Geoffrey Colin Shephard

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Geoffrey Colin Shephard (born August 16, 1927 , † August 3, 2016 in Norwich ) was a British mathematician who dealt with convex geometry (polytopes, reflection groups, tiling).

Shephard studied mathematics in Cambridge (BA 1948) and received his doctorate (Regular complex polytopes) under John Arthur Todd at the University of Cambridge (Queen`s College) in 1954 . He was at the University of Birmingham and from 1967 professor at the University of East Anglia , where he retired in 1984. He then taught for three years as a professorial fellow.

In his dissertation he examined complex polytopes and classified reflection groups in complex with Todd. With Branko Grünbaum he wrote a standard work on tiling. In it, as in other writings, he attached great importance to general comprehensibility and himself donated a prize from the London Mathematical Society for contributions to mathematics with a strong intuitive component that can also be communicated to non-specialists.

The Chevalley-Shephard-Todd phrase is named after him, Todd (and sometimes Claude Chevalley ). It concerns the structure of the invariant ring of a finite group that operates on a finite dimensional vector space V (defined over a body K). According to the proposition, it is a polynomial ring if and only if it is generated by pseudo reflections. Pseudo reflections leave a subspace of codimension 1 of V invariant and are not equal to the identity.

A problem he posed in 1964 and named after him was independently solved in 1967 by Rolf Schneider (see there) and the American Clinton Myers Petty.

Another problem posed by Shephard (1975) concerns polyhedral meshes . Does every convex polytope have such a mesh? The problem is open and is also known as the Dürer's conjecture. For non-convex polyhedra in three dimensions the guess is wrong.

Fonts

  • Vector spaces of finite dimension, Oliver and Boyd / Interscience 1966
  • with Peter McMullen : Convex Polytopes and the Upper Bound Conjecture, London Mathematical Society Lecture Notes 3, Cambridge University Press 1971
  • with Branko Grünbaum: Tilings and Patterns, Freeman, San Francisco 1987
  • with Branko Grünbaum: Lectures on Lost Mathematics: Reissued for the Special Session on Rigidity at the 760. Meeting of the American Mathematical Society (Syracuse University), American Mathematical Society 1978
  • with Branko Grünbaum: Tilings with congruent tiles. Bulletin AMS, 1980.

Like Victor Klee and Micha Perles, he made contributions to the second edition (Interscience 1967) of the standard work by Branko Grünbaum Convex Polytopes .

Web links

Individual evidence

  1. ^ Who's Who of British Scientists 1969
  2. ^ Obituary notice , Eastern Daily Press, Aug. 24, 2016.
  3. ↑ Geoffrey Colin Shephard in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  4. ^ Shephard, Todd, Finite unitary reflection groups, Can. J. Math., Vol. 6, 1954, pp. 274-304
  5. ^ Shephard, Shadow systems of convex sets, Israel Journal of Mathematics, Volume 2, 1964, pp. 229-236
  6. ^ Shephard, Convex Polytopes with Convex Nets, Math. Proc. Camb. Phil. Soc., Vol. 78, 1975, pp. 389-403
  7. ^ Weisstein, Shephard's Conjecture , Mathworld
personal data
SURNAME Shephard, Geoffrey Colin
BRIEF DESCRIPTION British mathematician
DATE OF BIRTH August 16, 1927
DATE OF DEATH 3rd August 2016
Place of death Norwich