Victor Klee

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Victor LaRue Klee (born September 18, 1925 in San Francisco , † August 17, 2007 in Lakewood , Ohio ) was an American mathematician .

Victor Klee at the annual DMV conference in Dortmund in 1980

Life

Klee studied mathematics and chemistry at Pomona College ( bachelor's degree 1945) and received his doctorate in mathematics with Edward McShane at the University of Virginia in 1949 ( convex sets in linear spaces ), where he was an instructor from 1947 and an assistant professor from 1949 to 1953. From 1953 he was Assistant Professor, 1954 Associate Professor and from 1957 Professor of Mathematics at the University of Washington . From 1974 he was adjunct professor for computer science and from 1976 to 1984 professor for applied mathematics. Since 1998 he has been Professor Emeritus. He was visiting professor at the University of Western Australia (1979), the University of Colorado (1971), UCLA (1955/56) and the University of Victoria (1975). In 1972 he was a consultant at IBM's Thomas J. Watson Research Center, from 1966 to 1970 a consultant to Rand Corporation , 1968 to 1972 from DuPont and 1963 to 1969 with Boeing . From 1958 to 1960 he was at the University of Copenhagen (as Sloan Research Fellow and Fellow of the National Research Council) and in 1992 as a Fulbright Fellow at the University of Trier . In 1951/52 he was at the Institute for Advanced Study .

Klee was a Guggenheim Fellow in 1980/81 (at the University of Erlangen-Nuremberg) and a Sloan Research Fellow from 1956 to 1959. In 1972 he received the Lester Randolph Ford Award and in 1980 and 1999 the Carl B. Allendoerfer Award of the Mathematical Association of America , of which he was president from 1971 to 1973. In 1977 he received their Distinguished Service Award. He served on the council of SIAM (1966 to 1968) and the American Mathematical Society (1964 to 1966 and 1969 to 1971). In 1992 he received the Max Planck Research Award and in 1980/81 he was the recipient of the Alexander von Humboldt Foundation. He was a member of the American Academy of Arts and Sciences (1997) and the American Association for the Advancement of Science . Klee received honorary doctorates from the Universities of Trier (1995), Liège (1984) and Pomona College (1965). In 1974 he was an invited lecturer at the International Congress of Mathematicians in Vancouver ( Convex polyhedra and mathematical programming ) and in 1962 in Stockholm ( The generation of affine hulls ).

He was married and had three daughters.

plant

Klee dealt with many areas of mathematics such as functional analysis , theory of convexity , optimization theory , algorithm theory , combinatorics , graph theory and geometry . In the 1960s he made important contributions to the theory of convex polyhedra . He applied his studies of convex polytopes to linear programming and showed with George Minty (using Klee-Minty polytopes and Klee-Minty cubes) that solving some problems with the simplex method requires exponential computational effort (instead of polynomial with the Size of the problem), although in practice the method usually reaches the goal faster. Klee showed (using special polyhedra, cloetopes ) that polyhedra exist in every dimension without Hamiltonian paths (which pass through all vertices exactly once).

The problem of the minimum number of guards in a museum comes from Klee, modeled as a flat polygon with n sides (Art Gallery Theorems, problem of museum guards ). Evidence for the minimal number assumed by Klee (the next smallest natural number to n / 3) comes from Vašek Chvátal (1973) and Steve Fisk.

Klee also worked on the monograph by Branko Grünbaum , a colleague at the University of Washington, on convex polytopes. He published over 245 scientific articles and had 36 doctoral students (34 of them in mathematics), including Bernd Sturmfels and Robert Phelps .

For many years he wrote a column on unsolved problems in the American Mathematical Monthly .

Fonts

literature

  • Peter Gritzmann , Bernd Sturmfels (editors): Applied Geometry and Discrete Mathematics - the Victor Klee Festschrift , American Mathematical Society 1990 (on Klee's 65th birthday)
  • Gritzmann, Sturmfels: Victor Klee (1925-2007) , Notices American Mathematical Society, Vol. 55, April 2008, online

Web links

References

  1. ^ Past Fellows 1956. Alfred P. Sloan Foundation, accessed June 2, 2019 .
  2. ↑ for the article What is a convex set? , American Mathematical Monthly, Vol. 78, 1971, pp. 616-631
  3. ↑ for Some Unsolved Problems in Plane Geometry , Mathematics Magazine, Vol. 52, 1979, pp. 131-145
  4. ^ For Klee, John R. Reay Surprising but easily proved geometric decomposition theorem , Mathematics Magazine, Vol. 71 (1998)
  5. ↑ The problem and its solution by Chvatál is dealt with in Aigner, Ziegler Proofs from the Book , Springer Verlag.
personal data
SURNAME Klee, Victor
ALTERNATIVE NAMES LaRue Klee, Victor
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH September 18, 1925
PLACE OF BIRTH San Francisco
DATE OF DEATH 17th August 2007
Place of death Lakewood , Ohio