Convexity, complexity, and high dimensions

• Autores: Stanislaw J. Szarek
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé, Javier Soria de Diego, Juan Luis Varona Malumbres, Joan Verdera, Vol. 2, 2006, ISBN 978-3-03719-022-7, págs. 1599-1622
• Idioma: inglés
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• Resumen

  • We discuss metric, algorithmic and geometric issues related to broadly understood complexity of high dimensional convex sets. The specific topics we bring up include metric entropy and its duality, derandomization of constructions of normed spaces or of convex bodies, and different fundamental questions related to geometric diversity of such bodies, as measured by various isomorphic (as opposed to isometric) invariants.