The idle ramblings of a Jack of some trades, Master of none

In August this year, Seoul will host the latest International Congress of Mathematicians. It's that quadrennial time when gossips begin to natter about Fields Medallists. A lot of people are talking up Manjul Bhargava. It is his last chance to win - by the time the next ICM comes around he will be older than 40. I'm hoping at least one woman will be awarded the prize this time.

In the run-up to the last ICM (in Hyderabad), I'd blogged about potential candidates for that year. None of them won. I hope to profile a few new names ahead of this year's ICM.

One that has popped up (new to me, at least) is Laure Saint-Raymond. Here is a loose translation of an interview that appeared a few days ago in Le Journal: "Laure Saint-Raymond, la boss des maths", by Louise Mussat (April 28, 2014).

Elected to the Academy of Sciences in December 2013, this top-flight researcher will participate at the International Congress of Mathematicians in Seoul in August.

The blackboard that stretches across one of the walls of her office at the École normale supérieure (ENS) is whitened by clouds of intertwined mysterious symbols. These are equations, and they are unsurprising - Laure Saint-Raymond is a mathematician, a pearl in
her field of partial differential equations applied to problems of physics. A winner of the European Mathematical Society's Prize in 2008 and of the Joliot-Curie "Young Woman Scientist" award in 2011, she was elected to the Academy of Sciences when she was 38 years old, the youngest ever. And in August she will present a lecture in Seoul at the ICM, an unmissable event that attracts thousands of mathematicians every four years, during which the famous Fields medals are awarded.

Stratospheric Research

What does the daily life of a top mathematician look like? Wracking one's brains before a sheet of blank paper before scribbling equations on a blackboard? "Not exactly!" says this energetic researcher, smiling. "I spend a lot of time teaching, attending seminars, trawling the literature to help me keep abreast of what is happening, and communicating the results of my own research. But thinking in front of a blackboard is part of my work, and most of the time it's with my team. It's the creative phase, a mutual game during which we sometimes find nothing or sometimes not what we were looking for!"

What Laure Saint-Raymond seeks with her collaborators is to capture physical phenomena with mathematics. "My training in physics helps me to better understand the language of physicists and exchange ideas and develop an intuition for the phenomena we are trying to describe," she says. That was the year she graduated with a degree in applied mathematics from the University of Paris VI, the same year she obtained her degree in plasma physics.

All these strings to her bow have enabled her to tackle a tricky problem, first posed in 1900 and still unresolved: how does one effect a transition from a physical model to another, less complex and less precise? The scientist explains, "When we are in the presence of a rarefied gas, for example in the Earth's upper atmosphere, and we want to simulate the re-entry of a spacecraft, we use the so-called kinetic theory in which the state of the gas is characterised by a function of several variables, such as time as well as the positions of the atoms." Meanwhile, to describe the behaviour of gases around us, infinitely denser in atoms, it suffices to use a model wherein all the atoms are considered as a single continuous medium.

"What interests me is to understand how one moves from one to the other of these models: is there a smooth transition or, on the contrary, is there a discontinuity between the two descriptions which renders them both invalid in the intermediate regime?" says Laure Saint-Raymond.

Fundamental and stratospheric, this mathematics nevertheless has some physical applications: they allow us to understand better the entanglement phenomena at diferent scales of time and space, and to better account for the observed air flow around an aircraft, for example, or the formation of persistent whirlpools in the ocean.

From the Cello to the Sciences

Laure Saint-Raymond readily admits: as a child or a teenager, she had no particular attraction for mathematics. Her main thing was the cello. Then in high school, equations finally overcame the scales. "I had a facility with maths and physics, and my parents, both maths teachers, undoubtedly influenced my change in direction."

As a newly-minted bachelor in mathematics, she found the arms of the engineering industry extending towards her. However, she chose research, it being "intellectually more stimulating". In 1994, she joined the ENS where she began work on her thesis under the supervision of François Golse on the "kinetic theory of gases". To be clear: on mathematics applied to the movements of gases. Recruited by the CNRS in 2000, she spent two years as a Research Fellow before being appointed as a professor at the University of Paris VI. In 2007, she obtained a secondment at the ENS where she was made director of the department of Analysis. Currently, she is the deputy director of the Department of Mathematics and its Applications.

An exceptional journey

Her exceptional and rapid-as-lighting journey demands respect as it has happened in a largely male-dominated universe. "That is irrelevant," she counters. "My being a woman has never been a handicap, I have never been a victim of discrimination. And to do research today, it is no easier for a boy than for a girl, it's difficult for both: young people don't obtain a job till after several years of post-doctoral work, which, in some disciplines, means they have to wait till nearly 35 years of age before they are in a stable situation and able to start a family..."

Still, says Laure Saint-Raymond, her eyes shining and with enthusiasm in her voice, the game is worth the effort. "I will no doubt make a lot more money in the industry, but one's work cannot be reduced to a mere salary. Not one of my days as a teacher-researcher is like any other, and at the ENS, I have the immense freedom to conduct research that I want to do, and I enjoy myself thoroughly. This is priceless."

When she is not playing with partial differential equations, or not coaching one of her students, or not tutoring one of her six children (five boys and one girl, aged between 4 and 14 years!), Laure Saint-Raymond escapes to the mountains. Skiing in the winter or hiking in the summer, whichever, the key is to be outdoors all the time. "I really need to recharge my batteries, to disconnect completely from work, to return to the office with new ideas," she admits, and returns to whitening her blackboard again.


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