Lancashire Yorkshire Model Theory Seminar

16th meeting of the model theorists in Leeds, Manchester and Preston, supported by the London Mathematical Society.

Arrival and coffee breaks will be in the Common Room on Level 9 of the School of Mathematics. Everyone is welcome to attend.

More details about the meeting and the series can be found on the LYMoTS page.

Timetable

10.30-11.00 Arrival, tea and coffee

11.00-12.00 Harry Schmidt (Manchester)
Mahler functions and Manin-Mumford on Gmn

I will report on work in progress on connections between algebraic independence of certain Mahler functions and the Manin-Mumford conjecture for the multiplicative group.

12.00-13.00 Tom Kirk (UCLan)
Definable Topological Dynamics in Metastable Theories

We consider a dynamical system where a definable group G acts on the space of complete types SG(M). Specifically, we will take G to be an affine algebraic group definable in a metastable theory and consider the minimal ideals of this action. We give a full description for the Minimal Flows, and Ellis Group, of SL2(C((t))), and note that this is not isomorphic to G/G00; providing a negative answer as to whether metastability is a suitable weakening of a since disproven conjecture of Newelski. Further, we discuss recent work in ACVF where G admits a stably dominated / fsg group decomposition (possibly with non-trivial intersection) and give a description of the Ellis Group in this setting.

Lunch break

14.30-15.30 Julia Wolf (Cambridge)
The structure of stable sets in finite abelian groups

We shall begin by explaining the idea behind the so-called "arithmetic regularity lemma" pioneered by Green, which is a group-theoretic analogue of Szemerédi's celebrated regularity lemma for graphs with wide-ranging applications. We will then describe recent joint work with Caroline Terry (University of Chicago), which shows that under the natural model-theoretic assumption of stability the conclusions of the arithmetic regularity lemma can be significantly strengthened, leading to a characterisation of stable subsets of finite abelian groups. In the latter part of the talk, we survey related work by various authors including Alon, Conant, Fox, Pillay, Sanders, Sisask, Terry and Zhao, further exploring this topic from both a combinatorial and a model-theoretic perspective.

Coffee break

16.00-17.00 Marcus Tressl  (Manchester)
On closed ordered differential fields

An ordered differential field is an ordered field K together with a derivation d : K→K; no interaction of d with the order is assumed. Michael Singer has shown that the existentially closed ordered differential fields (denoted CODF) are axiomatisable with quantifier elimination in the language of ordered differential rings. I will give an introduction to CODFs and report on some recent developments in the model theory of CODFs and its generalizations.

Pub and social dinner