Harrison Greven
The University of Adelaide
I am a masters student in mathematics at the University of Adelaide, where I am supervised by Thomas Leistner. Broadly speaking I am most interested in differential geometry and mathematical physics, although I’m yet to find an area of math that hasn’t excited me.
My path to mathematics has had many detours. I originally studied computer science, then philosophy, before finding myself a student in mathematics. Although my initial intention in studying math had been to learn statistics, after a course in real analysis I quickly found myself enamoured with pure math. Due to this background, I am fascinated by the interplay between math and philosophy. Outside of math I enjoy running, am an avid basketball fan, and can often be found outdoors hiking, camping, and generally enjoying the sun.
Can you give me a quick rundown about the type of mathematics you are studying and its potential impacts for the broader community (think how you would explain your work and studies to others who don’t study maths)
I study conformal differential geometry. In differential geometry, we study manifolds: objects that when we zoom in to small patches appear to resemble Euclidean space closely enough that we can take our familiar calculus and transfer it onto the manifold. Think of how the earth is a sphere, but very close it appears flat. Taking a manifold, if we add a metric (way of smoothly measuring distances and angles), we end up with what is called a (semi)-Riemannian manifold. In conformal geometry, we forget about the notion of length and focus only on angles and the ratios of lengths between vectors on the manifold.
The other objects I look at are Einstein manifolds, which can be thought of as a nice generalisation of manifolds that have constant curvature. The goal of my research is to study the question: If we have two manifolds that are in some sense “conformally” the same and one of them is an Einstein manifold, under what conditions is the other also Einstein?
How did you get into mathematics/statistics/data science? Was there someone or something that inspired you to this field?
I am something of a latecomer to math. After completing a degree in computer science, I found myself a capable coder, but scarcely understood the math underpinning machine learning (the area I was interested in at the time). I decided to return to studying while working to fill that gap in my knowledge. Early on in these studies, a friend of a friend studying pure math at the time had mentioned that I might enjoy the area. So on a whim, I took classes in real analysis and group theory. I found the classes so engaging that I completely pivoted my studies towards “purer” math and never looked back.
You received a Travel Grant to attend AMSI Summer School 2025. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields? Do you think it was an advantage to attend the program in-person?
Without the travel grant, I think it very unlikely that I would have been able to attend in person. Although I’m sure learning online would still have been a fulfilling experience, the benefits of meeting and spending time with peers, as well as being able to engage directly with lecturers teaching fields they are specialists in was the highlight of the experience.
What was the most valuable part of the program for you?
As I mentioned above, I think the two most valuable parts of the program for me were the camaraderie built between all of us who travelled to attend the summer school, as well as the opportunity to learn subjects that I would otherwise not have been able to from world-class specialists in their field.
In the long-term, what do you think are the benefits of having attended Summer School?
The key thing I took away from the summer school is a much broader view of what mathematics looks like across Australia, both in and outside of academia.
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?
The Careers Day gave me a much better sense of the ways that one can still engage in mathematics outside of academia.
What advice would you give to someone who is considering applying for Summer School in 2026? Should they apply and why?
I would say absolutely go for it, you will meet some incredible people, and learn so much more in four weeks than you could imagine.
What are your current career ambitions in the mathematical sciences sector?
I make a conscious effort not to worry too much about my career in the long term, as such plans rarely ever come to fruition. In the short term, I plan on studying for a PhD after my masters (hopefully international), and seeing where I go from there.
How did connecting with the community at AMSI Summer School support your experience?
The community was certainly the highlight of my experience. It is what I will remember most fondly as I reflect on the summer school years from now.
Any other feedback/comments you would like to provide on the AMSI Travel Grant or AMSI Summer School 2025?
Thank you for the incredibly well-organised event, and the opportunity to attend via the travel grant.