AMSI/AustMS WIMSIG Maryam Mirzakhani Award

Paula Verdugo (Macquarie University) exhibited an exceptionally strong publication record for her field, wide network of collaborators, and broad range of projects.

1. When did you first become interested in mathematics?
I have always been interested in numbers since I was a small kid. When I was about 10 years old, that is, when I was in grade 5 in Sri Lanka, I won the grade 5 prize for Mathematics at the school prize giving ceremony. This moment surely made me realise how passionate I am about Mathematics. Since then, I made sure to take home the grade award for Mathematics at the school’s annual prize giving ceremony.

2. Could you tell us about your life and career path so far?
I was born and raised in Colombo, Sri Lanka. Sri Lanka has a somewhat different educational system than Australia. Although it is free, it is extremely competitive. When you graduate from high school, the government informs you if you have been selected for admission to a state university based on your grades. Less than 16% of those who qualify get admission to state universities, the entrance is that tough. I was lucky enough to get accepted into the Faculty of Applied Sciences at the University of Sri Jayewardenepura. After the first two years, based on your results, a very limited number of students will be selected to pursue one subject majorly for the last two years of the honours degree. I was chosen to major in mathematics, and I completed my bachelor’s degree in 2017.

Soon after the completion of my bachelor’s, I was employed by the same university as a demonstrator for the department of Mathematics, and later, I was promoted to the post of temporary lecturer. I already knew I wanted to work in academics at that point. I moved to Australia in 2019 to do my PhD, and it was only recently completed. I am now working as a research fellow at Deakin University, Burwood campus.

3. What does your current research involves?

My research focuses on optimisation, approximation and their applications in different areas, mostly in the fast-growing area of Deep Learning. During my PhD, I studied rational and generalised rational Chebyshev approximation problems including multivariate settings and their applications. We investigated the theoretical aspects of this problem from the point of view of quasiconvexity. Apart from the theoretical side, my PhD study includes many applications of rational and generalised rational approximations in different fields including data analysis, Deep Learning and engineering.

While I was doing my PhD, I was able to publish a solo author paper which discusses the use of rational functions as activation functions in a neural network with loss functions in the form of uniform approximation. However, in that study, I was only focusing on a neural network with no hidden layers. Currently, I’m working to extend these results to an artificial neural network with hidden layers.

My PhD study laid the foundation for the research that I am currently doing. My main research focus now is to incorporate modern optimisation techniques to optimise a neural network with special features.

4. How do you achieve a balance between your work and life?
I consider myself to be someone who prefers to live in the present. We must enjoy the present moment since we have no idea what the future holds for us. When I work, I very much enjoy everything about it. I do a variety of things that I love while I’m not working, usually on weekends. With my family and friends, I enjoy travelling to new places to experience new cultures and, more generally, different cuisines. I also love to recreate traditional Sri Lankan dishes which is difficult, but it is a fun way for me to spend my leisure time. Sometimes, I just stay home and watch movies all day long. So, there is not one particular thing that I do to balance my work and life, but I always try to keep work and life separate.

5. What do you think are mathematician’s duties and responsibilities towards the society?

Mathematicians play an important role in this society. Many of the challenges we face are multi-disciplinary: overcoming them requires mathematicians to collaborate with scientists and engineers in different fields. The skill set of mathematicians are much needed to communicate the science, data and forecasts, and ensure that this information is meaningful to the people who need it. Mathematics is the binding glue of all the other disciplines, in fact, it is known as the queen of science. Therefore, mathematicians are responsible for providing the necessary background and knowledge for everyone, so that their skills can be used to make this society and the world a better place.

6. How has your experience doing mathematics in Australia been so far?
It has been great so far and I very much enjoy working with mathematicians in Australia. Everyone here is friendly, supportive, easy going and most importantly, you can call your supervisor by their first name. This was a culture shock for me when I first moved to Australia. But I believe that is how it should be. This friendly environment is much more encouraging, especially for the early career researchers to bring the best out of them. It is also surprising to see how much support we receive from some related organisations such as AustMS, AMSI, etc.. This support plays a crucial role in the development of mathematics here in Australia.

