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

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 FranzViktor Kuhlmann).
Journal of Symbolic Logic, 81:400–416, 2016.

The existential theory of equicharacteristic henselian valued fields
(with Arno Fehm).
Algebra & Number Theory, 103:665–683, 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

Axiomatizing the existential theory of $\mathbb{F}_{q}(\!(t)\!)$
(with Philip Dittmann and Arno Fehm).
Submitted, 2022.
arXiv:2205.05438 [math.LO]

The model theory of Cohen rings
(with Franziska Jahnke).
Submitted, 2021.
arXiv:1904.08297 [math.LO]
notes

Characterizing NIP henselian fields
(with Franziska Jahnke).
Manuscript, 2022.
arXiv:1911.00309 [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.

Onedimensional $F$definable sets in $F(\!(t)\!)$.
Manuscript, 2018.
arXiv:1503.05803 [math.LO]
talks: slides, notes, and abstracts

Henselian discretely valued fields and existential AKE principles. Slides, Logic Colloquium 2022, Reykjavik, June 2022

Shelah’s Conjecture and Johnson’s Theorem. Slides, ECIMT2022, Münster, March 2022

Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson]. Slides, 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, Oct 2017.

Viewing free homogeneous structures and bilinear forms as 'generalised measurable'.
Abstract, Logic Seminar, Manchester, Oct 2016.

Measure and dimension in model theory.
Slides, British Logic Colloquium, Edinburgh, Sep 2016.

Measure and dimension in model theory.
Abstract, British Logic Colloquium, Edinburgh, Sep 2016.

Generalized measurable structures with the Tree Property.
Slides, Logic Colloquium, Leeds, Aug 2016.

Generalized measurable structures with the Tree Property.
Abstract, Logic Colloquium, Leeds, Aug 2016.

Dimension and dividing in generalised measurable structures.
Abstract, Workshop on Finite and Pseudofinite Structures, Leeds, Jul 2016.

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.
 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, MSRI, Berkeley, 17th August  18th December 2020
 ALGAR, 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, BIRSCMO 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
 Modeltheoretic 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, Paris, 26th March  30th March 2018
 Model Theory of Valued Fields, 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
online tools
useful links