Interview with Romain Dujardin, invited speaker at ICM2022

Link to the virtual ICM 2022 talks

What is your research field?

Mainly, I study the dynamics of polynomial and rational transformations in one or more complex variables. Concretely, that means studying the asymptotic behaviour of recurrence sequences as defined by that transformation. A well-known example is Newton’s method for estimating the zeros of polynomials: their behaviour can be regular or chaotic, depending on the choice of the initial condition. This is a field with a long history that has been reinvented many times over through its encounters with other fields of mathematics. When it was founded by Fatou and Julia at the beginning of the 20th century, it was, rather, a branch of the “theory of functions”. Since the 1980s, the subject has been constantly renewed with the introduction of ever more varied and sophisticated methods in geometry and analysis. Recently, we have seen increasingly algebraic questions and methods. This broad diversity of tools, often used within one article, is something I greatly appreciate.

What brought you to mathematics?

I had a wonderful maths professor in junior high school who conveyed to us his implacable rigour and his love of solid reasoning. Of course, at that age, I had no idea that mathematical research even existed, but in view of the fact that an extraordinary proportion of my classmates took up maths as a career – including my childhood friend François Delarue who will also participate in the congress - I believe that teacher was the decisive factor!

What do you love about being a mathematician?

There are few occupations in which one is so free to do as one pleases. There are always some tedious tasks, but in general, what a pleasure! It is an immense privilege to be paid to learn new things, to think about them, and to share them with colleagues around the whole world. At a time when many are asking themselves about the utility of their work, each mathematician participates at their own level in an adventure that is greater than them.

Another fascinating aspect is the relationships that I create with my colleagues: we must have a lot of confidence to share our vague ideas, aborted attempts, and sometimes gross errors. And when colleagues have been working for a long time on a project, we’re like an old married couple, talking about things that are – literally – only understood by the two of us.

How involved are you in the transmission of ideas about mathematics to a broader audience?

I think that the dissemination of maths to the general public, pupils, and students is essential. Our scholarly community puts a lot of energy into that, but it is difficult to capture people’s attention. Myself, I participate through giving lectures for the “general public” from time to time, and I collaborate in the CNRS journal “Images des Mathématiques”; but we could certainly do more.