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

Bo'az Klartag

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

^*Corresponding author for this work

Research output: Contribution to conference › Paper › peer-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 language	English
Pages	1547-1562
Number of pages	16
State	Published - 2006
Externally published	Yes
Event	25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: 22 Aug 2006 → 30 Aug 2006

Conference

Conference	25th International Congress of Mathematicians, ICM 2006
Country/Territory	Spain
City	Madrid
Period	22/08/06 → 30/08/06

Keywords

Central limit theorem
Concentration phenomenon
Convex geometry
High dimension

Cite this

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KW - Central limit theorem

KW - Concentration phenomenon

KW - Convex geometry

KW - High dimension

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

Abstract

Conference

Keywords

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Cite this