Dr William Trad
AMSI Summer School and AMSI SRS 2018/2019
What is your role in the Mathematical Sciences?
I am currently a postdoc at HKUST in Hong Kong. People in my position usually do some mix of research and teaching. Though, my position is unfortunately purely research focused.
As an AMSI alumnus, how did participating in AMSI programs support your career trajectory?
The AMSI VRS program illuminated a microscopic aspect of the research conducted in partial differential equations. Despite my limited exposure, I found the project to be compelling enough to motivate me to want to work in something related to partial differential equations. Subsequent AMSI programs that I participated in allowed me to establish a broader mathematical knowledge bank. Specifically speaking, I was able to dip my toes in areas of math that I may never have even touched or known about during my undergraduate years. For example, I had the opportunity to partake in courses on Bayesian statistics as well as mathematical finance and machine learning.
Despite not explicitly working in these areas, the problems that I solved during my PhD involved analyzing the behavior of Brownian motions within confined non-Euclidean geometries via a tool known as microlocal analysis which is an offshoot of harmonic analysis used when studying partial differential equations via a phase space paradigm. As a result, I found that some of the partial differential equations, probability and stochastic analysis that I had learned prior gave me some level of intuition for my work.
Recently, I’ve drifted away from anything probability related and am more interested in geometry. Nonetheless, my understanding of probability has given me another vector when it comes to thinking about partial differential operators and their deep connections to stochastic processes, such as the Laplacian and Brownian motion or the less understood fractional Laplacian and Lévy process.
You are currently a postdoctoral fellow at the Institute for Advanced Study, the Hong Kong University of Science and Technology. 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?
I work in a field known as Inverse problems. Within this field I study variations of a problem that lies at a confluence of geometry and partial differential equations. In practice, the original problem was posed to model a noninvasive medical imaging procedure known as electrical impedance tomography wherein the conductivity of a body is reconstructed from boundary surface electrode measurements. Such variations of the problem can involve partial boundary measurements, questions regarding stability of the inferred conductivity given minor perturbations of the boundary current measurements and lastly the uniqueness of the conductivity given the boundary current measurements.
Personally speaking, despite the help and support that I received from my supervisor. I found it a little bit isolating and quite lonely when doing my PhD at USYD because the only other PhD students in Australia that worked with the tools that I used were at ANU and UNIMELB. Consequentially, I think I may have felt less isolated if I had applied to these universities or universities in the US or France where microlocal analysis is more commonly used in partial differential equations. Essentially, I believe that when choosing a postgraduate program, it is important to consider the liveliness of the research group that interests you.
A benefit of studying abroad in the US for example is the sheer density of universities and thus likelihood of stumbling upon an interesting conference that may be related to your work. This is like Europe, and it is in this sense that studying overseas has a clear upside. Consequently, it is usually much easier to establish an academic network when studying in the US or EU. When considering further study, you also must consider the length of PhD programs, as well as their structures and application procedures. In the US, PhDs are known to be quite long and involve a bit of coursework in comparison to other PhDs where there are no coursework requirements. Furthermore, means of PhD “funding” differ depending on location. In Australia, students are funded by RTP stipends. On the other hand, such funding is more complex in places such as the US and can be the result of your supervisors’ grant or internal or national fellowships.
AMSI’s State of the Mathematical Sciences Discipline Profile is releasing soon. It is reported that students these days prefer the basic maths subjects in Years 11 & 12 over more advanced maths subject options. What are some of the thoughts or opinions you would comment on this trend?
I don’t have any strong opinions regarding this issue, though I imagine this trend probably stems from the alienation of many students from mathematics during early schooling. Which I would hazard a guess is probably a result of shortages in good teaching. I don’t think there’s a simple fix for such an issue. Though, I believe that improving the working conditions for schoolteachers to incentivise more people to want to become teachers can only be a good thing when it comes to empowering students to succeed.
What do you hope for the future of mathematics in Australia and globally?
Once again, I haven’t really got any strong opinions on this question and can’t really speak for the entire world. Though I think it would be nice if more high school students did end up coming into our first-year courses open minded enough to pursue further math and had the confidence to partake in our more challenging courses.
What are your hobbies or interests outside of work?
I really enjoy reading novels. I also enjoy hiking, watching tv shows and movies, playing games and my guitar.
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.
