Max Carter
AMSI Vacation Research Scholarship 2018/19
AMSI Summer School 2020
What is your role in the Mathematical Sciences?
My primary role is in pure mathematics research. Currently I am doing my PhD in Belgium at the Université Catholique de Louvain and I intend to pursue further research positions after I complete my studies. My research focus lies primarily in the area of “abstract harmonic analysis”. While “classical harmonic analysis” focuses on studying Fourier analysis and related topics on the real line, the torus, the integers etc., “abstract harmonic analysis” studies analogues of Fourier analysis on arbitrary “topological groups”.
In working as a research mathematician, one typically also has a role in mathematical teaching, education and dissemination. As a researcher, you need to teach other mathematicians about your research and mathematics in general, teach courses for Bachelor and Master students, along with other related tasks. These activities are a secondary, though important, role as a research mathematician.
As an AMSI alumnus, how did participating in AMSI programs support your career trajectory?
My first AMSI experience was doing the AMSI Vacation Research Scholarship (VRS) program in the summer of 2018/19. When I applied for this program, I was in the middle of the second year of my Bachelor of Mathematics at The University of Newcastle. To apply for the AMSI VRS, I had to find a supervisor, and this is when I met George Willis and Stephan Tornier, who supervised me during my AMSI VRS project as well as later studies.
We made a small head-start on the project for my AMSI VRS before the summer of 2018 started and I made good progress on the problems George and Stephan assigned to me by the end of my AMSI VRS scholarship. Consequently, George and Stephan were keen to continue working with me, and I continued to do research with them throughout the third year of my Bachelor degree. This resulted in me having written two journal articles by the end of the third-year of my Bachelor degree, which were subsequently published in respectable journals.
On top of the extra research experience that came out of completing the AMSI VRS, the mentoring that George and Stephan have provided me since I met them has been really critical to my development as a mathematician and researcher. The way that the AMSI VRS enabled me to develop a professional relationship with some academics in my department early in my undergraduate degree is another way in which the AMSI VRS has supported my career trajectory.
You are currently studying a Doctor of Philosophy (Mathematics) at the Université Catholique de Louvain, Belgium. Could you tell us a little bit about what you are studying and advice you would give to students in the mathematical sciences interested in further study abroad?
In Belgium the Doctor of Philosophy (PhD) degree is a 4-year degree and is research focused. There are no requirements to complete any course work during the degree so my studies for my PhD are concentrated on completing research. This work includes making progress on open research problems, writing publications, and travelling around the world to conferences that are relevant to my research. There are a number of research projects that I am actively working on for my PhD, some of which I work on by myself, and others projects I collaborate on with other mathematicians.
In regards to advice for students interested in studying abroad, I will just comment on the case of completing a PhD abroad, as this is what I am most experienced with. I think the canonical option for many Australian mathematics students studying abroad is to study in the UK or the US since these are English speaking countries, and in the case of the UK, have a similar university education system to Australia. I would certainly compel students who are considering overseas PhD study to look at their options in continental Europe as well. There are many good mathematicians, mathematics PhD programs, and universities in continental Europe too. Also, many countries/universities in continental Europe consider PhD students more so as employees rather than students, and hence it is often possible to get a much better salary and quality of life when completing a PhD in continental Europe than in Australia/UK/US. On top of all this, experiencing European culture and getting the opportunity to learn a new language can be a fun experience for many, and the 4 years of a PhD in Europe gives a lot of opportunities to travel to many countries.
In saying the above, I should exclaim that it is critical when searching for a PhD position abroad, to find a good supervisor who you are compatible with, and a project that you will be interested in for the duration of a PhD. This should really be the primary consideration and you may need guidance from mentors at your current institution in finding appropriate positions. But if presented with many good options, I think the considerations in the above paragraph should certainly be taken into account.
AMSI’s State of the Mathematical Sciences Discipline Profile report is being released in the next few months. In Chapter 1, it states that compared to twenty years ago, there are fewer high school students that do very well in mathematics, and more that perform poorly. What are some words of advice you would give to high school students struggling to continue maths study?
I think the answer to the question certainly depends on why and how much an individual student is struggling with mathematics. If a student is unmotivated and/or doesn’t find mathematics interesting, and this is the primary reason why they are struggling, then, in general, I think they shouldn’t really concern themselves so much with their mathematics results and study. In my view, it would be better for them to concentrate on pursuing studies and career paths that they actually find interesting, and as a consequence, probably will struggle less with.
On the other hand, there could also be the situation where a student enjoys mathematics but is struggling to keep up or get the results they want. My advice to such a student would be that persistence and consistent hard work really pay off with mathematics, along with many other things in life. Even for the best mathematicians, I would say mathematics is always a struggle in some way or another: as your mathematical ability improves and develops, you are just left struggling with new harder mathematics problems or topics. And I think this is a good viewpoint to have: everyone’s mathematical abilities will progress at different speeds, but an individual students’ goal should just be to progress regularly, no matter how small the progress is. At each step of progression, you will still be struggling with some parts of mathematics while understanding other parts of mathematics better, but the focus should be on making frequent minor steps of progress, no matter how small, and a consistent and strong work ethic will be key to this.
What do you hope for the future of mathematics in Australia and globally?
Although this is not necessarily mathematics specific, at the level of Australia, I would like to see improved funding from the government for university level education. The base rate of the RTP stipend is significantly less than the minimum wage at the moment. Furthermore, you don’t receive any super when on the RTP stipend either. As a comparison, my salary as a PhD student in Belgium has approximately twice the Purchasing Power as an RTP scholarship in Australia when computed using a Purchasing Power Parity calculator. I would like to see the government increase the minimum rate of the RTP stipend much closer to the minimum wage while not reducing the number of available scholarships.
At a global level I would be interested to see improved use of technology and online communication to bring international research communities together. For example, I am currently apart of the following international online research community called RTNCG. The community hosts regular mini-courses, seminars and reading groups in the area of representation theory and non-commutative geometry. There are people from all over the world that participate in this online community and all the meetings are recorded and posted online so that you can view them later if you could not attend. I have found this particular research community to be very effective and captivating in my time participating in it. It would be interesting to see similar international online research communities developed for other large research areas in mathematics, and maybe a larger website/application that can host each of these communities together in a central location.
What are your hobbies or interests outside of work?
I am an avid powerlifter and spend a lot of time at the gym. I also like to go running regularly, particularly in forests near where I live in the south of Belgium. Outside of sports, I enjoy learning languages; currently I am learning Mandarin (Chinese) and French. Recently, I have also started playing/learning some chess and the online game “GeoGuessr” in my limited amount of spare time.
This interview is part of our AMSI alumni Series. If you’re an AMSI alumni, we would love to hear what you have been up to! Tag us in your posts on LinkedIn and X @DiscoverAMSI so we can share your achievements. Please contact us if you would like to be featured in our monthly newsletter: media@amsi.org.au.
