George Feng
The University of Sydney
George Feng is an Honours student in Pure Mathematics at the University of Sydney, supervised by Professor John Voight. His current research focuses on matrix groups, Cayley graphs, and related questions in algebra and number theory, combining theoretical ideas with computational methods.
George has previously undertaken research projects across several areas of mathematics and physics, including the spectra of finite matrix groups, symmetric functions, Hurwitz numbers, post-quantum cryptography, condensed matter physics, and asteroseismology. These experiences have developed his interest in exploring connections between different areas of mathematics and using computation to investigate theoretical problems.
Alongside his studies, George has been involved in student leadership and international student representation. He hopes to continue pursuing mathematical research and to develop a deeper understanding of algebra, number theory, and their connections with other areas of mathematics.
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 (how you would explain your work and studies to friends who don’t study maths?)
My research looks at groups generated by two matrices and the graphs that arise when these matrices are reduced modulo prime numbers. I am particularly interested in how the shortest cycles in these graphs grow, combining ideas from algebra, number theory, graph theory and computation.
How did you get into the mathematical sciences? Was there someone or something that inspired you to this field?
I became interested in mathematics through the satisfaction of understanding why something is true, rather than only obtaining an answer. As I studied more advanced topics, I became especially interested in abstract algebra and the way seemingly simple objects can reveal surprisingly rich and beautiful structures.
Winter School is designed to give students a deeper understanding of their area of research and expose them to others working in different fields/industries. Tell me about your Winter School experience. What was the most valuable part of the program for you?
Winter School was a valuable chance to step outside my usual research focus and engage with unfamiliar mathematics. I particularly enjoyed learning from researchers with different perspectives and discussing ideas with other students. Those conversations made the program feel much more interactive than simply attending a series of lectures.
What was your main take away/s from AMSI Winter School? Something you learnt? A connection you made? Do you have new ideas for your work/research or see it in a new light?
One important takeaway was that difficult research problems often require ideas from several areas of mathematics. This relates closely to my project, which combines group theory, graph theory, number theory and computation. The program encouraged me to be more open to techniques outside my immediate research area.
What surprised you most about Winter School?
I was surprised by how valuable the informal parts of the program were. Conversations between lectures often helped me understand ideas that initially seemed difficult. They also showed me that many other students experience similar challenges when learning advanced mathematics, which made discussions much easier and more enjoyable.
What is the importance of in-person communication at an event like Winter School?
In-person communication makes it much easier to ask spontaneous questions, clarify difficult ideas and develop conversations beyond the formal lectures. Informal discussions over breaks or meals can be especially valuable, because they often lead to new connections, explanations and research ideas that would be harder to create online.
You received a grant to attend AMSI Winter School. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields?
The travel grant was very important in making attendance practical and allowing me to participate fully without the financial pressure of travel costs. It also made it possible to stay engaged throughout the program and spend time meeting other students and researchers working in related areas.
What advice would you give to someone who is considering applying for Winter School? How would you describe the conference to them?
I would say apply and be willing to engage with topics outside your immediate interests. You do not need to understand everything. Ask questions, talk to other participants and attend as much as possible. Some of the most useful ideas may come from lectures or conversations you did not expect.
Tell us about a moment that changed a preconceived idea about your field?
Working on my current project changed my view of the relationship between pure mathematics and computation. I had thought of abstract algebra as mainly theoretical, but computing examples of Cayley graphs can reveal patterns and suggest questions that then motivate rigorous proofs and deeper theoretical understanding.
Where do you want the mathematical sciences to take you? Where do you see yourself in five, ten years time?
I would like to continue pursuing mathematical research and develop the independence needed to work on challenging open problems. In the longer term, I hope to contribute new mathematics, collaborate with researchers from different backgrounds and remain involved in both learning and communicating mathematics.
Any other feedback/comments you would like to provide on the travel grant or AMSI Winter School?
I appreciated having the opportunity to attend Winter School and meet students and researchers from across the mathematical sciences. The combination of lectures, informal discussion and financial support made the experience particularly valuable. I am grateful that the travel grant helped make full participation possible.