7 years ago, also in Oxford, Sylvy Anscombe and I asked this question, which is part of the general effort to try and understand the model theory of henselian valued fields through dividing lines. In 2024, Sylvy Anscombe and Franziska Jahnke completely classified NIP henselian valued fields. Their methods can be extended, with the help of works of Chernikov, Kaplan and Simon and of Kuhlmann and Rzepka, to NTP2 henselian valued fields, obtaining the following:

• if a henselian valued field is NTP2, then it is semitame and its residue field is NTP2;
• if a henselian valued field is separably algebraically maximal Kaplansky and its residue field is NTP2, then it is NTP2.

This covers a large class of fields, but there is still a gap. Notably, Fp((Q)) is in the middle: it is semitame but not Kaplansky.

To answer this question, we studied so called tame henselian fields with finite residue field, and derived quantifier elimination results, namely, we prove that any formula in the language of valued fields reduces to a formula of the form (∃y f(x,y)=0) ∧ φ(v(x)) ∧ ψ(res(x)), where φ and ψ are formulas in the language of ordered groups and of rings, respectively.

In Fp((Q)) specifically, the valuation ring itself is definable with a diophantine formula (ie of the form ∃y f(x,y)=0), reducing further our quantifier elimination result.

Finally, a large chunk of these formulas are known to be NTP2: when f(x,y) is additive in y, the formula ∃y f(x,y)=z is NTP2 (with respect to x and z). Unfortunately, that does not cover all formulas, so the answer to the titular question is still unknown.

Many biological reaction-diffusion systems are multiscale: in some regions molecules are abundant, while in others only a few are present. Where numbers are low, intrinsic noise is significant, and a stochastic model such as Gillespie's algorithm is needed to capture the fluctuations and rare events that shape the behaviour. Where numbers are high, this approach is too expensive, and a continuum PDE is sufficient.

Hybrid methods aim to apply each description where it is appropriate, but most require an explicit spatial interface separating the stochastic and deterministic regions. The Spatial Regime Conversion Method (SRCM) avoids this. Each region of space carries both discrete particles and continuous PDE mass, and moves mass between them through conversion events as local concentrations change. The method therefore adapts automatically as the system evolves, resolving stochastic detail wherever intrinsic noise matters and using the cheaper PDE everywhere else, with no fixed interface to track.

In this talk I introduce the method and show how it works, then illustrate it on examples including epidemic spread and a Turing instability driven by noise, where it reproduces the stochastic behaviour that a continuum model alone cannot capture.