SINGULARITY FORMATION FOR NONLINEAR PDES ST CATHARINE’S COLLEGE, 9-12 SEPTEMBER 2024

Current research interests

My works lie at the border of physics and mathematics. I am interested in the study of nonlinear waves, and in particular extreme regimes leading to concentration of energy mechanisms, and possibly the formation of singularities. These phenomenons are deeply connected to the study of fundamental nonlinear structures which occur in electromagnetism, astrophysics and turbulent fluid flows.

University positions

Herchel Smith Professor of Pure Mathematics at the Department of Pure Mathematics and Mathematical Statistics

Biography

Pierre Raphaël is the Herchel Smith Professor of Pure Mathematics. His research lies at the border between physics and pure mathematics, and aims in particular at understanding energy concentration mechanisms and singularity formation during the propagation of non-linear waves. After graduating from École Polytechnique (France), he received his PhD in Mathematics from the University of Cergy-Pontoise, and moved to Princeton (USA) as an Assistant Professor. He returned to France as the principal investigator of several European grants, and joined Cambridge’s Department of Pure Mathematics and Mathematical Statistics in 2019. He was invited to the International Congress of Mathematicians in 2014, received the Grand Prix Alexandre Joannides 2014 from the French Academy of Sciences and a Royal Society Wolfson Fellowship in 2019. His works on singularity formation for viscous compressible fluid equations (2022) have led to the discovery of new unsuspected blow up mechanisms for defocusing wave equation and opened a path towards the resolution of the Navier Stokes Clay problem, and for these he received jointly with his collaborators (Merle, Rodnianski and Szfeftel) the Clay research award (2023) and the memorial Bocher Prize (2023).

CV

ERC Advance Grant 

Part III Class Notes

Introduction to non linear analysis