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
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Denseness results in the theory of algebraic fields
(with Philip Dittmann and Arno Fehm).
Annals of Pure and Applied Logic, 172, 2021.
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A $p$-adic analogue of Siegel's theorem on sums of squares
(with Philip Dittmann and Arno Fehm).
Mathematische Nachrichten, 293:1434–1451, 2020.
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Approximation theorems for spaces of localities
(with Philip Dittmann and Arno Fehm).
Mathematische Zeitschrift, 296:1471–1499, 2020.
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Existentially generated subfields of large fields.
Journal of Algebra, 517C:78–94, 2019.
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Henselianity in the language of rings
(with Franziska Jahnke).
Annals of Pure and Applied Logic, 169(9):872–895, 2018.
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Characterizing diophantine henselian valuation rings and valuation ideals
(with Arno Fehm).
Proceedings of the London Mathematical Society, 115:293–322, 2017.
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Notes on extremal and tame valued fields
(with Franz-Viktor Kuhlmann).
Journal of Symbolic Logic, 81:400–416, 2016.
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The existential theory of equicharacteristic henselian valued fields
(with Arno Fehm).
Algebra & Number Theory, 10-3:665–683, 2016.
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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
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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]
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The model theory of Cohen rings
(with Franziska Jahnke).
Submitted, 2021.
arXiv:1904.08297 [math.LO]
notes
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Axiomatizing the existential theory of $\mathbb{F}_{p}(\!(t)\!)$
(with Philip Dittmann and Arno Fehm).
Manuscript, 2022.
arXiv:2205.05438 [math.LO]
-
An elementary geometric approach to linear prediction
(with Amery Gration).
Manuscript, 2021.
-
The mathematical structure of classical mechanics
(with Amery Gration).
Manuscript, 2019.
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One-dimensional $F$-definable sets in $F(\!(t)\!)$.
Manuscript, 2018.
arXiv:1503.05803 [math.LO]
-
Free homogeneous structures are generalised measurable.
Manuscript, 2016.
talks: slides, notes, and abstracts
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Shelah’s Conjecture and Johnson’s Theorem. Slides, ECIMT-2022, Münster, March 2022
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Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson]. Slides, Séminaire N. Bourbaki, IHP, Paris, November 2021
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Diophantine subsets and subfields of large fields.
Slides, SMTH2, June 2021
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Some existential theories of fields.
Slides, Illinois, April 2021
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Hilbert's Tenth Problem for Power Series.
Abstract, IMA Early Career Mathematicians' Conference, Lancaster, March 2019
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Research presentation.
Slides, Galway, Oct 2017.
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Viewing free homogeneous structures and bilinear forms as 'generalised measurable'.
Abstract, Logic Seminar, Manchester, Oct 2016.
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Measure and dimension in model theory.
Slides, British Logic Colloquium, Edinburgh, Sep 2016.
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Measure and dimension in model theory.
Abstract, British Logic Colloquium, Edinburgh, Sep 2016.
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Generalized measurable structures with the Tree Property.
Slides, Logic Colloquium, Leeds, Aug 2016.
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Generalized measurable structures with the Tree Property.
Abstract, Logic Colloquium, Leeds, Aug 2016.
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Dimension and dividing in generalised measurable structures.
Abstract, Workshop on Finite and Pseudofinite Structures, Leeds, Jul 2016.
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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.
- Special Session on Advances in Valuation Theory, Rutgers, 14th - 15th November 2015
- ALaNT 4, Telč, 13th - 17th June 2016
- SEEMOD, Oxford, 5th - 6th July 2016
- Geometry, Number Theory, and Logic, Oxford, 6th July 2016
- Workshop on finite and pseudofinite structures, Leeds, 27th - 29th July 2016
- Logic Colloquium, Leeds, 31st July - 6th August 2016
- British Logic Colloquium, Edinburgh, 6th - 8th September 2016
- visit to the Nesin Mathematics Village, Şirince, 10th - 17th September 2016
- Mathematisches Forschungsinstitut Oberwolfach, 23rd - 29th October 2016
- LYMoTS in Manchester, 30th May 2017
- Model Theory in Wrocław, Wrocław, 30th June - 2nd July 2017
- Model Theory in Będlewo, Będlewo, 2nd - 8th July 2017
- New Directions in the Model Theory of Valued Fields , Preston, 4th August 2017
- Homogeneous structures, permutation groups, and connections to set theory, Leeds, 10th - 12th September 2017
- Diophantine problems, Manchester, 11th - 15th September 2017
- LYMoTS, Preston, 21st October 2017
- Model Theory, Combinatorics and Valued Fields, Institut Henri Poincaré, Paris, 18th February - 7th April 2018
- Model Theory of Valued Fields, Paris, 5th March - 9th March 2018
- Model Theory and Applications, Paris, 26th March - 30th March 2018
- Model Theory of Finite and Pseudofinite Structures, Leeds, 9th - 11th April 2018
- Workshop on effectivity and ineffectivity for unlikely intersections , Manchester, 24th - 27th July 2018
- Model-theoretic methods in number theory and algebraic differential equations, Manchester, 3rd - 5th August 2018
- EWM General Meeting 2018, Graz, 3rd - 7th September 2018
- From permutation groups to model theory , ICMS, Edinburgh, 17th - 20th September 2018
- Neostability Theory, BIRS-CMO Workshop, Casa Matemática, 14th October - 19th October 2018
- Definability and decidability problems in number theory, American Institute of Mathematics, San Jose, California, 6th May - 10th May 2019
- Model Theory of Valued Fields and Applications, Münster, 10th June - 14th June 2019
- ALGAR, Antwerp, 6th -- 10th of July 2020
- Decidability, definability and computability in number theory, MSRI, Berkeley, 17th August -- 18th December 2020
- Short Model Theory Huddle 2, 16th – 18th June 2021
- ASL North American Annual Meeting, Notre Dame, South Bend, 22nd – 25th June 2021
online tools
useful links