Take 10 with... Melissa Lee

Dr Melissa Lee gives us 10 minutes of her time to discuss her research into the properties of symmetries, which can be used to describe complex systems.

Dr Melissa Lee, Research Fellow in the Department of Mathematics
Dr Melissa Lee, Research Fellow in the Department of Mathematics

1.  Describe your research to us in 10 words or less

Properties of primitive permutation groups, including representations and bases.

2.  Now explain it in everyday terms!

Complex systems in the real and abstract worlds can be usefully described by their symmetries. I study different properties of groups of symmetries. One concept that I have worked a lot on is the base size of a group, which gives a way of describing very large collections of symmetries using a relatively small amount of information.

3.  Describe some of your day-to-day research activities

I usually start my day by checking what’s new on the arXiv, the home of most mathematical preprints. I then spend a lot of my day puzzling over one of my (many) research problems, which involves scouring the literature for results or techniques that could be adapted for my application, or trying to come up with my own techniques. Recently I have also been doing quite a lot of coding to generate computational results which can inform theoretical proofs.

4.  What do you enjoy most about your research?

I most enjoy the collaboration aspect of research, which has picked up since I finished my PhD. It’s nice to bounce ideas off each other and generate new ideas to progress on a problem.

5.  Tell us something that has surprised or amused you in the course of your research

Just over a year ago, when I was working hard to ready my PhD thesis for submission, one of my examiners emailed to tell me that some of my results had been included in a just-submitted paper with another collaborator. He asked me whether I would be interested in working on a follow-up paper with him after my thesis was done. I agreed, but in the months-long process of examination and corrections, we both forgot to follow up about the collaboration.

A few weeks ago, I dug up his email, and asked him whether he was still interested in working on it. He agreed, and we somehow managed to write and finish a paper over the course of two weeks! If only all research was that speedy…

6.  How have you approached any challenges you’ve faced in your research?

A challenge that I have faced, that I think that many others in academia can relate to, is a very difficult “writing up” and examination process for my PhD thesis. There are rarely occasions in life where such perseverance is required, and where giving up is really not an option. During that process, especially during the pandemic, I worked hard to try to be kind to myself and to ask for help when I needed it. I think these are things that are important in all facets of life.

7.  What questions have emerged as a result?

I think that my writing up experience has encouraged me to broaden my horizons post-PhD. Certainly I have stumbled upon new research problems that I never would have if I had kept working in the area of my doctorate.

8.  What kind of impact do you hope your research will have?

My research on bases of primitive groups sheds light on how we might store large groups of symmetries, or symmetries of very large objects, on computers so that others can work with them. I hope my research will inform researchers about how existing algorithms implementing this process might be improved.

9. When you collaborate across the faculty or University, or outside the University, who do you work with and how does it benefit your research?

I recently started research collaborations with Professor Tim Burness from the University of Bristol, and Dr Tomasz Popiel, who is in the Department of Mathematics here in Auckland. Apart from the obvious academic advantages of collaborating (especially as an early career researcher!), I think that both of them have encouraged me to be clearer in the writing up of my research results, which has led to us submitting higher quality research papers than I could publish on my own.

10.   What one piece of advice would you give your younger, less experienced research self?

Take every opportunity to network at conferences etc. since people are much more likely to be receptive to you and your work if they’ve heard of you. Also learn more computer science!