Mani Shayestehfar
The University of Sydney
I am studying masters by coursework in representation theory at the University of Sydney. My research is focused on piecewise linear representation theory, particularly applied in the context of equivariant neural networks.
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
In representation theory, “linearity” of a representation’s action is fundamental and is essential in many important results in the field, such as Schur’s lemma. My research explores how an extended class of actions, such as “piecewise-linear” actions can break such important results. As a result, we seek to find fundamental results under these new sets of assumptions and clarify if there are any particularities with the decomposition of such representations. As a result of “piecewise-linearity”, an example of which is the famous ReLU function, the research has underlying impacts on the development and understanding of black-box ML models such as Equivariant Neural Networks.
How did you get into the mathematical sciences? Was there someone or something that inspired you to this field?
I was always fascinated by how anything could be explained at the very fundamental level, and every time I attempted to answer such scientific questions, I would reach the underlying mathematics, whether it was quantum systems, or the financial markets. I was particularly inspired by the late mathematician Maryam Mirzakhani and her dedication to her passions as an Iranian woman undergoing many hardships in her life.
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 certainly an advantage! Otherwise, travelling would be much more difficult and costly. It also meant that I could stay in an accommodation surrounded by other mathematicians which resulted in great friendships and discussions.
What was the most valuable part of the program for you?
I really enjoyed the coursework. I think it would be very difficult to tackle such novel research anywhere else as coursework. But my most valuable achievement was certainly the networking and being able to learn what other people are doing in their maths world. It also helped me articulate my own research at a higher level and be able to explain it better.
In the long-term, what do you think are the benefits of having attended Summer School?
I now know an approximately large cohort of mathematicians who I hope to see in conferences and future talks which is great. Another benefit is that I could not otherwise learn about the very latest research that Daniele and Agnese are doing!
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 definitely think being exposed to these firms and institutions is the way to show maths graduates that there indeed are different ways to do maths in the day to day life and that an academic life is not the only way!
What advice would you give to someone who is considering applying for Summer School in 2027? Should they apply and why?
They should 100% apply and make sure to communicate with many lecturers, tutors, and peers to exchange viewpoints and experiences.
What are your current career ambitions in the mathematical sciences sector?
My aim at the moment is to focus on my masters and produce a novel and substantial thesis. From then onwards, I aim to weigh my options for a PhD or a position in the industry that is mathematically rich.
How did connecting with the community at AMSI Summer School support your experience?
I don’t think I would find AMSI Summer School as much fun as I did If without the regular discussions with my peers.
Any other feedback/comments you would like to provide on the AMSI Travel Grant or AMSI Summer School 2026?
Thanks for organising everything 🙂