Year of Award: 1991
Publication Information: The American Mathematical Monthly, vol. 97, 1990, pp. 650-678
Summary: This survey of the notion of "convexity" includes historical examples, applications of the John-Loewner ellipsoid, examples and applications of convex functions, four elementary problems on polytopes, discussion of duality and addition, and a warning on the non-intuitive aspects of topology in the set of all convex bodies.
About the Author: (from The American Mathematical Monthly, vol. 97 (1990)) Marcel Y. Berger: Born Paris, France, 1927. After Ph.D. on “Holonomy groups of Riemannian manifolds” under A. Lichnerowicz, was professor at the universities of Strasbourg, Nice and Paris 1955-1974. From 1974-1985 Director of Research with the CNRS (Centre National de la Recherche Scientifique). Since 1985, Director of the IHES (Institut des Hautes Etudes Scientifiques). Visited a full year MIT 1956-57 and University of California, Berkeley 1961-62. President of the French Mathematical Society 1979-81. Corresponding member of the French Academy of Sciences since 1982. Rademacher lecturer (Univ. of Pennsylvania) 1981. Editor and managing editor of various mathematical journals, managing editor of the yellow Springer Grundlehren des Mathematischen Wissenschaften. Published around 45 papers on Riemannian geometry and three books (all with Springer): Geometry I and II, (with Gostiaux) Differential Geometry: Manifolds, Curves and Surfaces, and (with Berry, Pansu and St. Raymond) Problems in Geometry.