@inproceedings{7a3ef33fcf124302947e8ca3d6e79719,
title = "Harmonic measure: Algorithms and applications",
abstract = "This is a brief survey of results related to planar harmonic measure, roughly from Makarov{\textquoteright}s results of the 1980{\textquoteright}s to recent applications involving 4-manifolds, dessins d{\textquoteright}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.",
keywords = "Brownian motion, Conformal dynamics, Conformal mapping, Dessins d{\textquoteright}enfants, Harmonic measure, Hausdorff dimension, Hyperbolic manifolds, Optimal meshing",
author = "Bishop, \{Christopher J.\}",
note = "Publisher Copyright: {\textcopyright} Proceedings of the International Congress of Mathematicians, ICM 2018. All rights reserved.; 2018 International Congress of Mathematicians, ICM 2018 ; Conference date: 01-08-2018 Through 09-08-2018",
year = "2018",
language = "English",
series = "Proceedings of the International Congress of Mathematicians, ICM 2018",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
pages = "1529--1557",
editor = "Boyan Sirakov and \{de Souza\}, \{Paulo Ney\} and Marcelo Viana",
booktitle = "Invited Lectures",
}