# Lars Hörmander

Wolf Prize Laureate in Mathemstics 1988

**Lars Hörmander**

#### Affiliation at the time of the award:

**University of Lund, Sweden**

#### Award citation:

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

#### Prize share:

**Lars Hörmander**

**Friedrich Hirzebruch **

Professor Lars Hörmander 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). Hörmander 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 Hörmander in a masterly four volume treatise, which has become the standard of the field. Hörmander 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.