Quantum vortex matter: insights from computer algebra

Working with computer algebra in a research environment has led Professor of Physics Nicola Wilkin to make breakthroughs in areas ‘where neither pen and paper nor numerical solutions could shed light on the problem’. 

These include ultra-cold gases and the flow mechanisms of vortices in mesoscopic superconductors – superconductors on a scale between microscopic and macroscopic. 

The two physical systems were a main focus of Nicola’s recent Inaugural Lecture, entitled ‘Quantum vortex matter: insights from computer algebra’. Her address was in front of a wide-ranging audience, reflecting the breadth of activities with which she’s involved. ‘I was absolutely delighted to see, amongst others my current students, the Pro-Vice-Chancellor (Education), Professor Kathleen Armour, and colleagues from many of the professional services teams that are key to our education provision,’ she says. 

The lecture was part of a series of Inaugural Lectures run by the College of Engineering and Physical Sciences to showcase its leading scientists who are pushing the boundaries in their disciplines. These events, which are open to the public and free of charge, mark an academic’s promotion to Professor, but also provide a rare opportunity to hear first-hand about their research and academic journey. 

‘I talked about my research work involving superconductors – made of solid material – where the vortices within them are generated by an applied magnetic field, and other vortices in ultra-cold gases where the vortices are a response to rotation that is induced by lasers,’ explains Nicola. ‘Theoretical physicists like me have the luxury of being able to let their curiosity guide them between different fields, where underlying conceptual ideas may be related even if the laboratory set-ups are completely different.’ 

Nicola’s research is theoretical, and many of the advances she has made have benefitted from insights developed via computer algebra. This is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Computer algebra is also at the heart of the work Nicola leads in the rapidly evolving area of educational technology. Now working with the globally leading producer of online assessment systems for STEM courses, Maple T.A. (Maplesoft), Nicola’s research is helping to transform the way students learn and revise and how papers are marked. Her understanding of the power – and difficulties – of computer algebra systems has made Birmingham a world leader in the field. 

‘One of the main reasons I’ve made significant advances in my research field is the fact I use computer algebra, which, very simply, is a calculator that works for algebra rather than numbers,’ explains Nicola, who is the College’s Director of Education. 

‘Using it effectively has led to the physics breakthroughs I’ve made, and it’s also played a key role from the perspective of teaching innovation. One of the things it has allowed us to do is to generate more general automatically marked questions for STEM disciplines. To become confident in mathematical techniques, students need to practise, which ideally involves doing lots of questions. We want to be able to offer them as many questions as they would like, at whatever time they would like to study – and in order to do that, they need to be automatically marked! Computer algebra can work out whether it’s the right answer or not, and I’ve been developing that.’ 

Throughout her career, Nicola has had a longstanding interest in improving the representation of women in physics. She has been honorary secretary of the Institute of Physics’ Women in Physics Group, as well as a member of the Institute of Physics Council and its equality awards panel. More recently, she co-chaired the School’s successful equality awards – Institute of Physics JUNO champion and Athena SWAN Silver submission. 

‘Most of the time I haven’t experienced any problems being a woman in physics: colleagues and staff have been welcoming and encouraging. However, I did find the system wasn’t really set up for women returning from maternity leave, so what until then had felt like a level playing field no longer did. I could have whinged about it, or I could have decided to try and make things better for those coming after me – and I picked the latter!’