Beno Eckmann

Beno Eckmann ( born March 31, 1917 in Bern, † November 25, 2008 in Zurich ) was a Swiss mathematician who worked on algebraic topology, homological algebra, group theory and differential geometry.

Life and work

The son of a chemist attended high school in Berne from 1935 and studied mathematics at the ETH Zurich, where he was awarded a degree in 1939 and his doctorate in 1941 at Heinz Hopf with a thesis on algebraic topology. Besides Hopf among others George Pólya, Paul Bernays and Michel Plancherel ( whose assistant he was) were his teachers. He then worked as a lecturer at the University of Zurich and from 1942 at the University of Lausanne in Georges de Rham, where he was appointed associate professor in 1945. From 1948 until his retirement in 1984 he was a full professor at the ETH Zurich. There he founded in 1964, the Research Institute of Mathematics, whose director he was until 1984. In addition, he was a visiting scientist for example, at the University of California, Berkeley (1955), the University of Michigan (1950), the University of Illinois (1952 ), the Scuola Normale Superiore in Pisa (1958), the Institute for Advanced Study (1947, 1951/52 ) and MSRI.

Eckmann made ​​fundamental contributions to the development of category theory, cohomology of groups (from 1945) and algebraic topology in its development phase in the 1940s and 1950s. In 1943 he published a group-theoretic proof of the composition theorem of Hurwitz ( 1898) and Radon ( 1923) for quadratic forms in several variables ( from the set of Hurwitz implies the existence of Kompositionsalgebren only in 1,2,4 and 8 dimensions corresponding to the real numbers, complex numbers, quaternions, octonions ). From it follows by the theorem of Adams is also an upper limit for the number of linearly independent vector fields on spheres. 1942 certain Eckmann all rooms with vector product ( Continuous solutions of linear systems of equations ).

1956 to 1961 he was secretary of the International Mathematical Union, 1961/62 President of the Swiss Mathematical Society. 1972 to 1984 he was a member of the Research Council of the Swiss National Science Foundation. Eckmann is a member of the Academia Europaea and the Academy of Finland. Eckmann was for many years editor of the Yellow series (basic teachings of the Mathematical Sciences ) by Springer -Verlag in 1964 and co-founder of the series Lecture Notes in Mathematics.

In 1942, he received the Silver Medal of the ETH for his dissertation. He holds honorary doctorates from the University of Fribourg ( Switzerland ), the École Polytechnique Fédérale de Lausanne, the Technion in Haifa and Ben Gurion University in Be'er Sheva. In 1962 he gave a plenary lecture at the International Congress of Mathematicians in Stockholm ( Homotopy and Cohomology Theory). In 1994 he was Honorary President of the International Congress of Mathematicians in Zurich. In 1967 he was awarded the Prix Mondial Nessim Habif the University of Geneva. In 2008 he received the Albert Einstein Medal.

Among his students and doctoral candidates include Hans Grauert, Michel Kervaire, Ernst Specker, Peter Huber, Urs master Bach, Erwin Bolthausen, Manuel Castellet.

Eckmann also edited the collected works of his teacher Heinz Hopf.

He is the father of the mathematical physicist Jean -Pierre Eckmann.

In connection with the development of the ETH Hönggerberg site, Science City, the naming of a street in the planning stage by Beno Eckmann was decided.

Writings

  • Beno Eckmann Selecta. (Editor Max Albert Knusper, Guido Mislin, Urs Stammbachstrasse ), Springer-Verlag, 1987, ISBN 3-540-17518-0
  • Mathematical Survey Lectures 1943-2004. Springer 2006, ISBN 3-540-33790-3
  • Steady solutions of linear systems of equations. Commentarii Mathematici Helveticae, Bd.15, 1942/43, p.318
  • Continuous solutions of linear equations - some exceptional dimensions in topology. Battelle Rencontres 1967, S.516, Benjamin 1968
  • Systems of direction fields in spheres and steady solutions of complex linear equations. Commentarii Math.Helveticae Vol 15, 1942/43, p.1
  • Group Theoretical proof of the theorem of Hurwitz - Radon on the composition of quadratic forms. Commentarii Math.Helveticae, Bd.15, 1942/43, S.358
  • Georges de Rham 1903-1990. Elements of Mathematics 1992
  • On the 100th birthday of Heinz Hopf. Elements of Mathematics 1994
Swiss people Mathematical Sciences Research Institute Frank Adams Technion – Israel Institute of Technology Raghavan Narasimhan Jean-Pierre Eckmann Peter Hilton Integrated Authority File
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