Professor Jacek Brodzki is Professor of Pure Mathematics at the University of Southampton and has recently embarked on a year-long sabbatical fellowship at the Centre for Cancer Immunology. Here, he talks about how maths and immunology can enhance each other and what benefit that has on scientific research.

Please explain is your current research focus?

I am fascinated by interactions between pure mathematics and applications. Mathematics has always taken its inspiration from difficult problems in the sciences, especially physics. In recent years, breakthrough advances in the experimental technology has created a wealth of complex data which holds the key to some really important and difficult problems, like that of cancer immunology. The difficulty is that the data are very complex and not easy to analyse using the standard methods. Topological data analysis has been created to answer this challenge, and my group and I are working on developing this new methodology in a wide range of scientific and medical contexts.

How is your research applicable to cancer immunology?

Cancer immunology is based on cutting edge experiments which create vast amounts of really complex and multidimensional data. Topological data analysis, which is based on topology, a part of mathematics, offers powerful visualisation methodologies supported by new computable characteristics that can be used to provide new insights into the outcomes of experiments and suggest new ways to organise and interpret the data. To get started in this direction, it is crucial for me to be able to talk to the experts who created the data to understand the underlying problems and motivations for the experiments. The residency programme offers a direct access to the cutting edge experiments and shortens considerably the learning cycle.

Please explain how your sabbatical fellowship came about and how is it funded?

I have had many conversations with Professor Tim Elliott, the Director of the Centre for Cancer Immunology, over the recent years and I have been attracted to problems in genomics for a long time. The sabbatical fellowship created an ideal opportunity to put these ideas in action. The fellowship is funded jointly by the Faculty of Medicine and the School of Mathematical Sciences through sabbatical leave.

What attracted you to doing this fellowship within the Centre for Cancer Immunology?

The Centre has a wonderfully clear vision for its mission: How to make cancer visible to the immune system? Despite its simplicity, it’s very difficult to translate this vision into practical solutions. I find both the vision and the challenge of the problems it’s attempting to overcome very attractive.

What difference does working in an interdisciplinary environment make?

A lot of time is required to learn enough of a new discipline to be able to understand the key problems, and to report back any solutions. One needs to be prepared to move significantly out of one’s comfort zone, to learn, and to accept being a beginner again. Crossing boundaries in science is not easy, and it takes a lot of time and effort to find acceptance for them ideas and new research methods in an interdisciplinary context.

How will the new Centre benefit your research?

I plan to develop new methodology to support the work at the Centre. From my initial work carried out during my fellowship, I plan to set up a new research programme in applications of topology specifically to cancer immunology. I hope that the initial results obtained during my placement will be solid enough to secure funding for follow on projects.

The University of Southampton prides itself on translational research which positively impacts on patients – how will your fellowship support and enhance that process?

The research carried out at the Centre is all about helping patients, this is the main and very important motivation that focuses all that the Centre does. Given the complexity and importance of the challenges faced by the Centre, even incremental progress on any of the hard problems we are facing will influence the lives of patients and their families in a positive way.

As you know, the Centre was funded through philanthropic donations. How important is philanthropic support to the Centre and your work?

I strongly believe that fundamental science, mathematics, and medicine have the power to transform the lives of many and supporting this endeavour is the best way for positive change. The funding available through the national science and medicine foundations is not sufficient to fulfil the urgent need for new research. It is wonderful that there are individuals and companies willing to support this work, and I hope this will increase. Philanthropy is typically much more flexible than the established funding streams and can create significant results very quickly.

A few questions about yourself….

How long have you been in your research field?

After about twenty years of work in pure mathematics, I have started research in applications of topology about six or seven years ago. I have been privileged to work with great scientists at Southampton and elsewhere from whom I learned a great deal about current research in a number of exciting areas.

Why did you decide to focus your career on that particular area of research?

I like to understand how things work and it’s thrilling to achieve a proper mathematical understanding of a difficult problem. This takes time, and such research is quite risky, but when things work out, it’s very exciting.

What would you say is your proudest career achievement?

There are a few of my theorems that I really like, but there is a recent achievement that I like a lot. In collaboration with a team from Medicine led by Professor Ratko Djukanovic, we have been able to create new topological methodology to analyse and classify CT scans of patients with COPD (chronic obstructive pulmonary disease). We have demonstrated that our approach has the potential to transform the established methodology. We are currently investigating ways to develop our results into a useful diagnostic tool.

What excites you most about the future of your research field?

Mathematics has always taken inspiration from problems in the real world – the interactions between mathematics and physics have provided impetus for the development of mathematical ideas for centuries. For example, Newton developed Calculus to provide a proper understanding of the observations of the movements of planets, and to explain Kepler’s laws. It is very exciting that, thanks to significant progress in the experimental technologies and our understanding of the underlying processes, the interactions between biology and mathematics are growing and will keep growing significantly over the coming years. It’s a wonderful place to be.