L1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry

Research output: Chapter in Book/Report/Conference proceedingConference contribution

26 Scopus citations

Abstract

We survey connections between the theory of bi-Lipschitz embeddings and the Sparsest Cut Problem in combinatorial optimization. The story of the Sparsest Cut Problem is a striking example of the deep interplay between analysis, geometry, and probability on the one hand, and computational issues in discrete mathematics on the other. We explain how the key ideas evolved over the past 20 years, emphasizing the interactions with Banach space theory, geometric measure theory, and geometric group theory. As an important illustrative example, we shall examine recently established connections to the the structure of the Heisenberg group, and the incompatibility of its Carnot-Carathéodory geometry with the geometry of the Lebesgue space L1.

Original languageEnglish (US)
Title of host publicationProceedings of the International Congress of Mathematicians 2010, ICM 2010
Pages1549-1575
Number of pages27
StatePublished - Dec 1 2010
Externally publishedYes
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: Aug 19 2010Aug 27 2010

Publication series

NameProceedings of the International Congress of Mathematicians 2010, ICM 2010

Other

OtherInternational Congress of Mathematicians 2010, ICM 2010
CountryIndia
CityHyderabad
Period8/19/108/27/10

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Bi-Lipschitz embeddings
  • Heisenberg group
  • Sparsest Cut Problem

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    Naor, A. (2010). L1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry. In Proceedings of the International Congress of Mathematicians 2010, ICM 2010 (pp. 1549-1575). (Proceedings of the International Congress of Mathematicians 2010, ICM 2010).