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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 



On blow up for the energy super critical defocusing {nonlinear Schr\"odinger equations
P Raphael, F Merle, I Rodnianski, J Szeftel
On the implosion of a three dimensional compressible fluid
P Raphael, F Merle, I Rodnianski, J Szeftel
Strongly anisotropic type II blow up at an isolated point
C Collot, F Merle, P Raphaël
– Journal of the American Mathematical Society
On melting and freezing for the 2D radial Stefan problem
M Hadžić, P Raphaël
– Journal of the European Mathematical Society
On the Stability of Type I Blow Up For the Energy Super Critical Heat Equation
C Collot, P Raphaël, J Szeftel
A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line
P Gérard, E Lenzmann, O Pocovnicu, P Raphaël
– Annals of PDE
On small traveling waves to the mass critical fractional NLS
I Naumkin, P Raphaël
– Calculus of Variations and Partial Differential Equations
Strongly interacting blow up bubbles for the mass critical nonlinear Schrödinger equation
Yvan Martel, Pierre Raphaël
– Annales Scientifiques de l École Normale Supérieure
Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions
C Collot, F Merle, P Raphaël
– Communications in Mathematical Physics
Minimal mass blow up solutions for a double power nonlinear Schrödinger equation
S Le Coz, Y Martel, P Raphaël
– Revista Matemática Iberoamericana
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Research Group

Analysis & Partial Differential Equations




01223 764288