THE 1988 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Prize Committee in Mathematics has unanimously decided that the 1988 Wolf Foundation Prize be equally shared by:

**Lars Hormander University of Lund Lund, Sweden**

for fundamental work in modern analysis, in particular, the application of pseudo differential and Fourier integral operators to linear partial differential equations.

Friedrich Hirzebruch

Max-Planck-Institut fuer Mathematik and

University of Bonn

Bonn, Germany

for outstanding work combining topology, algebraic and differential geometry, and algebraic number theory; and for his stimulation of mathematical cooperation and research.

For the past three and a half decades, the name of Professor Friedrich Hirzebruch has been connected with famous results in the areas of topology, algebraic geometry, and global differential geometry, results which all mark the beginning of important theories and which have had an enormous influence on the development of modern mathematics.

Hirzebruch´s achievements include (1) the discovery of the signature theorem for differentiable manifolds and the formulation and proof of the Riemann-Roch theorem for algebraic varieties, (2) the integrality theorem for characteristic classes of differentiable manifolds, (3) the proportionality theorem for complex homogeneous manifolds and (with A. Borel) the general theory of characteristic classes of homogeneous spaces of compact Lie groups, (4) complex K-theory and its spectral sequence and various geometrical applications (with M.F. Atiyah), (5) the 'topological' proof of the Dedekind reciprocity theorem through 4-manifold theory and other fascinating relations between differential topology and algebraic number theory, and (6) the systematic study of Hilbert modular-forms and-surfaces and their relation to class numbers.

Many mathematicians have expanded and generalized Hirzebruch´s ideas. He himself has always been interested in the beautiful particular case and concrete problem, which he solves by creating new methods that combine unusual geometric, algebraic, and arithmetic intuition. Moreover, through his brilliant lecturing and writing, through the “Arbeitstagung Bonn' (yearly international meetings at the highest level), and through his dedicated work in scientific organizations he has greatly stimulated world-wide cooperation in research.

Professor Lars Hormander is the foremost contributor to the modern theory of linear partial differential equations. For his early work on equations with constant coefficients he was awarded the 1962 Fields Medal, the highest honor a young mathematician can receive. Since then, he has played a leading role in the development of the modern machinery of the subject, viz. pseudodifferential operators (which combine and perfect differential and singular integral operators) and Fourier integral operators (which originate from geometrical optics). Hormander applied these new tools with striking effect; the modern view of wave fronts and their singularities provides an outstanding example of the success of these methods.

The whole development has been described by Hormander in a masterly four volume treatise, which has become the standard of the field. Hormander has also achieved notable results concerning several complex variables, the Nash-Moser implicit function theorem, scattering theory, nonlinear hyperbolic equations, etc., illustrating in these subjects also his extraordinary technical power and versatility.