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Faculty of Mathematics


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


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, and was awarded the Grand Prix Alexandre Joannides 2014 from the French Academy of Sciences and a Royal Society Wolfson Fellowship in 2019.


ERC Advance Grant 



Blow up of the critical norm for some radial L2 super critical nonlinear Schrödinger equations
F Merle, P Raphäel
– American Journal of Mathematics
Stable self-similar blow up dynamics for the three dimensional relativistic gravitational Vlasov-Poisson system
M Lemou, F Méhats, P Raphaël
– Journal of the American Mathematical Society
Existence and stability of a solution blowing up on a sphere for an $L^2$-supercritical nonlinear Schrödinger equation
P Raphaël
– Duke Mathematical Journal
Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation
P Raphael
– Mathematische Annalen
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
F Merle, P Raphaël
– Annals of Mathematics
Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schrödinger Equation
F Merle, P Raphael
– Communications in Mathematical Physics
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
F Merle, P Raphael
– Geometric And Functional Analysis
On universality of blow-up profile for L2 critical nonlinear Schrödinger equation
P Raphael, F merle, P Raphael
– Inventiones Mathematicae
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Research Group

Analysis & Partial Differential Equations




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