SEEMOD is the South and East of England Model Theory Network, which has meetings at UEA, in London, and in Oxford. It is supported by a Scheme 3 grant from the London Mathematical Society. The co-ordinator is Jonathan Kirby.
Caroline's and Gabriel's work is around Szemeredi's regularity lemma and
generalisations which is a branch of Combinatorics.
Alex has agreed to give a survey of the Pila-Wilkie theorem about counting
rational points on analytic sets, which has become very useful in number
theory.
Zaniar works around amalgamation constructions and their automorphism groups.
Some money is available, particularly for PhD students, for travel expenses and to cover additional caring costs (e.g. childcare). Please also contact Jonathan Kirby if you would like to claim expenses.
12-1 arrival and lunch in room S1.20
1pm-1:50 Alex Wilkie in room S3.05
1:50-2:40 Caroline Terry
2:40-3:30 tea and discussions in S1.20
3:30-4:20 Gabriel Conant in S3.05
4:20-5:10 Zaniar Ghadernezhad
followed by drinks/dinner in Norwich city centre
Alex Wilkie
Title: The rational points of a definable set
This is the title of a paper by Jonathan Pila and me that appeared in the Duke Journal in 2006 (Vol. 133, No. 3), the main theorem of which has found many diophantine applications over the last ten years or so. My aims in this talk are to explain the statement of this theorem, to give a very rough idea of the proof and to present various improvements that have appeared since.
Caroline Terry
Title: A stable arithmetic regularity lemma in finite abelian groups
The arithmetic regularity lemma for F_p^n (first proved by Green in 2005) states that given a subset A of F_p^n, there exists a subgroup H of F_p^n of bounded index such that A is Fourier-uniform with respect to almost all cosets of H. In general, the growth of the index of H is required to be of tower type depending on the degree of uniformity, and must also allow for a small number of non-uniform elements. Previously, in joint work with Wolf, we showed that under a natural stability theoretic assumption, the bad bounds and non-uniform elements are not necessary. In this talk, we present results extending these results to stable subsets of arbitrary finite abelian groups. This is joint work with Julia Wolf.
Gabriel Conant
Title: VC-dimension in groups
I will discuss recent work on the structure of VC-sets in groups, i.e. subsets of groups whose family of left translates has finite VC-dimension. Many tools from model theory and additive combinatorics can be adapted for ``locally amenable" VC-sets, leading to stronger structural results than for arbitrary sets in (amenable) groups. These structure results can be applied to questions concerning sumset phenomena for VC-sets in infinite groups, as well as arithmetic regularity for VC-sets in finite groups.
Zaniar Ghadernezhad