What is it like to study geometry, algebra, and topology in the MAST programme?
Geometry, Algebra, and Topology are pure mathematics and essential to modern mathematical research. In the MAST programme, we study topics such as Riemannian geometry, algebraic topology, and differential geometry, and it’s quite common for people in other fields to need their knowledge – for example, in understanding general relativity. Through these courses, we gain see the evolution of abstract mathematical thinking, and you can gain tools to approach geometric concepts in a contemporary way.
Who are the studies suitable for?
The only real criterion is that you’re interested in maths – if you have that, it is typically enough. I've noticed that when students are genuinely curious about new concepts and ideas, they develop their own study skills, start finding materials, and gradually get the hang of it. This creates a positive cycle for learning. I wouldn’t say you need master every detail of your bachelor’s studies before joining MAST as well, as catching up is entirely possible if you're willing to invest the time to understand what’s going on.
What kind of career paths does studies in geometry, algebra, and topology open up?
The main pathway is toward graduate studies. But pure maths also has an interesting feature: it’s rarely wasted knowledge. For example, a former PhD student of mine, who specialized in mappings, gave a talk at this university about training large language models.
During your master’s studies, if you're interested in pure mathematics, you can always combine it with knowledge from other areas. Right now, AI and computer science are popular choices, but fields such as statistics and mathematical finance are also possible options. If you're drawn to mathematical research, we also have large groups in analysis and mathematical physics.
I want to emphasize the overlap between subjects as well, because people sometimes believe you must strictly commit to one path. This is not the case – it is always easy to learn from another neighboring field.
What do you find most interesting about this field of research? For instance, what are your favorite courses?
I’d say I have two favorite courses. One is Topology II, which is an interesting course in the sense that, at first, it feels a little bit dusty—like you take out an old book, blow the dust off the cover, and think, "Isn't this something people did in the 1920s, '30s, '40s?" But, when you learn the subject, you realize how many modern applications actually have their foundations in this material, and you can see how ideas have developed over time. Many students find the course exciting because they encounter phenomena they never expected, and it also prepares them for more abstract mathematics in future studies.
The second course I really enjoy is de Rham cohomology. It’s close to my own research because it brings together differential geometry and algebraic topology. Through it, you start to see connections—like how phenomena you encountered in complex analysis or electromagnetism actually come together in a unified, topological framework. That’s what makes it so fascinating.