Lars Hörmander

1931–2012, Mjällby, Sweden, Lund, Sweden

Differential equations and dynamical systemsAnalysisFields Medal 1962Wolf Prize in Mathematics 1988

Swedish mathematician who created the modern theory of linear partial differential equations and founded microlocal analysis; Fields Medal 1962, Wolf Prize 1988.

Lars Hörmander was born in Mjällby in southern Sweden and studied at Lund University, where he earned his doctorate in 1955 under Marcel Riesz and Lars Gårding with a thesis on the theory of general partial differential operators. His early work established fundamental existence theorems and the characterization of hypoelliptic constant-coefficient operators, bringing order to a field that had consisted largely of case-by-case results for elliptic, parabolic and hyperbolic equations.

After professorships at Stockholm University and Stanford University, and a period at the Institute for Advanced Study in Princeton, Hörmander returned to Lund in 1968, where he remained for the rest of his career. His four-volume treatise "The Analysis of Linear Partial Differential Operators" (1983–1985) codified the machinery of pseudodifferential and Fourier integral operators — developed with his student Johannes Sjöstrand and building on work of Maslov and others — that is now called microlocal analysis. He also made decisive contributions to several complex variables, introducing weighted $L^2$ methods for the $\bar\partial$ problem, and to scattering theory and the study of oscillatory integrals.

Hörmander received the Fields Medal in 1962 and the Wolf Prize in 1988. Known for an austere, complete style of exposition, he trained a generation of analysts at Lund and is widely regarded as the leading figure of twentieth-century linear PDE theory.

Workplaces: Lund University, Stockholm University, Institute for Advanced Study

Sweden

Award-winning work

Fields Medal 1962Awarded for his fundamental work on the theory of linear partial differential equations. Hörmander determined which constant-coefficient operators admit fundamental solutions and proved precise existence and regularity theorems for linear PDEs, building a systematic theory in a field where results had previously depended on the type of the operator. His methods introduced Fourier-analytic and functional-analytic techniques — a priori estimates and weighted

L^2

spaces — that later became the core of microlocal analysis. This work unified and greatly extended earlier results of Malgrange and Ehrenpreis and set the agenda of PDE theory for decades.

Contributions, linked to the library

Library topicLinear differential equationsCreated the systematic theory of linear partial differential operators, from fundamental solutions to hypoellipticity.