@inproceedings{8c4a1e0fa84f448ba3091bfaacfda647,
title = "The method of hypergraph containers",
abstract = "In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by the independent sets of uniform hypergraphs whose edges are sufficiently evenly distributed; more precisely, it provides a relatively small family of {\textquoteleft}containers{\textquoteright} for the independent sets, each of which contains few edges. We attempt to convey to the reader a general high-level overview of the method, focusing on a small number of illustrative applications in areas such as extremal graph theory, Ramsey theory, additive combinatorics, and discrete geometry, and avoiding technical details as much as possible.",
author = "J{\'o}zsef Balogh and Robert Morris and Wojciech Samotij",
note = "Publisher Copyright: {\textcopyright} 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 (US)",
series = "Proceedings of the International Congress of Mathematicians, ICM 2018",
publisher = "World Scientific Publishing Co. Pte Ltd",
pages = "3077--3110",
editor = "Boyan Sirakov and {de Souza}, {Paulo Ney} and Marcelo Viana",
booktitle = "Invited Lectures",
address = "Singapore",
}