Inria Awards 2012

Isabelle Bellin -

Pierre-Louis Lions : Grand Prize Inria

© Collège de France / Photo Patrick Imbert

The scientific influence of Pierre-Louis Lions, an exceptionally gifted and active mathematician, covers the worlds of academe, industry and commerce. For 30 years, he has generated highly original ideas in numerous domains such as mathematics, physics, economics, and industrial digital simulation. His theories have been adopted by many scientists, both theoretical and applied mathematicians.

“Absolutely do not study mathematics,” his father Jacques-Louis Lions advised him. Jacques-Louis was a respected mathematician, the first chairman of Iria (Inria’s predecessor) in 1980, and aware of the difficulties of being ‘the son of’. “He was reassured when I said I wanted to be an engineer, and then hoped I would study at Polytechnique,” Pierre-Louis Lions recalls. “But, during the preparatory classes, mathematics was the only thing that interested me.” As his father before him, he enters the Ecole normale supérieure (ENS). Even worse, he also wants to explore computer science. “I admit that I was very contrarian. With hindsight, I understand that my father inadvertently pushed me toward mathematics.” All things considered, Jacques-Louis did the right thing!

Being extremely curious, Pierre-Louis Lions has always wanted to know what use can be made of mathematics. Early on, he had a flair for finding the right subjects. At the ENS, he worked on mathematical modeling of queues to assess network performance. This led him to write a thesis on probabilities. “My first decisive encounter was with a book,” he says, “a book on analysis and applied mathematics from which I developed my first ideas.” After that it all happened very fast, driven by a constant desire to solve scientific problems presenting a mathematical basis, in an industrial context – thus connecting with his initial dream of being an engineer. At the age of 23, he successfully optimised an ultracentrifuge, increasing its output by 12%. “I was lucky enough to start with a success,” he notes simply. He calls mathematics a solitary sport for sluggards! He admits his work has touched almost all industrial sectors.

“I have always spent about a third of my time on problems in an industrial context, be it for image processing, physics, chemistry, space transport, or finance,” he says. “Industrial leaders are eager to find mathematicians likely to be interested in their particular challenges.” He develops his theories in response to his various encounters. Always meeting with success and questioning the normal models, in particular as regards modeling and mathematical proof. His abstrusely named theories (partial differential equation viscosity solutions, concentration-compactness method, Di Perna Lions technique, etc.) have created dynamics adopted by many scientists all over the world. Most of the French research groups he has launched are among the highest ranking worldwide.

For this indefatigable disseminator of ideas, teaching is at the heart of the researcher’s profession. Aged 25, he started lecturing at Paris-Dauphine University; a bold choice that yet again underlines his openness to the worlds of business, management and economics, domains about which he knew nothing. “With a student body that is not really mathematically inclined,” he adds, “the experience is all the more interesting.” It is completely different from the students of Polytechnique, where he has lectured in applied mathematics since 1992, or from the researchers at Collège de France who have attended his lectures for ten years now. He also lectures at several foreign universities and regularly participates in international symposiums.

“The common denominator of all my research is mathematics and analysis,” he concludes. “As for the rest, I am just as happy understanding a mathematical problem as I am an industrial one.” If a project does not amuse him and if it is not new, he turns it down. Something he did when Jean-Michel Lasry, a colleague at Dauphine, suggested he work on a financial mathematics problem, a problem Lions thought he already understood. He changed his mind and ended up discovering Monte-Carlo simulations, a statistical approach to risk. Jointly Lasry and Lions developed the theory of mean field games, likely to revolutionise several scientific domains, such as physics, biology, and economics. In 2009, they created MFG Labs, one of the few French start-ups in the field of applied mathematics. The company already employs a very young team of 20 people, all working on promising algorithms with numerous possible applications for finance and commodity price modeling, for instance. A year ago, applications on the Internet, mainly via social networks, became increasingly frequent. The young recruits are independent minded and develop their own algorithms with the guidance of their two elders.

He is very proud to receive this Grand Prize following Gérard Huet, who was awarded the prize in 2011. It reminds him of his father and brings him closer to the institute he so vehemently avoided at the outset of his career. Since his friend Bernard Larrouturou became chairman in 1996, things have changed completely. “I accepted, upon his urging, to chair the Inria assessment committee”, he says, “and I discovered Inria, in my opinion one of the best French research institutions, if not the best.” Pierre-Louis Lions has received many awards throughout his rich career, including the prestigious Fields Award in 1994, the top award for applied mathematics. This Inria Grand Prize particularly moves him as a token of his colleagues’ recognition. No doubt his father, deceased in 2001, with whom he always avoided discussing mathematics, would have appreciated the event. Pierre-Louis is well and truly a mathematician!

Statements

Jean-Michel Lasry, former professor at Paris-Dauphine University, a specialist in financial mathematics, creator with Pierre-Louis Lions of the mean field games theory and of MFG Labs

“Among the world-renowned mathematicians who have lectured at Paris-Dauphine University, Pierre-Louis Lions stands out as an exception. He made substantial contributions to the department’s excellence in terms of applied economic mathematics. Being specialists in the same domain, we have been exploring financial mathematics together since I joined the world of finance in the early 1990s. Notably, we applied the Malliavin calculus to finance, thus opening up for a very wide field of research and applications, and we invented the mean field games theory. The latter inspired us to create the start-up MFG Labs. This theory makes it possible to model the behavior of an infinite number of players or agents by using a continuum approximation. MFG Labs carries out studies and research in the financial domain, on behalf of industrial research centres and this past year for social networks. As regards the latter, we discovered that our algorithms can improve contact building, for instance as a function of personal tastes.”

Claude Le Bris, researcher at CERMICS, a laboratory at Ecole nationale des ponts et chaussées, manager of the Micmac research team at Inria Paris-Rocquencourt, thesis student under the supervision of Pierre-Louis Lions

“Beyond his exceptional scientific qualities and his impressive intellectual powers, it is the variety of the subjects covered by Pierre-Louis Lions that is, in my view, exceptionally rare. As my thesis advisor (from 1990 to 1993), he shared with me, as with all his students, his curiosity and interest for practical problems as sources for research topics. We continued to work together and, to date, we have written 20 articles and a book together. I am always impressed by his methodological progress and his inventiveness in terms of mathematical analysis techniques, which solve problems and offer new digital simulation techniques. Pierre-Louis has enormously widened the field of interest of the community of applied mathematicians, for instance by considering possible chemical applications.”

Keywords: Inria Awards 2012 Pierre-Louis Lions Grand Prize Inria

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