ICIAM Lagrange Prize

October 21, 2007

For "original and profound contributions that span the most varied areas of modern science," Joseph Keller of Stan-ford University received the ICIAM Lagrange Prize in Zurich. Shown here with Juan Luis Vazquez of SEMA, which with SMAI and SIMAI sponsors the prize, Keller was honored for deep results in applied mathematics that "have had great impact in science and engineering, as well as in pure mathematics."
In particular, Keller developed the geometrical theory of diffraction, which provided the first systematic description of wave propagation around edges and corners of an obstacle. The theory has been widely applied, to radar reflection from targets, elastic wave scattering from defects in solids, acoustic wave propagation in the ocean, radar, and many other fields. It also served as a starting point for the development of the modern theory of linear partial differential equations. Keller formulated the Einstein–Brillouin–Keller method for determining energy levels of atoms and molecules in quantum mechanics and for solving characteristic value problems in other fields. As part of this work, he derived the Keller–Maslov index for the change in a wave as it passes along a caustic. He has also made important and often seminal contributions to many other fields, including singular perturbation theory, bifurcation studies in partial differential equations, nonlinear geometrical optics and acoustics, inverse scattering, effective equations for composite media, biophysics, biomechanics, carcinogenesis, optimal design, hydrodynamic surface waves, transport theory, and waves in random media.
"Keller combines a very special creativity in the development of mathematical techniques with deep physical insight," the citation concludes. "He has the ability to describe real-world problems by simple yet realistic mathematical models, to create sophisticated techniques to solve these problems and to explain the results and their consequences in simple terms. He has greatly influenced several generations of applied mathematicians, including more than 50 PhD students, many postdoctoral researchers, and a large number of co-workers."

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