Associate Professor Regina Burachik
The University of South Australia
We ask Associate Professor Regina Burachik why programs like AMSI Summer School are so important and what she hopes students will get out of her upcoming course in January.
Can you tell us about your work? What drives your interest in this field?
I do research on optimization, which consists of finding the best decision among a set of admissible choices. What I find fascinating in this area is the way in which this fundamental problem can be formulated as a particular case of more general ones. These formulations, in turn, provide a rich and unifying theory, which can be used for solving the original optimisation problem. The theoretical tools for solving optimisation problems are convex analysis, numerical analysis, set-valued analysis, variational inequalities, and maximal monotone operators. You never get bored when you work on optimisation: with so many tools available you will always find a new way for tackling your problem. It is also easy to find new problems to work on.
What are the most interesting “big questions” or challenges facing researchers in your area?
From my perspective, the “big question” is to find efficient ways for solving certain families of non-convex optimization problems. Examples that are very important are nonconvex polynomial optimization problems, or new duality methods for certain structured nonconvex and non-differentiable problems.
What are your favourite applications of your work?
As examples, I have used my work for finding best dose calculation for cancer treatment, or for solving network communication problems using UAVs.
What are some other areas of your field that are particularly interesting to you?
A topic I enjoy is maximal monotone operators. These are point-to-set maps that generalize derivatives of convex functions. There is a fascinating interplay between these operators and convex functions. Indeed, many surprising connections can be established between these two mathematical objects. I enjoy finding new examples of such connections in my work!
Why did you become a mathematician/statistician?
I did three years of chemistry before migrating to maths. My change happened because I realised that I had a lot of fun doing math, much more than with chemistry! This is a decision I will never regret, maths has given me a lot of happiness. It gives you a way to lift yourself from everyday life. It provides you a special world where you can have fun on your own, or with your colleagues. At the same time, it helps people in solving concrete real-life problems.
Do you have any advice for future researchers?
Choose your own problems, those that you enjoy. Maths is a source of enjoyment, and you should work on a problem only if it is fun and you feel passionate about it, otherwise it is not worth. Follow your own path, and this will make you unique as a mathematician.
Deepening field knowledge and providing a networking platform, why are opportunities such as AMSI Summer School so valuable? What do you hope attendees take from your lectures?
I do hope my students will have fun, as much as I will have! Optimization is a way of approaching fundamental problems, and you can see it as a language that provides you the best answer to a given question. Once you learn that language, you can formulate your problem and solve it in your unique way. You will share your views with other students, and learn from them as well. You will understand whether optimization is the topic for you (I hope so), and if so, you will discover new aspects of yourself as a mathematician, including your abilities and your preferences. This may be important for determining your relationship with this topic in the future.
What do you consider your biggest achievement to date?
I am a bit shy to speak about my own achievements, I prefer to leave this topic to others! I am just very happy with my choice of maths as a profession. This has allowed me to travel everywhere, meet amazing people all around the world, and be able to work together with these people on an equal level. Once you start working on maths, you become a member of the mathematical world, and you are identified with (and appreciated for) the maths that you produce. Being a (very tiny, infinitesimal), part of that beautiful constellation, is an achievement that makes me very happy!
Associate Professor Brurachik is delivering the Optimisation topic at the 2019 Summer School.