Yves Meyer, Professor Emeritus at École Normale Supérieure de Cachan, France, has been selected for the 2010 Gauss Prize for fundamental contributions to number theory, operator theory and harmonic analysis, and his pivotal role in the development of wavelets and multiresolution analysis.
Meyer has made fundamental contribution to a number of mathematical areas. Around 1970, he developed the theory of model sets in number theory, which has become an important tool in the mathematical study of quasicrystals — space-filling structures that are ordered but lack translational symmetry — and aperiodic order in general. Together with Ronald Coifman and Alan MacIntosh he proved the continuity of the Cauchy integral operator on all Lipschitz curves, a long-standing problem in analysis.
Meyer played a leading role in the modern development of wavelet theory, which has had a spectacular impact in information sciences, statistics and technology. Fourier analysis is a universal tool in applied mathematics, and due in a large measure to Meyer’s work, wavelet theory has become the new name for Fourier analysis. He constructed the first non-trivial wavelet bases and wavepackets that dramatically extended the expressing power of wavelets. This led to many applications in practice – in image processing, data compression, statistical data analysis and elsewhere. Among the many applications of Meyer’s work, the techniques for restoring satellite images and the image compression standard JPEG-2000 deserve particular mention.
More recently, he has found a surprising connection between his early work on the model sets used to construct quasicrystals — the ‘Meyer Sets’ — and ‘compressed sensing’, a technique used for acquiring and reconstructing a signal utilizing the prior knowledge that it is sparse or compressible. Based on this he has developed a new algorithm for image processing. A version of such an algorithm has been installed in the space mission Herschel of the European Space Agency (ESA), which is aimed at providing images of the oldest and coldest stars in the universe.
Yves Meyer was born on July 19, 1939. He graduated from École Normale Supérieure, Paris, in 1960 and became a high school teacher until 1963. He then obtained a teaching assistantship at Université de Strasbourg from where he obtained his Ph. D. in 1966. He was his own thesis supervisor, which, according to him, was not uncommon those days. He has been a professor at École Polytechnique, Université Paris-Dauphine and has also held a full research position at Centre National de la Recherche Scientifique (CNRS). His current position as Professor Emeritus at École Normale Supérieure de Cachan, France, comes after having served as a professor during 1999-2009 at the same institution. He is a foreign honorary member of the American Academy of Arts and Sciences. He has also been awarded a Doctorate (Honoris causa) by Universidad Autonoma de Madrid.
Email: Yves.Meyer at cmla.ens-cachan.fr
Mailing address: ENS Cachan, 61, avenue du President Wilson, 94235 Cachan cedex, FRANCE