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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

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

CV

ERC Advance Grant 

 

Publications

Smooth type II blow-up solutions to the four-dimensional energy-critical wave equation
M Hillairet, P Raphaël
– Analysis & PDE
(2012)
5,
777
Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
F Merle, P Raphaël, I Rodnianski
– Inventiones Mathematicae
(2012)
193,
249
Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
P Raphaël, I Rodnianski
– Publications mathématiques de l'IHÉS
(2012)
115,
1
Orbital stability of spherical galactic models
M Lemou, F Méhats, P Raphaël
– Inventiones Mathematicae
(2011)
187,
145
A New Variational Approach to the Stability of Gravitational Systems
M Lemou, F Méhats, P Raphaël
– Communications in Mathematical Physics
(2011)
302,
161
Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS
P Raphaël, J Szeftel
– Journal of the American Mathematical Society
(2010)
24,
471
Stable Self-Similar Blow-Up Dynamics for Slightly L 2 Super-Critical Nls Equations
F Merle, P Raphaël, J Szeftel
– Geometric and Functional Analysis
(2010)
20,
1028
Two‐soliton solutions to the three‐dimensional gravitational Hartree equation
J Krieger, P Raphaël, Y Martel
– Communications on Pure and Applied Mathematics
(2009)
62,
1501
Rough blowup solutions to the L 2 critical NLS
J Colliander, P Raphaël
– Mathematische Annalen
(2009)
345,
307
Standing Ring Blow up Solutions to the N-Dimensional Quintic Nonlinear Schrödinger Equation
P Raphaël, J Szeftel
– Communications in Mathematical Physics
(2009)
290,
973
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Research Group

Analysis & Partial Differential Equations

Room

E2.03

Telephone

01223 764288