Geoffrey Colin Shephard

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Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups. He asked Shephard's problem on the volumes of projected convex bodies, posed another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant theory of finite groups, began the study of complex polytopes, and classified the complex reflection groups.

In mathematics, Shephard's problem, is the following geometrical question asked by Geoffrey Colin Shephard (1964): if K and L are centrally symmetric convex bodies in n-dimensional Euclidean space such that whenever K and L are projected onto a hyperplane, the volume of the projection of K is smaller than the volume of the projection of L, then does it follow that the volume of K is smaller than that of L?

In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one.

In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.

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Shephard earned his Ph.D. in 1954 from Queen's College, Cambridge, under the supervision of J. A. Todd. [1] He was a professor of mathematics at the University of East Anglia until his retirement. [2]

John Arthur Todd FRS was a British geometer.

University of East Anglia university in Norwich, England

The University of East Anglia (UEA) is a public research university in Norwich, England. Established in 1963 on a 320 acres campus west of the city centre, the university has four faculties and 26 schools of study. The annual income of the institution for 2016–17 was £273.7 million of which £35.6 million was from research grants and contracts, with an expenditure of £262.6 million.

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References

  1. Geoffrey Colin Shephard at the Mathematics Genealogy Project
  2. Retired Faculty, University of East Anglia School of Mathematics, accessed 2011-10-09.