WIMSIG Maryam Mirzakhani Award

Vinesha’s research is on generalised rational Chebyshev problems, their extensions and their applications into different disciplines, such as data analysis and deep learning.

Maud came to her postgraduate studies in applied mathematics with a background in computer science.  Her undergraduate training and Master’s thesis involved the development of computational algorithms for approximating gradient operators using novel GPU approaches.  Given Maud’s background in computer science and numerical methods, her PhD program focuses on the analysis (formal asymptotics and numerical methods) to study partial differential equation models of invasion that are often used in mathematical biology.

 
Maud’s research focuses on comparing classical models, such as the well-known Fisher-Kolmogorov model, with more recent approaches that re-cast these models as moving boundary problems.  This work seeks to overcome a key limitation of the Fisher-Kolmogorov model which, when non-dimensionalised, leads to travelling wave solutions with a positive wave speed, c > 2.  This means that standard analysis neglects slower travelling wave solutions with c < 2.  These slow travelling wave solutions are routinely disregarded on the grounds of being non-physical owing to arguments that arise in the phase plane.  One of the limitations of traditional mathematical approaches to understand invasion is that the underlying biology is highly idealised, and a consequence is that travelling wave solutions with c < 2 are completely disregarded. Maud’s work has carefully compared the classical application of the Fisher-Kolmogorov model with the more recent approach of studying the same partial differential equation reformulated with a moving boundary.  This reformulated problem, that Maud has called the Fisher-Stefan model, allows us to study travelling wave solutions with arbitrary speed.  This includes travelling wave solutions with c < 2, and even travelling wave solutions with c < 0, which Maud has called a receding travelling wave.  Maud’s work has been published in the Bulletin of Mathematical Biology, Physica D: Nonlinear Phenomena and Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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.