research interests

My research interests lie in Model Theory, a part of Mathematical Logic, including connections to algebra and number theory.

Keywords: Mathematical logic, model theory, applications of model theory to algebra and number theory, Diophantine equations, asymptotic classes, measurable structures, pseudofinite structures, valued fields, henselianity, definable henselian valuations, Hilbert's Tenth Problem, arithmetic, homogeneous structures, infinite graphs

research articles

published
  1. Denseness results in the theory of algebraic fields (with Philip Dittmann and Arno Fehm). Annals of Pure and Applied Logic, 172, 2021.
  2. A $p$-adic analogue of Siegel's theorem on sums of squares (with Philip Dittmann and Arno Fehm). Mathematische Nachrichten, 293:1434–1451, 2020.
  3. Approximation theorems for spaces of localities (with Philip Dittmann and Arno Fehm). Mathematische Zeitschrift, 296:1471–1499, 2020.
  4. Existentially generated subfields of large fields. Journal of Algebra, 517C:78–94, 2019.
  5. Henselianity in the language of rings (with Franziska Jahnke). Annals of Pure and Applied Logic, 169(9):872–895, 2018.
  6. Characterizing diophantine henselian valuation rings and valuation ideals (with Arno Fehm). Proceedings of the London Mathematical Society, 115:293–322, 2017.
  7. Notes on extremal and tame valued fields (with Franz-Viktor Kuhlmann). Journal of Symbolic Logic, 81:400–416, 2016.
  8. The existential theory of equicharacteristic henselian valued fields (with Arno Fehm). Algebra & Number Theory, 10-3:665–683, 2016.
  9. 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
  1. Axiomatizing the existential theory of $\mathbb{F}_{q}(\!(t)\!)$ (with Philip Dittmann and Arno Fehm). Submitted, 2022. arXiv:2205.05438 [math.LO]
  2. Characterizing NIP henselian fields (with Franziska Jahnke). Submitted, 2022. arXiv:1911.00309 [math.LO]
  3. The model theory of Cohen rings (with Franziska Jahnke). Submitted, 2021. arXiv:1904.08297 [math.LO]
notes
  1. An elementary geometric approach to linear prediction (with Amery Gration). Manuscript, 2021.
  2. The mathematical structure of classical mechanics (with Amery Gration). Manuscript, 2019.
  3. One-dimensional $F$-definable sets in $F(\!(t)\!)$. Manuscript, 2018. arXiv:1503.05803 [math.LO]

talks: slides, notes, and abstracts

  1. Henselian discretely valued fields and existential AKE principles. Slides, Logic Colloquium 2022, Reykjavik, June 2022
  2. Shelah’s Conjecture and Johnson’s Theorem. Slides, ECIMT-2022, Münster, March 2022
  3. Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson]. Slides, Séminaire N. Bourbaki, IHP, Paris, November 2021
  4. Diophantine subsets and subfields of large fields. Slides, SMTH2, June 2021
  5. Some existential theories of fields. Slides, Illinois, April 2021
  6. Hilbert's Tenth Problem for Power Series. Abstract, IMA Early Career Mathematicians' Conference, Lancaster, March 2019
  7. Research presentation. Slides, Galway, Oct 2017.
  8. Viewing free homogeneous structures and bilinear forms as 'generalised measurable'. Abstract, Logic Seminar, Manchester, Oct 2016.
  9. Measure and dimension in model theory. Slides, British Logic Colloquium, Edinburgh, Sep 2016.
  10. Measure and dimension in model theory. Abstract, British Logic Colloquium, Edinburgh, Sep 2016.
  11. Generalized measurable structures with the Tree Property. Slides, Logic Colloquium, Leeds, Aug 2016.
  12. Generalized measurable structures with the Tree Property. Abstract, Logic Colloquium, Leeds, Aug 2016.
  13. Dimension and dividing in generalised measurable structures. Abstract, Workshop on Finite and Pseudofinite Structures, Leeds, Jul 2016.
  14. Characterizing Diophantine henselian valuation rings and valuation ideals. Talk, AMS Rutgers, Nov 2015.

meetings, conferences, workshops

Here are some links to meetings that I have attended or will attend.

online tools

useful links