## Autumn 2018

The colloquia (unless otherwise stated) will take place on **Tuesdays at 3.00pm in ****Room B15 in the Darwin Building**. See the map for further details. There will be a small reception afterwards in Mathematics Room 502 (25 Gordon Street - see the map). If you require any more information on the Departmental Colloquia please contact Prof Dima Vassiliev e-mail: d.vassiliev AT ucl.ac.uk or tel: 020-7679-2442.

## 16 October 2018

### Speaker: Dr Julia Wolf (University of Cambridge)

##### Title: The structure of stable sets: from additive number theory to model theory

**Abstract**

A long-standing open problem in additive number theory is the following: how dense does a set of integers have to be before it is guaranteed to contain a non-trivial arithmetic progression of length 3?

In the first half of this talk we shall survey recent progress on this problem, and the techniques used to solve it and related questions about additive structures in finite abelian groups. In particular, we shall explain 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.

In the second half of the talk we shall 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.

This talk will not assume any particular background knowledge, and should be accessible to postgraduate students across mathematics.