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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 consolidator grant SingWave

Publications

Codimension One Threshold Manifold for the Critical gKdV Equation
Y Martel, F Merle, K Nakanishi, P Raphaël
– Communications in Mathematical Physics
(2015)
342,
1075
Type II blow up for the energy supercritical NLS
F Merle, P Raphaël, I Rodnianski
– Cambridge Journal of Mathematics
(2015)
3,
439
Blow up for the critical gKdV equation. II: Minimal mass dynamics
Y Martel, F Merle, P Raphaël
– Journal of the European Mathematical Society
(2015)
17,
1855
Quantized slow blow-up dynamics for the corotational energy-critical harmonic heat flow
P Raphaël, R Schweyer
– Analysis & PDE
(2014)
7,
1713
Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton
Y Martel, F Merle, P Raphaël
– Acta Mathematica
(2014)
212,
59
On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation
F Merle, P Raphaël, J Szeftel
– Duke Mathematical Journal
(2014)
163,
369
On the stability of critical chemotactic aggregation
P Raphaël, R Schweyer
– Mathematische Annalen
(2013)
359,
267
Nondispersive solutions to the L2-critical Half-Wave Equation
J Krieger, E Lenzmann, P Raphaël
– Archive for Rational Mechanics and Analysis
(2013)
209,
61
The instability of Bourgain-Wang solutions for the L2 critical NLS
F Merle, P Raphaël, J Szeftel
– American Journal of Mathematics
(2013)
135,
967
Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow
P Raphaël, R Schweyer
– Communications on Pure and Applied Mathematics
(2012)
66,
414
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Research Group

Analysis & Partial Differential Equations

Room

E2.03

Telephone

01223 764288