- Lars Hörmander
.

**Biography****Education**Hörmander was born in

Mjällby , a village inBlekinge in southern Sweden where his father was a teacher. Like his older brothers and sisters before him, he attended the local elementary school,realskola in a nearby town to which he commuted by train, and the gymnasium (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, a

docent atLund University who encouraged him to study university level mathematics.After proceeding to receive a

Master'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 inclassical 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 for

military service from 1953 to 1954, but due to his position indefense research was able to proceed with his studies even during that time. His Ph.D. thesis "On the theory of general partial differential operators" was finished in 1955, inspired by the nearly concurrent Ph.D. work of Bernard Malgrange and techniques forhyperbolic differential operator s developed byLars Gårding andJean Leray .**Fields medal and years in the**U.S. Hörmander applied for professorship at

Stockholm 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 . 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.Full professorship at

Stockholm University was granted Hörmander in 1957. He again visited the United States in 1960 and 1961, then as a member of theInstitute for Advanced Study and in the summers as a lecturer atStanford University . He wrote the major parts of his first book on partial differential equations while at Stanford, and completed it in 1962 in Stockholm. The same year, Hörmander was "as a complete surprise" awarded theFields medal at theInternational Congress of Mathematicians which he helped organise in Stockholm.Regarding Hörmander's part in developing the general theory of linear differential operators, Lars Gårding writes that "many people have contributed but the deepest and most significant results are due to Hörmander".ref|garding

Hörmander was given a position as part time professor at Stanford in 1963, but was soon thereafter offered full professorship at the Institute for Advance Study. 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. Incidentally, he notes that his best work at the Institute was done during the remaining year.

**Later years**Hörmander mostly remained at

Lund University as 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 the winter 1990. He 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 retired emeritus in Lund in January 1996.He received the 1988

Wolf Prize "for fundamental work in modern analysis, in particular, the application of pseudo differential andFourier integral operators to linear partial differential equations".ref|wolf2**Important publications**His book "Linear 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 by Springer-Verlag in 1963 as part of the "

Grundlehren " series.Hörmander devoted five years to compiling the four-volume

monograph , "The Analysis of Linear Partial Differential Operators", first published between 1983 and 1985. A follow-up of his "Linear Partial Differential Operators", it "illustrate [d] the vast expansion of the subject" ref|auth over the past 20 years, and is considered the "standard of the field"ref|wolf3. In addition to these works, he has written a recognised introduction tomultivariate complex analysis based on his 1964 Stanford lectures, and wrote the entries ondifferential equation s inNationalencyklopedin .* "Linear Partial Differential Operators" (Springer-Verlag, 1963)

* "The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis" (Springer-Verlag)

* "The Analysis of Linear Partial Differential Operators II: Differential Operators with Constant Coefficients" (Springer-Verlag)

* "The Analysis of Linear Partial Differential Operators III: Pseudo-Differential Operators" (Springer-Verlag)

* "The Analysis of Linear Partial Differential Operators IV: Fourier Integral Operators" (Springer-Verlag)

* "An Introduction to Complex Analysis in Several Variables". (1966, revisions in 1973 and 1990)

* "Notions of Convexity" (Birkhäuser , 1994, ISBN 0817637990)**References*** Hörmander, Lars. Autobiography. "Fields Medallists' Lectures". M. Sir Atiyah & D. Iagolnitzer (editors). World Scientific. ISBN 9812382593

* J. J. O'Connor & E. F. Robertson. " [*http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Hormander.html Lars Hörmander*] ".MacTutor archive biography. RetrievedSeptember 20 ,2005

* Wolf Foundation. "The 1988Wolf Foundation Prize In Mathematics". RetrievedSeptember 20 ,2005 . [*http://www.wolffund.org.il/full.asp?id=72*]

* L. Garding. "Hörmander's work on linear differential operators". Proceedings of theInternational Congress of Mathematicians .Stockholm , 1962 (Stockholm, 1963). As quoted by O'Connor & Robertson.

* Wolf Foundation.

* Unknown. "About the Author".Amazon.com entry for "The Analysis of Linear Partial Differential Operators I". RetrievedSeptember 20 ,2005 [*http://www.amazon.com/exec/obidos/tg/detail/-/3540006621*]

* Wolf Foundation.**External links***

*

*Wikimedia Foundation.
2010.*

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