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Researchers of l’X at the International Congress of Mathematicians in Brazil

Four École Polytechnique researchers have been invited to the International Congress of Mathematicians (ICM) to present the results of their work. This year, the Congress will take place in Rio de Janeiro, Brazil, from August 1st till August 9th.

The International Congress of Mathematicians gathers every four years more than 4 000 mathematicians coming from all over the world. The Fields Medalists will be announced and around 100 selected researchers will expose the results of their work. Four researchers of École Polytechnique are invited to present their work at the ICM: Sébastien Boucksom and Yvan Martel from the Laurent Schwartz Mathematics Center, Joris van der Hoeven from the Computer Science Laboratory and Josselin Garnier from the Center for Applied Mathematics.

About their research:

Sébastien Boucksom’s work focuses on fundamental aspects of geometry, and more precisely on the construction of Kähler-Einstein metrics in complex geometry. He recently gave a new proof of the famous Yau-Tian-Donaldson conjecture using original methods based on non-Archimedean geometry. 

Yvan Martel is working on the theoretical study of universal equations of Physics such that the Schrödinger, the Korteweg-de Vries and the wave equations, with a particular emphasis on the description of the qualitative behavior of the solutions in large time. He constructed blowup solutions for critical models and proved results of inelasticity of collision of solitary waves.

Joris van der Hoeven studies strongly monotonic asymptotic solutions of ordinary differential equations. From an analytical perspective, such solutions belong to Hardy fields ; formally speaking, they can be modeled by transseries. With Matthias Aschenbrenner and Lou van den Dries, he isco-author of the book Asymptotic Differential Algebra and Model Theory of Transseries(Karp Prize 2018) in which they prove a quantifier elimination result for asymptotic differential equations.

Josselin Garnier is interested by the modelling of random phenomena. His research focuses on several aspects of the probability theory, especially wave propagation and imaging in random media, uncertainty quantification and stochastic algorithms. Recently, he introduced and studied new methods of imaging using signals transmitted by opportunistic or ambient noise sources.