SEEMOD Workshop 6

12th June 2018, School of Mathematics, UEA, Norwich

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.


Speakers

Caroline Terry (Maryland), Gabriel Conant (Notre Dame), Alex Wilkie (Oxford), Zaniar Ghadernezhad (Imperial)

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.

Directions

This SEEMOD workshop is in the School of Mathematics at UEA. Directions to UEA can be found on this page and directions to the School of Mathematics can be found on this page. If you enter the building by the door indicated, go through the doors to the left and up the stairs to Level 1. At the top of the stairs there is a corridor just to your right, leading in the same direction. At the end of this corridor is room S1.20 where the lunch and the tea break will be. The talks will take place in Lecture room S3.05 which is two more flights of stairs up the same staircase.

Registration and funding

If you intend to come, please email Jonathan Kirby, by 31st May. We will provide a sandwich-style lunch so this is to have approximate numbers. Please also let me know of any particular dietary requirements.

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.

Provisional schedule

The first two talks will be aimed at a general pure mathematical audience. The third and fourth talks may be more aimed at model theorists.

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

Abstracts

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

Thanks

The workshop is supported by an LMS Scheme 3 grant and by the School of Mathematics at UEA.


School of Mathematics
University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, UK
Tel: +44(0)1603 591436
Email: jonathan.kirby _at_ uea.ac.uk