7. Where do you see yourself 10 years from now?
In 10 years, I want to establish myself as a recognised mathematician in Australia and internationally for the research I am conducting in optimisation and its real-world applications. I believe I am on the right path to accomplish my goals, and I am making an effort to do so. At the same time, I wish to hold a more senior academic position, so that I may continue educating students in mathematics and helping them to shape their future. 

8. What advice would you offer to young women who are just starting their careers in the mathematical sciences?

Just believe in yourself, have confidence in your own abilities. There will be many ups and downs along the way, but always have faith in your ability to go through them. Keep striving towards your goals. Learning mathematics and conducting research in mathematics might be challenging at times, but I can assure one thing. The delight that comes when an answer to a challenging math issue is found, cannot be felt by anything else.

9. Any last words?
‘What goes around, comes around’ is a saying I wholeheartedly concur with. Be good, do good, and most of all, show kindness to one another. It will ultimately find its way back to you and do wonders to your life.

1. When did you first become interested in mathematics?
I started being interested in maths when I was a kid at school. Maths exercises were stimulating and fun to do. Our high school teacher would pass us the Canadian Open Mathematics Challenge some years, and we could get practices beforehand. I used to get the first price in school, not because I was especially competitive but because I got hooked on those exercises. I found them so creative!

2. Could you tell us about your life and career path so far?
I grew up in Canada. I have graduated in computer engineering years ago, and I was teaching programming. Now I am completing my PhD in applied maths in Australia.

3. What does your current research involves?

My current research is about partial differential equations used to study biological invasion. The Fisher-KPP equation is a simple reaction-diffusion equation that admits a travelling wave solution that represents well invasion. We modified this equation by adding a moving boundary, to obtain a sharp-fronted wave, where the position of moving front is known. From there, we studied the solution with numerical solver, phase plane and perturbation methods. Once we understood the main features of the solution, as the speed and the shape of travelling wave, we moved our analysis to a model of two populations. We considered for each population a Fisher-KPP equation with a moving boundary. We also considered a simplified model of two populations that could represent cancer invading skin. This model included the diffusion and the proliferation of cancer population and the degradation of the skin by cancer cells.

4. How do you achieve a balance between your work and life?
Doing a PhD is like having a full-time job. It does not prevent me from enjoying life or doing the tasks of everyday life.

5. What do you think are mathematician’s duties and responsibilities towards the society?

A good example of mathematician’s duties and responsibilities is what is happening during COVID-19. The work of mathematicians contributes to understanding how the pandemic is evolving and allows to make predictions of what is coming. It helps people having a sense of control over their life. It helps society making decisions in the interest of the people.

6. How has your experience doing mathematics in Australia been so far?
It is true that there is lack of popular and financial investment in research and in education.

But it is a problem common to many countries. What is special about Australia is that it so far from the rest of the world, and mathematicians still manage to collaborate with researchers from other countries.

7. Where do you see yourself 10 years from now?
Teaching and doing research. I believe a lot in teaching and forming the new generation.

8.What advice would you offer to young women who are just starting their careers in the mathematical sciences?

Find opportunities to learn and achieve a career goal, have a long-term view of life and career, and keep your integrity.

9. Any last words?
Thank you for your attention and your support.

1. When did you first become interested in mathematics?

I did not have a particular interest in mathematics until the 6^th grade. This is the first year that students in Vietnam learn how to do a proper mathematical proof like induction, or proof by contradiction. I enjoyed so much that I spent the whole year writing a book, which I called “number theory”, to collect my thoughts and proofs. It was mainly just a collection of my homework. Of course, this book has never been published. Nevertheless, I am very proud of it.

2. Could you tell us about your life and career path so far?

I was born in a small town in middle of Vietnam. I moved to Ho Chi Minh city to study my bachelor’s degree in maths. I have always admired all of my maths teachers and wanted to be a maths teacher myself.

