Isomorphic and almost-isometric problems in high-dimensional convex geometry

Research output: Contribution to conferencePaperpeer-review

Abstract

The classical theorems of high-dimensional convex geometry exhibit a surprising level of regularity and order in arbitrary high-dimensional convex sets. These theorems are mainly concerned with the rough geometric features of general convex sets; the so-called "isomorphic" features. Recent results indicate that, perhaps, high-dimensional convex sets are also very regular on the almost-isometric scale. We review some related research directions in high-dimensional convex geometry, focusing in particular on the problem of geometric symmetrization.

Original languageEnglish
Pages1547-1562
Number of pages16
StatePublished - 2006
Externally publishedYes
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: 22 Aug 200630 Aug 2006

Conference

Conference25th International Congress of Mathematicians, ICM 2006
Country/TerritorySpain
CityMadrid
Period22/08/0630/08/06

Keywords

  • Central limit theorem
  • Concentration phenomenon
  • Convex geometry
  • High dimension

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