Mathematician Martin Leguil Honored with the Lounsbery 250 Years Award

The winners of the Lounsbery 250 Years award were announced at a bilateral symposium held on May 20 and 21, 2026, by the French Academy of Sciences and the National Academy of Sciences (United States) to celebrate 250 years of scientific cooperation since the American Revolution. Martin Leguil is among them. It was at École Polytechnique, where he is now Monge Professor, that his career path began.

“I was already very interested in math when I entered École Polytechnique. My professors advised me to do my third-year internship at the National Institute of Pure and Applied Mathematics in Brazil, and that’s where I discovered what research was all about,” recalls Martin Leguil.

Mathematician Harold Rosenberg introduced him specifically to Artur Avila, who would go on to receive the Fields Medal in 2014. Upon returning to France, Martin Leguil completed his thesis under Avila’s supervision, as well as that of Julie Déserti, at Université Paris-Cité (formerly Paris 7).

His field of research is dynamical systems. Take a law of evolution such as the law of gravitation, which describes the trajectories of celestial bodies based on the position and velocity of the planets (the initial conditions). The goal is to determine the properties of motion over the long term—often complex, with unstable or chaotic trajectories.

Understanding chaotic dynamic systems 

One of the pioneers in this field of research, which is relatively new in the history of mathematics, is another alumnus and professor at École Polytechnique, Henri Poincaré, who focused in particular on the stability of the orbits of the planets in the solar system.

“One of the things I like about dynamics is that it’s a field that interacts with many other branches of mathematics, such as number theory or geometry,” explains Martin Leguil.

Together with his collaborators, including Davi Obata, a professor at Brigham Young University in the United States, he focuses specifically on so-called “partially hyperbolic” dynamical systems. These systems exhibit a combination of stable, unstable, and neutral behaviors. They model real-world situations where long-term predictions are difficult due to their sensitivity to initial conditions.

A central objective is to determine in which cases the statistical properties of these systems can be well described by a limited number of invariant probability measures, capable of accounting for the behavior of most initial conditions. This question is directly linked to a major conjecture formulated by the Brazilian mathematician Jacob Palis.

The Lounsbery 250 Years Award will enable Martin Leguil and his colleagues to deepen their collaboration on this topic.

*CMLS: a joint research unit CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France