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
  1. Sylvy Anscombe. Definability in Henselian Fields. DPhil Thesis, University of Oxford, 2013. Supervised by Dr Jochen Koenigsmann.
published
  1. 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.
  2. Sylvy Anscombe and Arno Fehm. The existential theory of equicharacteristic henselian valued fields. Algebra & Number Theory, 10-3:665–683, 2016.
  3. Sylvy Anscombe and Franz-Viktor Kuhlmann. Notes on extremal and tame valued fields. Journal of Symbolic Logic, 81:400–416, 2016.
  4. Sylvy Anscombe and Arno Fehm. Characterizing diophantine henselian valuation rings and valuation ideals. Proceedings of the London Mathematical Society, 115:293–322, 2017.
  5. Sylvy Anscombe and Franziska Jahnke. Henselianity in the language of rings. Annals of Pure and Applied Logic, 169(9):872–895, 2018.
  6. Sylvy Anscombe. Existentially generated subfields of large fields. Journal of Algebra, 517C:78–94, 2019.
  7. Sylvy Anscombe, Philip Dittmann, and Arno Fehm. Approximation theorems for spaces of localities. Mathematische Zeitschrift, 2020.
  8. Sylvy Anscombe, Philip Dittmann, and Arno Fehm. A $p$-adic analogue of Siegel's theorem on sums of squares. Mathematische Nachrichten, 2020.
accepted
  1. Sylvy Anscombe and Franziska Jahnke. The model theory of Cohen rings. Accepted, 2019. ( arXiv:1904.08297 [math.LO] )
submitted
  1. Sylvy Anscombe, Philip Dittmann, and Arno Fehm. Denseness results in the theory of algebraic fields. Submitted, 2020. ( arXiv:1909.12188 [math.LO] )
notes
  1. Sylvy Anscombe and Amery Gration. The mathematical structure of classical mechanics. Manuscript, 2019.
  2. Sylvy Anscombe. One-dimensional $F$-definable sets in $F((t))$. Manuscript, 2018. ( arXiv:1503.05803 [math.LO] )
  3. Sylvy Anscombe. Free homogeneous structures are generalised measurable. Manuscript, 2016.
  4. 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.
  1. Questions of definability in fields of formal power series. Talk, Leeds, 2010.
  2. Existential definability in t-henselian fields. Poster, Leeds, 2011.
  3. Aspects of definability in henselian fields of positive characteristic. Talk, Konstanz, 2011.
  4. $F$-definability in $F((t))$. Talk, Oxford, 2012.
  5. Definable henselian valuations. Poster, Edinburgh, 2014.
  6. Free homogeneous structures are generalised measurable. Talk, Durham, 2015.
  7. Characterizing Diophantine henselian valuation rings and valuation ideals. Talk, AMS Rutgers, Nov 2015.
  8. Dimension and dividing in generalised measurable structures. Abstract, Workshop on Finite and Pseudofinite Structures, Leeds, Jul 2016.
  9. Generalized measurable structures with the Tree Property. Abstract, Logic Colloquium, Leeds, Aug 2016.
  10. Generalized measurable structures with the Tree Property. Slides, Logic Colloquium, Leeds, Aug 2016.
  11. Measure and dimension in model theory. Abstract, British Logic Colloquium, Edinburgh, Sep 2016.
  12. Measure and dimension in model theory. Slides, British Logic Colloquium, Edinburgh, Sep 2016.
  13. Viewing free homogeneous structures and bilinear forms as 'generalised measurable'. Abstract, Logic Seminar, Manchester, Oct 2016.
  14. Research presentation. Slides, Galway, Oct 2017.
  15. 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.

online tools

useful links