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Harmonic measure: Algorithms and applications

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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Abstract

This is a brief survey of results related to planar harmonic measure, roughly from Makarov’s results of the 1980’s to recent applications involving 4-manifolds, dessins d’enfants and transcendental dynamics. It is non-chronological and rather selective, but I hope that it still illustrates various areas in analysis, topology and algebra that are influenced by harmonic measure, the computational questions that arise, the many open problems that remain, and how these questions bridge the gaps between pure/applied and discrete/continuous mathematics.

Original languageEnglish
Title of host publicationInvited Lectures
EditorsBoyan Sirakov, Paulo Ney de Souza, Marcelo Viana
PublisherWorld Scientific Publishing Co. Pte. Ltd.
Pages1529-1557
Number of pages29
ISBN (Electronic)9789813272927
StatePublished - 2018
Event2018 International Congress of Mathematicians, ICM 2018 - Rio de Janeiro, Brazil
Duration: Aug 1 2018Aug 9 2018

Publication series

NameProceedings of the International Congress of Mathematicians, ICM 2018
Volume3

Conference

Conference2018 International Congress of Mathematicians, ICM 2018
Country/TerritoryBrazil
CityRio de Janeiro
Period08/1/1808/9/18

Keywords

  • Brownian motion
  • Conformal dynamics
  • Conformal mapping
  • Dessins d’enfants
  • Harmonic measure
  • Hausdorff dimension
  • Hyperbolic manifolds
  • Optimal meshing

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