life and work
McMullen is the son of a mathematician and studied from 1960 at Trinity College in Cambridge and at the University of Birmingham , where he received his doctorate in 1968. He then worked at universities in London , Siegen , the University of British Columbia ( Vancouver ), the University of Freiburg and from 1991 professor at University College London . In 1978 he received the D. Sc. at University College. Today he is professor emeritus there.
McMullen is a leading scientist in combinatorial geometry, especially the polyhedron theory , which he treats with abstract algebraic methods and where he works e.g. B. set up the G-conjecture proven by Richard P. Stanley .
In 1970 he proved the Upper Bound Conjecture (established by Theodore Motzkin in 1957) over the maximum number of 1, 2, 3, .., (d-1) dimensional surfaces of a d-dimensional convex polyhedron with a given number of vertices. In 1993 he proved a theorem on the number of faces of simple polyhedra ("On simple polytopes", Inventiones Mathematicae, Vol. 113, 1993, pp. 419-444) using methods of algebraic geometry.
In 1974 he was invited speaker at the International Congress of Mathematicians in Vancouver ( Metrical and combinatorial properties of convex polytopes ). He is a fellow of the American Mathematical Society .
- with Egon Schulte: Abstract Regular Polytopes , Encyclopedia of Mathematics and its Applications, Cambridge University Press 2002, ISBN 0-521-81496-0
- with GCShephard : Convex Polytopes and the upper bound conjecture , Cambridge University Press, London Mathematical Society Lecture Notes, 1971
- The numbers of faces of simplicial polytopes , Israel J. Math., Volume 9, 1971, pp. 559-570
- On simple polytopes , Inventiones Mathematicae, Volume 113, 1993, pp. 419-444
- Peter Gruber "On the history of convex geometry and the geometry of numbers", in G. Fischer u. a. (Editor) “100 Years of Mathematics”, Vieweg 1990
- The inequalities given by him characterize the so-called f-vectors, which count the area numbers according to dimension, but they do not determine them. McMullen The numbers of faces of simplicial polytopes , Israel Journal Mathematics, Vol. 9, 1971, pp. 559-570
- A conjecture about the minimal number, the minimally bound conjecture, was proven by David Barnette from 1971 to 1973.
|BRIEF DESCRIPTION||British mathematician|
|DATE OF BIRTH||May 11, 1942|
|PLACE OF BIRTH||Hillingdon|