School of Mathematics

Johan Martens

Laura O’Sullivan has written the following article as part of our series of Academic Interviews; featuring Johan Martens!

Journey into Academia

Johan Martens was born and raised in Belgium. From a young age he was interested in mathematics, and he became passionate about deepening his understanding during high school. Johan read many books pertaining to the boundary between mathematics and physics such as “A Brief History of Time”. He knew prior to entering university that he wanted to study mathematics and pursue a career in academia. However, engineering was considered the most prestigious degree in Belgium at this time, and you were expected to pursue it if you had an aptitude for mathematics. Johan’s subsequent choice to study mathematics at university resulted in surprise and friction from his teachers and family, but he remained confident in his decision and ultimately started a degree at his local university.

Johan achieved the top results of his class during his undergraduate years and continued to deepen his understanding of mathematics, with his true passion for the boundary between and physics emerging. He then, again, chose the path less travelled by studying abroad; in his final year, he spent a semester in Paris. He also applied for PhD positions around the world, which was unusual as normally those who wanted to work in academia completed their undergraduate and postgraduate degrees, and became Postdocs, at the same university. As a result, Johan had little guidance on applying to programmes outside of Belgium. This was a very testing period in his life as he was rejected by four top PhD programs in the US; despite this, he made the drastic decision to withdraw his funding application for a PhD in Belgium. Serendipitously, Johan secured a place on a master’s program at the University of Oxford, where he spent an intense and enjoyable year. He was captivated by the difference in approach towards mathematics between Belgium and the UK.

Following his master’s degree, Johan went on to complete a PhD at Columbia University and then a post-doc at the University of Toronto; during this time he spent a year at a research institute in Germany.

At this stage in an academic career, it is traditional to apply for permanent positions, however Johan felt his publication record was still relatively thin. Furthermore, there were very few job openings in academia at the time due to the financial crisis. Therefore, he accepted another postdoc position at Aarhus University and spent six months at a research institute in Brazil. Afterwards, Johan secured his position at the University of Edinburgh.

He feels very lucky to be where he is today, however, he was greatly aided by his willingness to be geographically mobile. This has almost become a necessity with many academics having not just international but also intercontinental careers. This, in his opinion, is creating a bottleneck, as those who successfully obtain academic careers are those who are flexible, which can greatly impact those with children or caring responsibilities. Johan believes this aspect of the academic career must be addressed when tackling gender inequality.

 

Current research and teaching

Johan’s current research lies on the boundary between geometry and theoretical physics. His work involves moduli space which is a geometric space parametrising an object. The most basic example is the Grassmanian where you fix a vector space of some dimension, and you can look at all the subspaces of this vector space with a fixed dimension, for example all the 2-dimensional subspaces in a fixed 5-dimensional vector space. This comes equipped with geometric structure. Many questions in theoretical physics involve moduli spaces. Cross-disciplinary work is something that Johan has learned to navigate over time. There are differences in rigour, motivation and dynamics between mathematics and physics, and working between the two areas is not always easy. It is very important that mathematicians and physicists do work together, which has not always been the case over the years, however it plays a key role in mathematics. Not only does mathematical research have an impact in physics, but discoveries in physics have also been relevant in mathematical areas, such as number theory.

Johan is presently teaching a 3rd year geometry course and finds the historical perspective of it, tied with its mathematical beauty, fascinating. Classical geometry dates back to the Ancient Greeks who developed an axiomatic way of thinking. It wasn’t until the 19th century when the field went through great change with the Euclid’s 5th axiom, of which University of Edinburgh’s Professor John Playfair made a formulation. This axiom states that there is a unique line which goes through a point which is parallel to another line, and it emerged it was not in fact true for all geometries. Einstein’s theory of general relativity also brought great change with differential geometry, and this has had a huge impact on today’s world as GPS systems must take the curvature of space time into account to function correctly. This has been a very enjoyable course for Johan to teach, however it has been particularly challenging during the COVID-19 pandemic as geometry is a particularly visual topic and there was a steep learning curve with learning the practical aspects of video editing.

 

Life outside Academia

In his free time, Johan enjoys reading about general history and the history of ideas, spending time with family and friends, and spending time in nature such as participating in rock climbing, skiing, and scuba diving. He has found Scotland to be the perfect place to pursue these passions