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
thesis

Sylvy Anscombe.
Definability in Henselian Fields.
DPhil Thesis, University of Oxford, 2013.
Supervised by Dr Jochen Koenigsmann.
published

Sylvy Anscombe and Jochen Koenigsmann.
An existential $\emptyset$definition of $\mathbb{F}_{q}[[t]]$ in $\mathbb{F}_{q}((t))$.
Journal of Symbolic Logic, 79:1336–1343, 2014.

Sylvy Anscombe and Arno Fehm.
The existential theory of equicharacteristic henselian valued fields.
Algebra & Number Theory, 103:665–683, 2016.

Sylvy Anscombe and FranzViktor Kuhlmann.
Notes on extremal and tame valued fields.
Journal of Symbolic Logic, 81:400–416, 2016.

Sylvy Anscombe and Arno Fehm.
Characterizing diophantine henselian valuation rings and valuation ideals.
Proceedings of the London Mathematical Society, 115:293–322, 2017.

Sylvy Anscombe and Franziska Jahnke.
Henselianity in the language of rings.
Annals of Pure and Applied Logic, 169(9):872–895, 2018.

Sylvy Anscombe.
Existentially generated subfields of large fields.
Journal of Algebra, 517C:78–94, 2019.

Sylvy Anscombe, Philip Dittmann, and Arno Fehm.
Approximation theorems for spaces of localities.
Mathematische Zeitschrift, 2020.

Sylvy Anscombe, Philip Dittmann, and Arno Fehm.
A $p$adic analogue of Siegel's theorem on sums of squares.
Mathematische Nachrichten, 293:1434–1451, 2020.
accepted

Sylvy Anscombe and Franziska Jahnke.
The model theory of Cohen rings.
Accepted, 2019.
( arXiv:1904.08297 [math.LO] )
submitted

Sylvy Anscombe, Philip Dittmann, and Arno Fehm.
Denseness results in the theory of algebraic fields.
Submitted, 2020.
( arXiv:1909.12188 [math.LO] )
notes

Sylvy Anscombe and Amery Gration.
The mathematical structure of classical mechanics.
Manuscript, 2019.

Sylvy Anscombe.
Onedimensional $F$definable sets in $F((t))$.
Manuscript, 2018.
( arXiv:1503.05803 [math.LO] )

Sylvy Anscombe.
Free homogeneous structures are generalised measurable.
Manuscript, 2016.

Sylvy Anscombe and Franziska Jahnke.
Characterizing NIP henselian fields.
Manuscript, 2019.
( arXiv:1911.00309 [math.LO] )
talks and meetings
slides, notes, abstracts, and posters
Here are various slides, notes, and abstracts of talks, as well as one or two posters.

Free homogeneous structures are generalised measurable.
Talk, Durham, 2015.

Characterizing Diophantine henselian valuation rings and valuation ideals.
Talk, AMS Rutgers, Nov 2015.

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

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

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

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

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

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

Research presentation.
Slides, Galway, Oct 2017.

Hilbert's Tenth Problem for Power Series.
Abstract, IMA Early Career Mathematicians' Conference, Lancaster, March 2019
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
 Modeltheoretic 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, BIRSCMO 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
online tools
useful links