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

research articles
published
-
Axiomatizing the existential theory of $\mathbb{F}_{q}(\!(t)\!)$,
with Philip Dittmann and Arno Fehm.
Accepted in Algebra & Number Theory, 2023. arXiv:2205.05438 [math.LO] -
The model theory of Cohen rings,
with Franziska Jahnke.
Confluentes Mathematici, 14, no. 2, 1–28, 2022. -
Denseness results in the theory of algebraic fields,
with Philip Dittmann and Arno Fehm.
Annals of Pure and Applied Logic, 172, 2021. -
A $p$-adic analogue of Siegel's theorem on sums of squares,
with Philip Dittmann and Arno Fehm.
Mathematische Nachrichten, 293:1434–1451, 2020. -
Approximation theorems for spaces of localities,
with Philip Dittmann and Arno Fehm.
Mathematische Zeitschrift, 296:1471–1499, 2020. -
Existentially generated subfields of large fields.
Journal of Algebra, 517C:78–94, 2019. -
Henselianity in the language of rings,
with Franziska Jahnke.
Annals of Pure and Applied Logic, 169(9):872–895, 2018. -
Characterizing diophantine henselian valuation rings and valuation ideals,
with Arno Fehm.
Proceedings of the London Mathematical Society, 115:293–322, 2017. -
Notes on extremal and tame valued fields,
with Franz-Viktor Kuhlmann.
Journal of Symbolic Logic, 81:400–416, 2016. -
The existential theory of equicharacteristic henselian valued fields,
with Arno Fehm.
Algebra & Number Theory, 10-3:665–683, 2016. -
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
-
Definability in Henselian Fields.
DPhil Thesis, University of Oxford, 2013.
Supervised by Prof. Jochen Koenigsmann.
submitted
- Characterizing NIP henselian fields, with Franziska Jahnke. Submitted, 2022. arXiv:1911.00309 [math.LO]
talks

