Yvain Bruned

Early life and education: 

Yvain grew up in France and so, naturally, went through the French education system. As he himself noted, it’s very different to most other systems in that rather than going straight to university, stronger students attend preparatory classes for two years. At these, they undergo rigorous training to participate in the national competition, the Concours Ecoles d'Ingénieurs, after which they select which university they would like to attend. 

This is the route Yvain took, choosing to complete a degree in mathematics and computer science. However, in his third year he switched to studying mathematics solely as he found that he was more attracted to it, although he still appreciates having done computer science as it helped to impart upon him knowledge of programming languages.

One of the things he remarked upon that benefits the Scottish higher education system in particular, is being able to choose courses outside of your main degree program. Having studied some humanities subjects, such as Greek, Latin and French Literature at school, he sees the benefit in being able to pursue those avenues further whilst still doing a different degree. However, a major benefit to the path that he took was that he obtained a paid scholarship which covered his entire degree!

During his undergraduate studies, Yvain was strongly encouraged to go abroad for an internship. He developed an idea to combine his interest in stochastics with differential equations, one that eventually saw him under the tutelage of Martin Hairer of (at the time) the University of Warwick. He found Hairer (who has, since Yvain’s internship, been awarded both the Fields Medal in 2014 and the Breakthrough Prize in 2020) to be highly inspiring, and they worked on a small project together.  After completing his undergraduate degree Yvain completed an MSc in probability and stochastics, and then went on to do a PhD in the same vein in Paris. 

PhD years: 

In his first year, Yvain found that he could already understand all the material presented to him, but he couldn’t see a way to actually come up with something new himself. He likens it to reading a novel that you greatly enjoy: you can understand all the literary techniques the author uses, but that alone doesn’t allow you to write something of similar quality- insight and innovation are required. Ultimately, Yvain found it hard to identify where he could actually contribute. From there it took a long time for him to come up with an original idea that could be pursued further, which should be a, somewhat comforting thought to a student faced with their first research task: it does and should take time to figure out something new.  

Research: 

After completing his PhD, Yvain spent time as a postdoc under the aforementioned Martin Hairer, with the aim of systematically solving a large class of equations derived from physics. Initially he intended to stick to his own field, however an opportunity presented itself to collaborate on a paper in numerical analysis. To do this, he needed to translate his techniques intended for the field of stochastics into a different context. What they were working on was fairly abstract (approximations to solutions of dispersive equations, to be exact), but his collaborator was very skilled at creating simulations to apply what they had found to more tangible situations. This showed him a “different direction” to what he had previously been considering career wise and that contributing to other branches of mathematics was possible. He recommends, as much as it’s nice to have a plan, keeping an open mind, as a chance meeting at a conference, or even perhaps the idea of a student, can set you working on something you would never expect.  

Teaching or research? 

Yvain says that research is his main focus, but teaching has its own benefits. For example, when teaching less-advanced courses he can present them in more interesting and intuitive manners due to his greater experience and knowledge. However, in having to explain concepts and ideas to students just starting out in their degrees he has to be much more careful and thorough than when teaching students more familiar with the subject matter; this reinforces his own knowledge and improves his teaching ability.

He also finds teaching the latter year’s students interesting, as due to their more advanced knowledge he can go further and even explain some of his own research. This can be beneficial for reaffirming his ideas and even potentially seeing a new perspective on them through the students he teaches.