Symposium on the Model Theory of Fields
University of Manchester · 6 July 2026
This is an afternoon meeting dedicated to the model theory of fields. It will take place on Monday 6 July 2026 at the University of Manchester. The meeting is funded by an LMS Celebrating New Appointments grant and the local department of mathematics.
All are welcome to attend. Please register (free of charge) to help estimate numbers. There is a small amount of travel support available for students; if you wish to be considered for this, indicate this on the form and register by 14 June. For any queries, contact the organiser at [email protected].
You may also be interested in the separate Manchester Existential Closedness Workshop, which takes place Tuesday to Friday of the same week.
Schedule
All talks are in the Alan Turing Building, room G.207.
1 pm · Franziska Jahnke (Universität Münster) · AKE principles for henselian fields in mixed characteristic
The celebrated Ax–Kochen/Ershov Theorem allows us to reduce model-theoretic questions about a henselian valued field of residue characteristic 0 to corresponding questions about the value group and residue field. In this talk, I will start by introducing the basic definitions (including ‘valued field’ and ‘henselianity’). I will then discuss a number of results in mixed characteristic, from the unramified setting (already implicit in the work of Ax and Kochen) to current developments regarding henselian roughly deeply ramified fields.
2 pm · Coffee break
2.30 pm · Dugald Macpherson (University of Leeds) · Simple groups definable in henselian fields
I will discuss joint work with Gismatullin and Halupczok. We describe groups G definable in characteristic 0 henselian valued fields (with G living in the valued field sort) which are ‘definably almost simple’; that is, G has no proper infinite definable normal subgroup. Our actual context is broader, including the ‘1-h-minimal’ framework developed by Cluckers, Halupczok, Rideau-Kikuchi, and Vermeulen, which allows analytic structure such as that introduced by Denef and van den Dries, as well as examples arising from power bounded o-minimal expansions of a real closed field. Our context also includes, under a linearity assumption on G, the case when K is a ‘pure’ algebraically closed valued field of characteristic p. The main theorem is that there is a K-isotropic simple algebraic group H defined over K such that G is very close to H(K). In certain cases this combines with work of Halevi, Hasson and Peterzil to give strong information on definably simple groups interpretable in valued fields.
3.30 pm · Philip Dittmann (University of Manchester) · Asymptotic theories of fields
What are the properties of a ‘random’ or ‘generic’ field? I will discuss precise versions of this question (and appropriate answers) in two settings, namely for the class of algebraic extensions of ℚ and for the class of completions (in the sense of valuation theory) of a function field (both joint work with Fehm). It turns out that a central role in both cases is played by pseudo-algebraically closed fields, a beautiful class originating in work of Ax on the model theory of finite fields. I will also highlight some similarities and differences with the more well-known model-theoretic setting of random graphs and the 0-1-law.