Werner Fenchel

Moritz Werner Fenchel(German:[ˈfɛnçəl];3 May 1905 – 24 January 1988) was a German-Danishmathematicianknown for his contributions togeometryand tooptimization theory.Fenchel established the basic results ofconvex analysisand nonlinear optimization theory which would, in time, serve as the foundation fornonlinear programming.A German-born Jew and early refugee from Nazi suppression of intellectuals, Fenchel lived most of his life in Denmark. Fenchel's monographs and lecture notes are considered influential.

Moritz Werner Fenchel
Fenchel in 1972
Born	(1905-05-03)3 May 1905 Berlin, Germany
Died	24 January 1988(1988-01-24)(aged 82) Copenhagen,Denmark
Alma mater	University of Berlin
Known for	Fenchel's duality theorem Fenchel's theorem Fenchel–Moreau theorem Fenchel–Nielsen coordinates Fenchel–Young inequality Alexandrov–Fenchel inequality Legendre–Fenchel transformation
Awards	Rockefeller Fellowship(1930) Membership in theRoyal Danish Academy of Sciences and Letters(1946)
Scientific career
Fields	Mathematics: Geometry Optimization
Institutions	University of Copenhagen University of Göttingen
Doctoral advisor	Ludwig Bieberbach
Doctoral students	Birgit Grodal Troels Jørgensen

Biography

Early life and education

Fenchel was born on 3 May 1905 inBerlin,Germany,his younger brother was the Israeli film director and architectHeinz Fenchel.

Fenchel studied mathematics and physics at theUniversity of Berlinbetween 1923 and 1928.He wrote his doctorate thesis ingeometry(Über Krümmung und Windung geschlossener Raumkurven)underLudwig Bieberbach.

Professorship in Germany

From 1928 to 1933, Fenchel was ProfessorE. Landau's Assistant at theUniversity of Göttingen.During a one-year leave (onRockefeller Fellowship) between 1930 and 1931, Fenchel spent time in Rome withLevi-Civita,as well as inCopenhagenwithHarald BohrandTommy Bonnesen. He visited Denmark again in 1932.

Professorship in exile

Fenchel taught at Göttingen until 1933, when theNazi discrimination lawsled tomass-firings of Jews.

Fenchel emigrated to Denmark somewhere between April and September 1933, ultimately obtaining a position at theUniversity of Copenhagen.In December 1933, Fenchel married fellow German refugee mathematicianKäte Sperling.

WhenGermany occupied Denmark,Fenchel and roughly eight-thousand other Danish Jewsreceived refugein Sweden, where he taught (between 1943 and 1945) at the Danish School inLund.After the Allied powers'liberation of Denmark,Fenchel returned to Copenhagen.

Professorship postwar

In 1946, Fenchel was elected a member of theRoyal Danish Academy of Sciences and Letters.

On leave between 1949 and 1951, Fenchel taught in the U.S. at theUniversity of Southern California,Stanford University,andPrinceton University.

From 1952 to 1956 Fenchel was the professor in mechanics at the Polytechnic in Copenhagen.

From 1956 to 1974 he was the professor in mathematics at theUniversity of Copenhagen.

Last years, death, legacy

Professor Fenchel died on 24 January 1988.

Geometric contributions

Convex geometry

Main article:Convex geometry

See also:Alexandrov–Fenchel inequality

Optimization theory

Main article:Convex analysis

See also:Convex set,Convex cone,andConvex function

See also:Legendre-Fenchel transformationandFenchel's duality theorem

Fenchel lectured on "Convex Sets, Cones, and Functions" at Princeton University in the early 1950s. His lecture notes shaped the field ofconvex analysis,according to the monographConvex AnalysisofR. T. Rockafellar.

Hyperbolic geometry

Main article:Hyperbolic geometry

Books

• Fenchel, Werner; Bonnesen, Tommy (1934).Theorie der konvexen Körper.Ergebnisse der Mathematik und ihrer Grenzgebiete. Vol. 3. Berlin: 1. Verlag von Julius Springer.
• Fenchel, Werner (1953).Convex Cones, Sets, and Functions(PDF).Princeton, New Jersey: Princeton University Dept. of Mathematics.
• Fenchel, Werner; Bonnesen, Tommy (1971).Theorie der konvexen Körper.(Reprint of the 1948 German language edition). Bronx, New York: Chelsea Publishing Co.
• Fenchel, Werner; Bonnesen, Tommy (1974).Theorie der konvexen Körper.Berlin-New York: Springer-Verlag.
• Fenchel, Werner; Bonnesen, Tommy (1987).Theory of convex bodies.Moscow, Idaho: L. Boron, C. Christenson and B. Smith. BCS Associates.ISBN9780914351023.
• Fenchel, Werner (1989).Elementary geometry in hyperbolic space.De Gruyter Studies in mathematics. Vol. 11. Berlin-New York: Walter de Gruyter & Co.
• Fenchel, Werner;Nielsen, Jakob(2003). Schmidt, Asmus L. (ed.).Discontinuous groups of isometries in the hyperbolic plane.De Gruyter Studies in mathematics. Vol. 29. Berlin: Walter de Gruyter & Co.

See also

• Convex analysis
  • Convex cone
  • Convex function
  • Convex set
  • Legendre–Fenchel transformation
• Convex minimization
  • Fenchel's duality theorem
• Geometry
  • Convex geometry
    • Brunn–Minkowski theorem
  • Differential geometry
    • Fenchel's theorem
  • Hyperbolic geometry
    • Jakob Nielsen
    • Fenchel–Nielsen coordinates
• Nonlinear programming

External links

• Werner Fenchelat theMathematics Genealogy Project
• Werner Fenchel website– contains CV, biography, links to archive, etc.