Ott-Heinrich Keller

Eduard Ott- Heinrich Keller ( born June 22, 1906 in Frankfurt am Main, † December 5, 1990 in Halle an der Saale ) was a German mathematician who worked on geometry, topology and algebraic geometry.

Life and work

Keller studied at the universities of Vienna, Berlin, Göttingen and Frankfurt. In Frankfurt, he became a member of the Corps Austria. In 1931 he received his doctorate in Frankfurt with Max Dehn (over the complete filling of space with cubes ). After that, he was an assistant in Frankfurt and from 1931 at the TH Berlin with Georg Hamel, where he habilitated in 1933 and 1941 was an adjunct professor. During World War II, he taught mathematics and mechanics at the Naval Academy Flensburg- Mürwik. In 1946 he was a professor in Münster and in 1947 full professor at the Technical University Dresden. From 1952 he was a follower of Heinrich Jung professor at the University of Halle, where he retired in 1971.

Keller dealt among other things with geometry. In his thesis he presented to Keller's conjecture about the filling of the d- dimensional space with d-dimensional cubes of equal size, in 1937 for dimensions d = 5.6 proved ( and Oskar Perron 1940 for dimensions d less than or equal to 6 ). The conjecture states that in such a filling at least two dice a whole ( d-1) - dimensional face area have in common. It is related to a conjecture of Hermann Minkowski on Diophantine approximation together ( the geometrically expressed in an analogous conjecture for grid arrays of cubes ). 1992 was shown by Jeffrey Lagarias and Peter Shor by a counterexample that it is wrong in more than 9 dimensions. In 2000 it was shown by John Mackey by an 8 -dimensional counter-example, that it is wrong for more than 7 dimensions, so that only the case d = 7 is open. The falsity of the conjecture in higher dimensions had suspected cellar in his original work.

In algebraic geometry he dealt among other things with Cremona transformations (for example, in his habilitation in 1933), which are for classification and resolution of singularities of algebraic curves of importance. Here he turned to the later of Shreeram Abhyankar and other so-called Jacobian conjecture. The name comes from the fact that the Jacobian J of a system F of n polynomials in n variables is received ( over an algebraically closed field ) in the conjecture. The conjecture was proved in some special cases, as in the 1970s by Tzuong - Tsieng Moh and others for two polynomials in two variables with degree less than or equal to 100 Moreover, Keller wrote works on the ideal theoretical construction of algebraic geometry and topological investigations of algebraic surfaces.

In 1961 he was president of the German Mathematical Society. He was a member of the Saxon Academy of Sciences and the Leopoldina.

Writings

  • About the complete filling of space with cubes, Crelle Journal 163, 1930, pp. 231-248
  • The Homoiomorphie of compact convex sets in Hilbert space, Mathematische Annalen 105, 1931, pp. 748-758
  • Cremona transformations of algebraic curves, Crelle Journal 169, 1933, pp. 193-218 ( Habilitation of the basement at the TH Berlin 1933)
  • A theorem on the complete fulfillment of the 5 - and 6 -dimensional space with cubes, Crelle Journal 177, 1937, pp. 61-64
  • About a covariate in Cremona transformations, Mathematische Annalen 114, 1937, pp. 700-741
  • Geometry of numbers, Encyclopedia of Mathematical Sciences, BG Teubner, 1954
  • Analytical Geometry and Linear Algebra, German Academic Publishers, Berlin 1957
  • Lectures on algebraic geometry, Geest and Portig, Leipzig 1974

Source

  • Renate Tobies: Biographical Dictionary of mathematics doctorate People, 2006
  • Ott- Heinrich Keller (1906-1990) - website of the University of Halle, October 17, 1998
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