# David Bradley-Williams

**Course**: PhD Pure Mathematics

## How have you found the PhD so far?

I have found it enjoyable and it's definitely been a good academic experience.

## Where did you do your undergraduate degree?

I did an MMath at York.

## What made you decide to do a PhD?

There was an interesting sounding project here and I asked my lecturers at York what they knew about this department and I decided that I wanted to study mathematical Logic as an interesting area of mathematics but I hadn't had much experience of it at undergraduate level because it's not something which is studied everywhere. The lecturers who knew about the group here in Mathematical Logic highly recommended it and so when I came here to visit, I had some very inspiring conversations with the professors. So I spoke to my supervisor John Truss before I came. The project sounded interesting with lots of different aspects to it. It involved algebra and combinatorics and it had this edgy mathematical logic to it which was quite exciting to me.

## What is your area of research?

I am in the Pure Mathematics research section and quite a large part of that is made up of the Mathematical Logic research group. What's quite unique about Leeds is that the mathematical logic is very diverse. Most places which do it in the UK just pick one or two aspects of mathematical logic but in Leeds we have all three areas; model theory, proof theory and computability theory. I am studying in the model theory section, studying how we can take infinite limits of mathematical structures and get a new structure and also construct a new infinite structure. The important thing is how you take those limits and what I quite like about it is how creative it is because there's not many people who have spent that much time thinking about these mathematical structures. So, I get to draw lots of pictures of trees and then I take limits down other trees and then end up with a new structure. What's interesting is that you get to a structure which you can't draw but you can draw small segments of it and so you feel like you kind of have a graph and you can see the sides of the structure you are looking it. I like that it's on the realms of imagination.

## Have you had any thoughts about what you want to do next? Do you think that you will stay in academia?

It's a hard bet to call but yes I am interested in staying in academia. I do a lot of teaching and so I already play a dual role where I teach sometimes and I do research. I really enjoy the teaching. I enjoy explaining things to people, even though sometimes it takes quite a while. I enjoy coming up with new ways to explain the same concept. It's very satisfying when someone finally gets it.

## How have you found the academic staff?

I find them very approachable. I actually have two supervisors who I see regularly and I can see other members of staff and other post-docs etc. In terms of facilities I think that it's good that we all have a good choice of office space. We all get a desk and we can select where that is. There are quieter offices or more social ones and there's the library of course as well. So, I have everything I need.

## What kind of challenges would you say you've had during your PhD?

It's like learning a lot of hard concepts and it's trying to get your head around them all. There's been times when you just need to work on your own for a while and get the books you need and get through them. Managing time is also challenging. There's a lot of things going on and so sometimes it's quite challenging to manage your time and making sure you are in the right frame of mind.

## What kind of skills have you enhanced?

Definitely my communication of mathematics, managing my time which has improved a lot and being able to get through and summarise information quite quickly.

## Any advice for someone thinking of doing a PhD?

Yes I would say research the department, look at what the members of staff have done and definitely talk to them and interview them as to what they are doing and what they might have in mind for your study with them. Make sure you are happy with the University and the place you are looking at.