Paawan Jethva
The University of Adelaide
Paawan Jethva is a commencing Master of Philosophy (MPhil) student at the University of Adelaide, where he previously obtained a Bachelor of Mathematical Sciences (Advanced) in 2023.
In 2022, Paawan completed a summer research project on numerical methods for improved tsunami modelling. It involved numerically solving non-linear partial differential equations and investigating how to extend them to include dispersive effects. The same year, he participated in the Mathematical Contest in Modelling (MCM) in a team with two other students. Their chosen problem was designing an optimal trading strategy for Bitcoin and gold, which involved developing a price forecasting model and a portfolio rebalancing model to optimise future returns given past pricing data. Their team was designated a meritorious winner. In 2023, he received an AMSI Summer Research Scholarship for which he explored the Euler characteristics of dessins d’enfants—especially their behaviour under morphisms.
Paawan takes interest in many different areas of mathematics. Although, his MPhil research is concerned with algebraic topology and differential geometry, especially in the context of 4-manifolds.
1. 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)
The field I am studying in my MPhil is called algebraic topology. Topology—coming from Greek topos (meaning position) and logos (meaning study)—is the ‘study of positions.’ It is the geometry we get when we forget about proportions and only consider relative positions. However, often geometric problems are difficult. Algebraic topology aims to convert these geometric problems to algebraic ones, as algebra is better understood and often easier.
An interesting class of topological spaces (points with relative positional information) are manifolds which are spaces that locally look like flat (Euclidean) space and hence allow us to use the wide array of Euclidean techniques developed over centuries. For example, standing on the Earth, the horizon seems quite flat. It is not until we go much higher that the horizon appears to curve. Indeed, a sphere is a 2-dimensional manifold (or simply 2-manifold).
I am particularly interested in 4-manifolds as they are less understood than manifolds of other dimensions and exhibit peculiar behaviour. Results often have implications in physics since general relativity models spacetime as a 4-manifold.
2. How did you get into mathematics/statistics/data science? Was there someone or something that inspired you to this field?
As a child, I was always curious about everything and asked many questions. Getting interested in maths and science was a natural course as they help me answer some of those questions. Increased accessibility to the internet meant that I was perpetually watching and reading about maths and science, which retained my interest. I think I have been fortunate to have many passionate and competent teachers throughout my education who helped persevere through otherwise difficult concepts at the time and prevented me from being deterred.
Nonetheless, I had never thought about a career in mathematics. I was resolved to study aviation. But after an uninspiring aviation course in year 12, I decided to take a safe option and complete a maths degree. This period of my undergrad reignited my childhood passion for mathematics—so much so that I am now pursuing a higher degree by research in the field.
3. You received a Travel Grant to attend AMSI Summer School 2024. 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?
The opportunity to meet like-minded people was my primary motivation in attending AMSI Summer School. (The fascinating course on hyperbolic knot theory was obviously a bonus.) As such, it was imperative for me to attend in person. Attending talks, discussing each other’s research interests, and the sense of community I felt living on campus was enjoyable to me.
4. What was the most valuable part of the program for you?
For me, the most valuable part of the program was being able to participate in the community that developed on campus.
5. In the long-term, what do you think are the benefits of having attended Summer School?
In the long-term, I think I will value the connections I made with so many awe-inspiring future mathematicians and experts in adjacent fields. When I attend other similar events in the future, I will feel delighted to see some familiar faces.
6. 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?
Careers Day has introduced me to exciting career paths which I was not aware of before. Furthermore, it exposed me to avenues learn about even more career options. I feel a sense of security in knowing that there is such a variety of compelling careers for me to choose from.
7. What advice would you give to someone who is considering applying for Summer School in 2025? Should they apply and why?
I would say that if you are even considering applying, that is a sign that you are interested and will most likely enjoy it. I would advise you ask yourself the following question: “Would I rather do something and not enjoy it much or regret not trying it at all?” The Summer School environment may seem a little out of your comfort zone, but the experience is what you make of it. Without trying new experiences, you will never know if you like them or not.
8. What are your current career ambitions in the mathematical sciences sector?
Currently, my ambition is to have a career in which challenges me intellectually and forces me to apply many of the skills I have learned through my maths degree. I am presently more inclined towards academia than industry as I believe it has the best chance of meeting my ambitions. However, it is difficult to decide because I have not started my MPhil research yet, so I do not know whether I will like it as much I think I will. Regardless, I am one to keep my options open until the end.
9. How did connecting with the community at AMSI Summer School support your experience?
As I have mentioned throughout the answers, I believe the community is what made Summer School fun and worthwhile to attend in person rather than online.
10. Any other feedback/comments you would like to provide on the AMSI Travel Grant or AMSI Summer School 2024?
AMSI Summer School was an important experience for me in my journey as a mathematics student. I made many cherishable memories and grew as a person—even more so than a mathematician.