Warren Ambrose
Warren Arthur Ambrose (born October 25, 1914 in Virden , Illinois , † December 4, 1995 in Paris ) was an American mathematician who dealt with differential geometry .
Life
Ambrose studied mathematics at the University of Illinois at Urbana-Champaign with a bachelor's degree in 1935, a master's degree in 1936 and a doctorate under Joseph L. Doob in 1939 ( Some properties of measurable stochastic processes ). He then went to the University of Alabama , the Institute for Advanced Study and Princeton University , the University of Michigan and Yale University . In 1947 he became an Assistant Professor , 1950 Associate Professor and 1957 Professor at the Massachusetts Institute of Technology . With Isadore M. Singer , he made MIT one of the centers of differential geometry in the USA in the 1950s (alongside Chicago, where SS Chern was at that time). In 1985 he retired.
He was several times at the Institute for Advanced Study (1939 to 1941, 1948/49, 1959) as well as visiting professor in Latin America, Italy, India and Belgium. In 1954 he did research for the United States Air Force in Brussels and Paris.
In the 1960s he was visiting professor in Buenos Aires (where he was first visiting professor in Brazil and Buenos Aires in 1948). After he and other faculty members and students at the University of Buenos Aires were ill-treated by the military police (after a coup, the military had occupied the universities) in 1966, he was a staunch opponent of the right-wing military dictatorships in Latin America and especially in Argentina and Chile. He also took many students from Buenos Aires to MIT. Also in the 1960s he was active in protest against the participation of the USA in the Vietnam War and in 1967 signed an appeal for a tax boycott in this regard.
plant
At first he dealt with stochastic processes (topic of his dissertation with Doob), then with ergodic theory and measure theory (where he published with Paul Halmos and Shizuo Kakutani ).
Ambrose and Singer's theorem connects the curvature form with the holonomy of the coherent form in a main fiber bundle (clearly the curvature tensor, applied to a tangential vector, yields the difference when the tangential vector is transported in parallel on infinitesimal closed paths).
He is known for the Cartan-Ambrose-Hicks theorem (1956, also named after his doctoral student Noel Hicks), which answers the question to what extent the Riemann curvature tensor determines the Riemann metric. The local problem had already been solved by Élie Cartan . The global problem of determining the metric from parallel transport and curvature is also known as the Ambrose problem.
Honors, private matters
In 1948/49 he was a Guggenheim Fellow .
He was married twice and had two children from his first marriage. His second marriage was to a French woman, with whom he moved to France after his retirement in 1989.
Fluent in French, Portuguese and Spanish, he was a wine lover and jazz fan ( Charlie Parker ).
Fonts
- with Singer A theorem on holonomy , Trans. Amer. Math. Soc., Vol. 75, 1953, pp. 428-443
- Parallel translation of Riemannian curvature , Annals of Mathematics, Volume 64, 1956, pp. 337-363
- with Singer On homogeneous Riemannian Manifolds , Duke Math. J., Volume 25, 1958, pp. 647-669
Web links
Individual evidence
- ^ In the 1980 membership book of the IAS, Verdun, Illinois
- ^ Mathematics Genealogy Project
| personal data | |
|---|---|
| SURNAME | Ambrose, Warren |
| ALTERNATIVE NAMES | Ambrose, Warren Arthur (full name) |
| BRIEF DESCRIPTION | American mathematician |
| DATE OF BIRTH | October 25, 1914 |
| PLACE OF BIRTH | Virden , Illinois |
| DATE OF DEATH | 4th December 1995 |
| Place of death | Paris |