The course offered great flexibility in fields of mathematics I had not yet seen

Bradley Ashley
Bradley Ashley
PhD student, University of Sheffield
Mathematics MSc
Bradley came to the University of Sheffield to do the Mathematics MSc, which prepared him for a PhD in pure mathematics.

What made you decide to do your masters degree?

I chose to do a masters degree as I thoroughly enjoyed my field of study, namely mathematics, but I felt there was so much more to learn. The course here at Sheffield offered a great flexibility of modules, allowing me to broaden my knowledge in fields of mathematics I had not yet seen. The most notable modules were Algebraic Topology and Directed Reading, where in the latter I studied category theory. These were fields I found an interest in whilst doing my undergraduate degree, and so I chose the MSc to find the opportunity to gain a much deeper understanding of these.

What did you enjoy most about your masters degree?

I’d certainly say what I enjoyed most was the challenge the degree presented. I had the opportunity to take on a range of new mathematics from functional analysis to special and general relativity in mathematical physics and come out the other side victorious. Amongst this, I thoroughly enjoyed the summer dissertation. The freedom of reading a topic I had a great interest in, and tackling problems within it, felt very rewarding.

What are you now studying for your PhD project?

I am now studying open problems within algebraic coarse geometry and model categories, fields with strong ties to category theory and algebraic topology. Specifically, I am trying to construct model structures following the recent development of generalised bornological coarse spaces, and in doing so gain a greater control over a coarse form of homotopy theory.

How did your masters degree help you secure your PhD?

This problem I am working on is one my supervisor has pondered for a while. It requires an extensive knowledge of category theory, as well as a good comprehension of the core ideas in algebraic topology due to the strong connections between topology and coarse geometry. My time on my MSc made me uniquely suited to this problem having studied both of these fields extensively in my selected modules.

What are you enjoying most about your PhD?

The thing I am enjoying most in my PhD is the freedom of exploration. I have the amazing opportunity to study and engage with the mathematics that interests me the most. I have even begun to construct some original results, an incredible feeling in itself. Furthermore, I’ve had the opportunity to visit some amazing new places by attending conferences, including an upcoming trip to Copenhagen, Denmark, in July 2022.

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