Shurui Cao
The University of Sydney
Super Cao completed a Bachelor of Science in Applied Statistics in China in 2021. In 2024, she obtained a Master of Mathematical Sciences at the University of Sydney. Her master’s thesis focused on webs for SO(3) and the Four Colour Theorem. From 2025 to the present, she has been a PhD student in Pure Mathematics at the University of Sydney, working in representation theory and diagrammatic algebra.
Give me a quick overview of the type of mathematics you are studying, and/or the aims of your research and its potential applications/outcomes
I study pure mathematics, mainly in areas like representation theory, category theory, and diagrammatic algebra. A big part of my work is about using diagrams to understand abstract algebraic structures more clearly. What I really like about this area is that it creates a link between visual ideas and very abstract algebraic theory, so pictures are not just illustrations but part of the mathematics itself. My master’s thesis was on webs for SO(3) and the Four Colour Theorem, and now in my PhD I am continuing to work in related areas. Although this is very theoretical, one of the nice things about this kind of maths is that it helps build better ways of organising and understanding complex ideas, and those ways of thinking often end up being useful well beyond mathematics itself.
How did you get into the mathematical sciences? Was there someone or something that inspired you to this field?
I had always liked mathematics, but during my master’s I realised I really enjoyed doing research. Working with my supervisor, Associate Professor Daniel Tubbenhauer, helped me see the fun and satisfaction in exploring ideas more deeply. They are an outstanding mathematician, and while I was learning to enjoy mathematics more, I also started to hope that one day I could become someone like them. They have been a real role model for me, and that was a big reason I decided to continue into a PhD.
You received a grant to attend AMSI Summer School. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields?
It was very important. The grant made it much easier for me to attend in person, and that really changed the whole experience. Being there meant I could fully take part in the lectures, activities, and conversations outside class, and I also got to meet many other students who are studying maths. I think attending in person was a big advantage.
What was the most valuable part of the program for you?
For me, the most valuable part was meeting people. It was nice to spend time with other students who are interested in mathematics, and also to talk with academics in a more relaxed setting.
In the long-term, what do you think are the benefits of having attended Summer School?
I think the long-term benefit is definitely the connections. It was a great chance to get to know people in the mathematical community, and I think those connections can be very valuable later on, both academically and personally.
Summer School included a special Careers Day program which aims to help give students an idea of the kinds of career paths available to maths graduates in industry and private sector research areas. Do you feel better equipped to explore career options in the mathematical sciences after attending AMSI Summer School?
Yes, I do. The Careers Day gave me a broader picture of what people can do with a maths background, especially outside the usual academic path. It was helpful to hear about different roles and industries that I had not really thought about before.
What advice would you give to someone who is considering applying for Summer School in 2027? Should they apply and why?
I would definitely encourage them to apply. It is a great opportunity to study something interesting and challenging, meet other students, and be part of a wider maths community.
What are your current career ambitions in the mathematical sciences sector?
At the moment, I would like to continue in academia and hopefully work as a researcher in pure mathematics.
How did connecting with the community at AMSI Summer School support your experience?
Connecting with the community at AMSI Summer School was a real highlight for me. Being around like-minded people who understand both the excitement of a good idea and the challenge of a difficult problem made the whole experience much more enjoyable and motivating. It also made Summer School feel much less intimidating, because I felt like I was part of a community rather than just attending on my own.
Any other feedback/comments you would like to provide on the AMSI Travel Grant or AMSI Summer School 2026?
I am very grateful for the support. The grant made it possible for me to attend in person, and Summer School was a really valuable experience for me. If you’re thinking about applying, go for it.