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

Assaf Naor

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

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 - 2010
EventInternational Congress of Mathematicians 2010, ICM 2010 - Hyderabad, India
Duration: Aug 19 2010Aug 27 2010

Other

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

Fingerprint

Isoperimetry
Heisenberg Group
Graph in graph theory
Geometric Measure Theory
Lebesgue Space
Combinatorial Optimization
Discrete mathematics
Group Theory
Lipschitz
Banach space
Interaction

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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)

L1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry. / Naor, Assaf.

Proceedings of the International Congress of Mathematicians 2010, ICM 2010. 2010. p. 1549-1575.

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

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, International Congress of Mathematicians 2010, ICM 2010, Hyderabad, India, 8/19/10.
Naor A. L1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry. In Proceedings of the International Congress of Mathematicians 2010, ICM 2010. 2010. p. 1549-1575
Naor, Assaf. / L1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry. Proceedings of the International Congress of Mathematicians 2010, ICM 2010. 2010. pp. 1549-1575
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