## 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.

**Upcoming Departmental Colloquiuia**

## Spring 2019

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.

## 05 February 2019

### Speaker: Prof Piers Bursill-Hall (University of Cambridge)

##### Title: EuclId's *Elements*: this is the answer to *what *question?

**Abstract**

Well, we all know the answer to that: because axiomatising geometry puts it on a sound and certain footing; that's a good thing, and allows us to build the rest of mathematics on a sure and certain basis. And once you have read the *Elements *(not that you have), you might almost believe this. But until you know that axiomatics does this, you wouldn't know that there is a sure and certain foundation to geometry out there. How on earth did Euclid come up with the idea of axiomatising geometry in the first place? It is not as if axiomatising things is something human beings do naturally ... so there must be some story that leads up to Euclid's axiomatisation (and it wasn't a system to teach geometry, either). So ... why? How did ancient Greek thinking about proof develop in the couple of centuries before Euclid?