Sue Sierra

Niharika Peddinenikalva has written the following article as part of our series of Academic Interviews; featuring Sue Sierra!

Susan Sierra is a Reader in the School of Mathematics at the University of Edinburgh, who completed her PhD in Mathematics at the University of Michigan. Her research interests include noncommutative algebra and algebraic geometry.

How Sue entered a career in maths

Sue has always enjoyed understanding, and learning new, mathematics. As a person who tends to live in the now, she hadn’t always thought about pursuing a career in maths. However, with every turning point in her life, she slowly realised that this was where her interests were taking her. She went to grad school so she could continue her studies, applied for post-docs to get into the world of research and only chose a career in maths when she accepted the position of lecturer at the University of Edinburgh!

Life as a researcher at the University of Edinburgh

Sue enjoys her life as a researcher, stating that, ‘A big part of my job is thinking about what I want to think about; that’s fantastic and I’m very lucky.’ Her interest for finding answers to problems and discovering new things has fuelled her enthusiasm for research. However, she recognises that studying mathematics is inherently difficult as, given the abstract nature of the subject, it requires the understanding of things that one typically does not comprehend innately.

A researcher could spend hours to months trying to prove a theorem that may, in reality, never be solved, or may even turn out to be false. Sue confirmed, ‘It can be frustrating - to keep trying to do something you can’t do. But when it does work, you figure out something new and it’s great!’

Sue believes that asking good questions is one of the most challenging aspects of research. These can lead to interesting answers and pave the way to progress. Students tend to question their abilities and skills when they get stuck on mathematical problems, which can be quite unproductive. In light of this, Sue says, ‘As a mathematician at any level, including a student, you need to be able to push that feeling aside and say “Okay, I’m not going to worry about if I’m smart enough. I’m just going to think about the mathematics”.’

Preference between teaching and research

Sue loves both teaching and research, and is very glad that she can do both. To explain some complicated piece of mathematics and watch other people understand it for the first time is a really great experience. She enjoys teaching some beautiful mathematics and watching her students fall in love with the maths as well! As she mentioned earlier, she loves her research and is glad that she can conduct it while also educating.

Sue’s research on non-commutative algebra

Sue studies non-commutative algebra. To put it simply, it involves the algebra where x.y is not the same as y.x. A significant portion of her career has gone into thinking about relationships between non-commutative rings and algebraic geometry. To give a bit of background to the reader, Lie algebra is a way of thinking about symmetries. Using Lie algebra to understand the symmetry of a group is analogous to using the first derivative of the function with the Taylor series is used to approximate a function at a point. Finite dimensional Lie Algebras can be turned into non-commutative rings that have a fascinating structure and mathematicians know almost everything that needs to be known about them.

However, we know nothing about the rings that you get from infinite dimensional Lie algebras (also called enveloping algebras). The most fundamental question about these non-commutative rings is whether they are Noetherian (named after the renowned mathematician Emmy Noether). About 10 years ago, Sue was able to answer this question of Noetherianity for a very interesting infinite dimensional lie algebra and she’s been thinking about these rings ever since. Since there is not much known about these algebras, their infinite dimensional property would make one think that they would have no good properties at all, but much to her surprise, she has discovered that they are quite well-behaved. She says, “I like the contrast between how we expect these to be horrible but they’re actually well behaved and the more non-commutative they are, the better behaved they are”. She finds it interesting that most people do not appreciate non-commutativity because they think it’s a bad property, but she’s actually found that it is a good property and it makes things better.

Being a woman in STEM

As a woman in STEM herself, Sue has, over time, seen some improvements in this area, however, it is still quite disappointing to see their underrepresentation in mathematics. She says, ‘I absolutely believe that mathematical talent is distributed equally across the population without regard to gender, race or social class’. So, it can be frustrating to see that this equal distribution isn't represented in higher education, as it suggests that there is a lot of talent being missed out on. She says, ‘think about all the mathematics we would know about if everyone with mathematical talent had equal opportunities to pursue it’. As such, there is definitely room for more development in this context.