At the end of my bachelor’s, I attended a spring school organised by the Vietnamese Mathematical Society. At the end, I was really sad when I realised that this was meant to be my last mathematics lecture. I distinctly remember that the last lecture was about Random and Galton-Watson trees and was really enjoyable. After the spring school, I decided to postpone my teaching dream and seek an opportunity for studying PhD in mathematics.

I was lucky that my university lecturers, especially my honour supervisor, were very supportive. They gave me valuable advice regarding studying PhD in Australia.

3. What does your current research involves? 

My research involves both theoretical and applied mathematics with a particular focus on variational analysis, optimization and graph theory, and their applications in the real world.

During my PhD at the Federation University, I explored generalisations of convex separation theorem for nonconvex settings and characterised certain irregularity behaviours of the intersections of sets. I have published several papers on this topic. One of my current goals is to apply the theory to practical real world problems. Since most real-world problems are inherently non-convex, I want to utilize some important optimisation properties of convex functions beyond the convex framework. I have published one paper in this regard and have an on-going project, in which I develop some related computational tools.

During my PhD, I also got involved in a reading group on graphs of polytopes. I was fascinated with the topic and decided to pursue graph theory as my secondary research field. I first studied the connectivity and linkedness of graphs of cubical polytopes and obtained publications in this direction. Currently, I am working on proving certain graph colouring conjectures for polytope graphs.

I enjoy all mathematical topics and continuously try to broaden my research to connect with other more diverse branches of mathematics. I understand and value the importance of publications; however, I place more importance in further developing my knowledge of mathematics and my appreciation of its beauty through discussions and problem solving with my collaborators and students.

After PhD graduation, my passion for mathematics has grown into a more practical direction. Thus, currently I am applying what I have learned during three years of PhD to solve real world problems. My ultimate goal in the next five years is to answer many of my applied questions and to carry my principle research further.

At the moment, I am working as a postdoc with an operations research group at Curtin University. I am leading a project on scheduling problems for industry companies. It is very fascinating. I had never imagined that my theorems, obtained in a theoretical setting, could be useful in real world setting. The experience has given me a new perspective on the applications of mathematics.

4. How do you achieve a balance between your work and life?

I enjoy painting and photography and have a goal to sell my paintings at the City Beach Market in Perth. I think the key thing is that we should enjoy everything we are doing. If that is the case, all else will fall into place.

5. Where do you see yourself 10 years from now? 

Academically, I want to be a strong independent researcher in a senior academic position. I would like to have some breakthroughs in my field of research, and I am working towards that. In addition, I will keep doing more industrial and other real-world applications. I hope these will have real impact in the world. Of course, I hope to still enjoy what I am doing.

6. What advice would you offer to young women who are just starting their careers in the mathematical sciences? 

“Be yourself” is the only advice I can offer at the moment. It is, for me, a very strong statement. I wasn’t a person who follows the standard norms and I have never minded that. I am very lucky to have my parents’ encouragement and my teachers full support. Many of my female friends have not been that fortunate. They have followed the mindsets (or standard norms) of other people, which has occasionally meant giving up on their dreams.

7. How has your experience doing mathematics in Australia been so far?

Doing mathematics is fun regardless of where you are. Specifically, in Australia, having my supervisors and other researchers to discuss maths brings me great joy. I like the friendly environment where I can call professors by their first name. I feel like there is no distance between students and faculty members. I find this approachable environment helpful for learning and collaborations.

1. When did you first become interested in mathematics?

When I started high school, it dawned on me that I can sit for hours and hours struggling with complicated mathematical problems, without getting tired or bored. The pleasure and satisfaction of being lost in maths were beyond anything else I had experienced. I was lucky to have a highly encouraging teacher who guided me throughout this journey.  Additionally, I had wonderful friends who were intelligent and hardworking students.

In fact, in Iran there are many smart and successful women who are outperforming men in engineering and mathematics. I was a part of and a beneficiary of this environment in my teenage years. Being an outstanding student, I always received complements from my parents and teachers, which further motivated me to work even harder.

