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Lars Hörmander | |
|---|---|
 Hörmander in 1969 | |
| Born | Lars Valter Hörmander (1931-01-24)24 January 1931 |
| Died | 25 November 2012(2012-11-25) (aged 81) |
| Alma mater | Lund University |
| Known for | Theory of linearpartial differential equations, hyperbolic partialdifferential operators, the development ofpseudo-differential operators andFourier integral operators as fundamental tools |
| Awards | Leroy P. Steele Prize (2006) Wolf Prize (1988) Fields Medal (1962) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Stockholm University Stanford University Institute for Advanced Study Lund University |
| Thesis | On the theory of general partial differential operators (1955) |
| Doctoral advisor | Marcel Riesz Lars Gårding |
| Doctoral students | Germund Dahlquist Nils Dencker |
Lars Valter Hörmander (24 January 1931 – 25 November 2012) was aSwedishmathematician who has been called "the foremost contributor to the modern theory of linearpartial differential equations".[1] Hörmander was awarded theFields Medal in 1962 and theWolf Prize in 1988. In 2006 he was awarded theSteele Prize for Mathematical Exposition for his four-volume textbookAnalysis of Linear Partial Differential Operators, which is considered a foundational work on the subject.[2]
Hörmander completed hisPh.D. in 1955 atLund University. Hörmander then worked atStockholm University, atStanford University, and at theInstitute for Advanced Study inPrinceton, New Jersey. He returned to Lund University as a professor from 1968 until 1996, when he retired with the title ofprofessor emeritus.
Hörmander was born inMjällby, a village inBlekinge in southern Sweden where his father was a teacher. Like his older brothers and sisters before him, he attended therealskola (secondary school), in a nearby town to which he commuted by train, and thegymnasium (high school) inLund from which he graduated in 1948.
At the time when he entered the gymnasium, the principal had instituted an experiment of reducing the period of the education from three to two years, and the daily activities to three hours. This freedom to work on his own, "[greater] than the universities offer in Sweden today", suited Hörmander "very well". He was also positively influenced by his enthusiastic mathematics teacher, adocent atLund University who encouraged him to study university-level mathematics.
After proceeding to receive aMaster's degree from Lund University in 1950, Hörmander began his graduate studies underMarcel Riesz (who had also been the advisor for Hörmander's gymnasium teacher). He made his first research attempts in classical function theory andharmonic analysis, which "did not amount to much" but were "an excellent preparation for working in the theory of partial differential equations." He turned to partial differential equations when Riesz retired andLars Gårding who worked actively in that area was appointed professor.
Hörmander took a one-year break formilitary service from 1953 to 1954, but due to his position in defense research was able to proceed with his studies even during that time. HisPh.D. thesisOn the theory of general partial differential operators was finished in 1955, inspired by the nearly concurrent Ph.D. work of Bernard Malgrange and techniques for hyperbolic differential operators developed byLars Gårding andJean Leray.
Hörmander applied for a professorship atStockholm University, but temporarily left for theUnited States while the request was examined. He spent quarters from winter to fall in respective order at theUniversity of Chicago, theUniversity of Kansas, theUniversity of Minnesota, and finally at theCourant Institute of Mathematical Sciences inNew York City. These locations offered "much to learn" in partial differential equations, with the exception of Chicago of which he however notes theAntoni Zygmund seminar held byElias Stein andGuido Weiss to have strengthened his familiarity with harmonic analysis.
In the theory of linear differential operators, "many people have contributed but the deepest and most significant results are due to Hörmander", according to Hörmander's doctoral advisor, Lars Gårding.[2] Hörmander won theFields Medal in 1962.[3]
Hörmander was given a position as a part-time professor at Stanford in 1963 but was soon thereafter offered a professorship at theInstitute for Advanced Study in Princeton, New Jersey. He first wished not to leave Sweden but attempts to find a research professorship in Sweden failed and "the opportunity to do research full time in a mathematically very active environment was hard to resist", so he accepted the offer and resigned from both Stanford and Stockholm and began at the Institute in the fall of 1964. Within two years of "hard work", he felt that the environment at the institute was too demanding, and in 1967 decided to return to Lund after one year. He later noted that his best work at the institute was done during the remaining year.
Hörmander mostly remained atLund University as a professor after 1968 but made several visits to the United States during the two next decades. He visited the Courant Institute in 1970, and also the Institute for Advanced Study in 1971 and during the academic year, 1977–1978 when a special year inmicrolocal analysis was held. He also visited Stanford in 1971, 1977, and 1982, and theUniversity of California, San Diego in winter 1990. Hörmander was briefly director of theMittag-Leffler Institute in Stockholm between 1984 and 1986 but only accepted a two-year appointment as he "suspected that the administrative duties would not agree well" with him, and found that "the hunch was right". He also served as vice president of theInternational Mathematical Union between 1987 and 1990. Hörmander retiredemeritus in Lund in January 1996. In 2006 he was honored with theSteele Prize for Mathematical Exposition from theAmerican Mathematical Society.
He was made a member of theRoyal Swedish Academy of Sciences in 1968. In 1970 he gave a plenary address (Linear Differential Operators) at theICM inNice.
He received the 1988Wolf Prize "for fundamental work in modern analysis, in particular, the application ofpseudo differential andFourier integral operators to linear partial differential equations".[3]
In 2012 he was selected as a fellow of theAmerican Mathematical Society, but died on 25 November 2012,[4] before the list of fellows was released.[5]
His bookLinear Partial Differential Operators, which largely was the cause for his Fields Medal, has been described as "the first major account of this theory". It was published bySpringer-Verlag in 1963 as part of theGrundlehren series. In the U.S., this book is now in the public domain and reprints are available under ISBN 978-1014977045.
Hörmander devoted five years to compiling the four-volumemonograph,The Analysis of Linear Partial Differential Operators, first published between 1983 and 1985. A follow-up of hisLinear Partial Differential Operators, "illustrate[d] the vast expansion of the subject"[4] over the past 20 years, and is considered the "standard of the field".[5] In addition to these works, he has written a recognised introduction toseveral complex variables based on his 1964 Stanford lectures, and wrote the entries ondifferential equations inNationalencyklopedin.
