Mathematics

© J.-F. Dars/CNRS Photothèque

We arrange to meet in the heart of Paris, a stone's throw from the Ecole Normale Supérieure, one of his headquarters when he's not “in the countryside,”–i.e., at his lab in Orsay.^{1} With his little spectacles and tousled, curly hair, Wendelin Werner could easily be mistaken for one of his own PhD students. However, at the age of 38, he is the most recent recipient of the highly respected Fields Medal, awarded to mathematicians under the age of forty. This is the first time the medal is awarded to a probabilist. It's an acknowledgment of his entire work on random walks and Brownian motion,^{2} which model many physical phenomena.

“The image of probability theory has changed, so it was natural for the medal to be awarded in this field,” he explains, deflecting personal credit for such an honor. And he immediately adds, “it feels strange to win this prize, because others before me certainly deserved it just as much.” It's his way of paying tribute to other scientists including his two US-based associates Greg Lawler and Oded Schramm. In a seven-year long-distance collaboration, they physically met up only four times. But they have still been able to jointly publish several seminal papers which confirm predictions made by physicists based on “conformal field theory.”^{3} “The trick was to combine several tools from probability theory and complex analysis.” Werner appears disarmingly straightforward, whether describing a random trajectory or his own path through life. He has never questioned his own love of math, not even as a highschool student when he landed a part in a Jacques Rouffio film, alongside actress Romy Schneider. Does he wish he'd pursued a career in cinema? “No, although it was a great experience and I received offers to work in other films, I wasn't happy with that change in direction. And it was already clear to me at that time that I would rather pursue a scientific career.”

Born into a German family with literary leanings, he arrived in

But any clichés about mathematicians being locked away in ivory towers alone with their equations can be cast aside, as proven by his productive collaboration where “three minds work together,” or his active participation in seminars. “Nonetheless, I like to be on my own to think. I can work anywhere, in my office, in a café, in a train, or at the airport.” The subjects he applies himself to are often familiar to theoretical physicists. “They tackled and solved a number of problems well before we did, but by playing according to different rules. Essentially, we are trying to understand random phenomena, which are complicated since they derive from a range of tiny random contributions that together make up a macroscopic phenomenon. An example would be the random form of clouds caused by the condensation of tiny particles.”

To describe such so-called “critical temperature” systems–the temperature at which a given medium changes from one physical state to another–the interfaces between the spaces of the different phases need to be described. “At a mathematical level, we described the interfaces in the plane as well as their properties, and proved the physicists' predictions. Our advantage was that we could offer them tools and a new approach to these phenomena. And we feel lucky that they requested our help.”

As in other fields, peer review is the rule for mathematicians. Therefore, Werner and his colleagues spend a lot of time editing journals, supervising PhD students, writing reports, and taking part in commissions, all “as objectively as possible.” Mathematics is first and foremost an intellectual challenge, where competition for funds or grants matters very little. So, what's the secret to being a good mathematician? “There are many ways of being proficient. You have to find the right fit between the context, the subject, and the way you tackle it.” Something that he does with great inspiration, according to his colleagues.

Patricia Chairopoulos

1. Département de mathématiques et applications (DMA) (CNRS/Ecole normale supérieure joint lab).

2. This is the random movement of particles which are subject to no interactions other than collisions between one another like pollen grains in a liquid.

3. This unifying language makes it possible to describe systems made up of a large number of interacting components.

> Wendelin Werner

Laboratoire de Mathématiques, Orsay

wendelin.werner@math.u-psud.fr

> www.math.u-psud.fr/~werner/

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