Charles L. Fefferman
Charles Louis Fefferman is Full Professor at Princeton University. He was born in 1949 in Silver Spring, Maryland, USA. In 1966, he received his bachelor's degrees in physics and mathematics from the University of Maryland and, three years later, a PhD in mathematics from Princeton University under the supervision of Elias Stein. In 1971, Fefferman received full professorship at the University of Chicago. He returned three years later to Princeton.
Among the honors and prizes received along his career are the Alan T. Waterman Award in 1976 (the first mathematician to get the award) and the Fields medal at the International Congress of Mathematicians at Helsinki in 1978. Other honors are the Salem Prize, the Bôcher Prize, and the Bergman Prize.
Fefferman's research has had a great impact in many fields: mathematical analysis, partial differential equations, Fourier analysis, mathematical physics, fluid dynamics, neural networks and differential geometry.
The research proposal for the CSIC Lab at the ICMat is a joint project with the team lead by Prof. Diego Córdoba and funded by the research project ”Contour dynamics and singularities in incompressible flows”, European Research Council, Starting Grants, CSIC, 2008-2013.
The research is focussed in solving problems of ﬂuid mechanics which involve the possible formation and propagation of singularities. For this purpose several physical scenarios of interest from a mathematical point of view are presented. Those scenarios have well-known applications too. It is an enormous challenge to approach these problems. For this matter the combination of analytic techniques, asymptotics, numerics and modelling is required.
With the more sophisticated numerical tools now available, the subject has recently gained considerable momentum. The major theme of work is the interplay between computer calculations and rigorous mathematics. Numerical computations are used as a part of rigorous proofs and the production of computer-assisted proofs for the formation of a singularity in fluid mechanics is proposed.
An additional goal of this project is the involvement of undergraduates, grad students and postdocs.
Recent work by Charles Fefferman and his collaborators at ICMat:
Castro, A., Córdoba, D., Fefferman, C.L. and Gancedo, F. “Breakdown of smoothness for the Muskat problem” (2011).
Castro, A., Córdoba, D., Fefferman, C.L., Gancedo, F. and Gómez-Serrano, J. “Finite time singularities for the free boundary incompressible Euler equations”. Preprint,arXiv:1106.2120 (2011).
Castro, A., Córdoba, D., Fefferman, C.L., Gancedo, F. and López-Fernández, M. “Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves”. To appear in Annals of Math. arXiv:1102.1902 (2011).
Castro, A., Córdoba, D., Fefferman, C.L., Gancedo, F. and Gómez-Serrano, J. “Splash Singularities for water waves” To appear in Proceedings of the National Academy of Sciences. Preprint, arXiv:1106.2120 (2011).
Castro, A., Córdoba, D., Fefferman, C.L., Gancedo, F. and López-Fernández, M. Turning waves and breakdown for incompressible ﬂows, Proceedings of the National Academy of Sciences, 108 (12) (2011), 4754–4759.