short courses
- Introduction to logic: first-order and categorical (slides, handout, questions), ALGAR 2022, Antwerp, September 2022.
- Shelah’s Conjecture and Johnson’s Theorem (slides), ECIMT-2022, Münster, March 2022.
- Les $p$-adiques via la théorie des modèles (slides, questions), École d'été 2021 du GDR JC2A, Paris, August 2021.
- Diophantine subsets of henselian fields (slides, questions), ALGAR 2020: Valuations, quadratic forms and definability, Antwerp, July 2020.
conference talks and seminars (a selection)
- Le Xème problème de Hilbert - un problème pour le XXème et le XXIème siècle, (slides), «Des Mathématiques», ENS, Paris, February 2023.
- Hilbert's Tenth Problem: Between logic and number theory (slides), ASL Tutorial Lectures, JMM 2023, Boston, January 2023.
- Hilbert's Tenth Problem and henselian valuations (slides, abstract), TMD 2022, online, December 2022.
- Existential theories of classes of fields --- henselian and otherwise (abstract), Oberseminar Modelltheorie, Geometrie und Gruppentheorie, Münster, December 2022.
- Asymptotic classes of finite structures and their ultralimits (slides, abstract), DaLFI 2022, IRIF, Paris, November 2022.
- Cohen rings and existential AKE principles (abstract), Théorie des Modèles et Groupes, IMJ-PRG, Paris, November 2022.
- Generalized measurable structures (slides, handout), MWMT2022, Chicago, October 2022.
- Existential AKE principles for henselian valued fields (video), Decidability, definability and computability in number theory, Part 2, MSRI, July 2022.
- Henselian discretely valued fields and existential AKE principles (slides), Logic Colloquium 2022, Reykjavik, June 2022.
- Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson] (notes), Séminaire N. Bourbaki, IHP, Paris, November 2021.
- Diophantine subsets and subfields of large fields (slides), SMTH2, June 2021.
- Some existential theories of fields (slides), Illinois, April 2021.
- Hilbert's Tenth Problem for Power Series (abstract), IMA Early Career Mathematicians' Conference, Lancaster, March 2019.
- Research presentation (slides), Galway, October 2017.
- Viewing free homogeneous structures and bilinear forms as 'generalised measurable' (abstract), Logic Seminar, Manchester, October 2016.
- Measure and dimension in model theory (slides), British Logic Colloquium, Edinburgh, September 2016.
- Measure and dimension in model theory (abstract), British Logic Colloquium, Edinburgh, September 2016.
- Generalized measurable structures with the Tree Property (slides), Logic Colloquium, Leeds, August 2016.
- Generalized measurable structures with the Tree Property (abstract), Logic Colloquium, Leeds, August 2016.
- Dimension and dividing in generalised measurable structures (abstract), Workshop on Finite and Pseudofinite Structures, Leeds, July 2016.
- 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.
- Logique à Paris 2023, IMJ-PRG, Paris, 9th – 12th May 2023
- JMM 2023, 4th – 7th January 2023
- DaLFI 2022, IRIF, Paris, 17th November 2022
- MWMT 2022, 14th – 16th October 2022
- ALGAR 2022, Antwerp, 5th – 9th September 2022
- Women in Numbers Europe 4, Utrecht, 29th August – 2nd September 2022
- Decidability, definability and computability in number theory: Part 2, MSRI/SLMath, Berkeley, 18th July – 12th August 2022
- Logic Colloquium 2022, Reykjavik, June 2022
- Model theory of valued fields and resolution of singularities, Dresden, 17th June 2022
- ASL North American Annual Meeting, Notre Dame, South Bend, 22nd – 25th June 2021
- Short Model Theory Huddle 2, 16th – 18th June 2021
- Decidability, definability and computability in number theory: Part 1 - Virtual Semester, MSRI, Berkeley, 17th August – 18th December 2020
- ALGAR 2020, Antwerp, 6th – 10th of July 2020
- Model Theory of Valued Fields and Applications, Münster, 10th June – 14th June 2019
- Definability and decidability problems in number theory, American Institute of Mathematics, San Jose, California, 6th May – 10th May 2019
- Neostability Theory, BIRS-CMO Workshop, Casa Matemática, 14th October – 19th October 2018
- From permutation groups to model theory, ICMS, Edinburgh, 17th – 20th September 2018
- EWM General Meeting 2018, Graz, 3rd – 7th September 2018
- Model-theoretic methods in number theory and algebraic differential equations, Manchester, 3rd – 5th August 2018
- Workshop on effectivity and ineffectivity for unlikely intersections , Manchester, 24th – 27th July 2018
- Model Theory of Finite and Pseudofinite Structures, Leeds, 9th – 11th April 2018
- Model Theory and Applications, Institut Henri Poincaré, Paris, 26th March – 30th March 2018
- Model Theory of Valued Fields, Institut Henri Poincaré, Paris, 5th March – 9th March 2018
- Model Theory, Combinatorics and Valued Fields, Institut Henri Poincaré, Paris, 18th February – 7th April 2018
- LYMoTS, Preston, 21st October 2017
- Diophantine problems, Manchester, 11th – 15th September 2017
- Homogeneous structures, permutation groups, and connections to set theory, Leeds, 10th – 12th September 2017
- New Directions in the Model Theory of Valued Fields, Preston, 4th August 2017
- Model Theory in Będlewo, Będlewo, 2nd – 8th July 2017
- Model Theory in Wrocław, Wrocław, 30th June – 2nd July 2017
- LYMoTS in Manchester, 30th May 2017
- Mathematisches Forschungsinstitut Oberwolfach, 23rd – 29th October 2016
- visit to the Nesin Mathematics Village, Şirince, 10th – 17th September 2016
- British Logic Colloquium, Edinburgh, 6th – 8th September 2016
- Logic Colloquium, Leeds, 31st July – 6th August 2016
- Workshop on finite and pseudofinite structures, Leeds, 27th – 29th July 2016
- Geometry, Number Theory, and Logic, Oxford, 6th July 2016
- SEEMOD, Oxford, 5th – 6th July 2016
- ALaNT 4, Telč, 13th – 17th June 2016
- Special Session on Advances in Valuation Theory, Rutgers, 14th – 15th November 2015
research students
PhD- Piotr Szewczyk — co-supervised with Arno Fehm, TU Dresden.
- Paulo Andrés Soto Moreno.
- Paulo Andrés Soto Moreno. Inflators and diffeo-valued fields, 2022.
useful links

- journals
- seminars
- my pages on
- Université Paris Cité
- other institutions
- professional organisations
- online resources