To this day, a mathematical problem can mesmerise me to a degree that makes me forget about my surroundings. I do not consider working with mathematics as just a job and derive tremendous satisfaction from dealing with complicated mathematical problems and coding.  

2. Could you tell us about your life and career path so far?

I was blessed to be born in a family that placed high emphasis on education. Before I commenced primary school, my mother had taught me the alphabet. I have vivid memories of my childhood when I was practicing reading my first sentences. At that time, fancy colourful books were not common in Iran and I used to gather any parts of newspapers that I could find and learn new words, a habit that has stayed with me throughout my life.

I obtained my Master’s degree in electrical engineering in Iran. After a couple of years of working in the industry, I realised that my brain craved more mathematics! Therefore, I commenced my Ph.D. in mathematics at Swinburne University focusing on an applied mathematical project involving concepts which were totally new to me. In particular, I needed to learn some biology since my project was on modelling cancer cells regression in response to chemotherapy. Initially, some of my colleagues were surprised when they heard about my research background. But with effort, everything is possible! I completed my Ph.D. on time and my thesis was accepted by the referees immediately without any revisions. Much to my delight, my Ph.D. research was published in the “Applied Mathematical Modelling” journal. 

3. What does your current research involve? 

Currently, I am about to finish a research fellowship with an excellent team at Deakin University. Since my performance was above satisfactory, my supervisors suggested that I start a new Ph.D. in machine learning and artificial intelligence, starting in October 2020. At this stage, my focus is on heterogenous scene understanding in graph neural networks. 

4. How do you achieve a balance between your work and life?

I usually get up around 6 am in the morning. The first thing I do is a 30 minute exercise routine and then I start doing some chores and preparing food. By 9 am, I have completed all my chores and the rest of day is mine! 

I spend most of the day on mathematics. In the evening, I enjoying watching some TV and chatting to friends and family. By the conclusion of the day I am usually so exhausted that I fall asleep with ease at around 11:30. The inner satisfaction I get because of my productive day allows me to have a sound sleep, preparing me for another day. 

5. Where do you see yourself 10 years from now? 

I think about this almost every day. I have written my most important goals on a piece of paper which I keep beside me on my desk, so that I may regularly view my goals. I believe that my potentials and hard work should pave the way for a bright future. Hopefully, I will be a senior data scientist and be able to collaborate with leading universities. Besides my career, I feel that being a kind and wise mother will complete my life as a woman.  

6. What advice would you offer to young women who are just starting their careers in the mathematical sciences? 

In the modern world, there are many distractions for young people, especially for young women. I believe that in order to be successful it is important that one thinks of long-term satisfaction, rather than being drawn into instant satisfaction. By maintaining their focus on long term objectives and having a clearly devised plan, one can move towards and attain their career goals. I am blessed because my friends have had similar experiences and have similar goals as myself. Sharing thoughts and experiences with them gives me renewed hope and strength, enhancing my chances of achieving success in my academic endeavours. 

7. How has your experience doing mathematics in Australia been so far?

In Australia, there are lots of facilities and opportunities for doing mathematics. During my Ph.D., I received several scholarships for summer and winter schools, involving wonderful lectures by outstanding professors. However, I have noticed that in Australia there are not as many job opportunities in mathematics as there are in other countries, and I hope that this trend will soon change as Australia’s economy transitions into one which is more technologically driven. I believe that many companies will benefit from hiring mathematicians as analytical reasoning has proven to be an important factor for ingenuity and progress.

8. What achievements are you most proud of?  

I have had many achievements and received numerous certificates during my studies, but the one which I am most proud of is winning the prestigious Maryam Mirzakhani Award conferred by the Australian Mathematical Society. I am very proud of winning this award since the late Maryam Mirzakhani was one of my heroines during my high school years. She blossomed in a male-dominated society and is a role model for all women who believe in their abilities and aim to break the glass ceilings of their societies.