slides), Illinois, April 2021.
  19. Hilbert's Tenth Problem for Power Series (abstract), IMA Early Career Mathematicians' Conference, Lancaster, March 2019.
  20. Research presentation (slides), Galway, October 2017.
  21. Viewing free homogeneous structures and bilinear forms as 'generalised measurable' (abstract), Logic Seminar, Manchester, October 2016.
  22. Measure and dimension in model theory (slides), British Logic Colloquium, Edinburgh, September 2016.
  23. Measure and dimension in model theory (abstract), British Logic Colloquium, Edinburgh, September 2016.
  24. Generalized measurable structures with the Tree Property (slides), Logic Colloquium, Leeds, August 2016.
  25. Generalized measurable structures with the Tree Property (abstract), Logic Colloquium, Leeds, August 2016.
  26. Dimension and dividing in generalised measurable structures (abstract), Workshop on Finite and Pseudofinite Structures, Leeds, July 2016.
  27. Characterizing Diophantine henselian valuation rings and valuation ideals (slides), AMS Rutgers, November 2015.

meetings, conferences, workshops

A selection of meetings that I have attended or will attend.

research students

PhD
  • Piotr Szewczyk — co-supervised with Arno Fehm, TU Dresden.
  • Paulo Andrés Soto Moreno.
Master/Memoire
  • Paulo Andrés Soto Moreno. Inflators and diffeo-valued fields, 2022.
If you're interested in studying with me, please contact me.

useful links