International Congress of Mathematicians
2022 July 6–14
Editors
Dmitry Beliaev
University of Oxford, United KingdomStanislav Smirnov
Université de Genève, Switzerland
This book is published open access.
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress.
The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library.
The contents of the ICM 2022 Proceedings are available online with open access.
pp. i–iv Front matterpp. v–xvi Contentspp. 578–608 What is the point of computers? A question for pure mathematiciansKevin Buzzard
pp. 610–651 Reciprocity in the Langlands program since Fermat’s Last TheoremFrank Calegari
pp. 652–676 A survey of gravitational wavesFrans Pretorius
pp. 678–711 Groups acting on hyperbolic spaces—a surveyMladen Bestvina
pp. 712–748 Algebraic geometry in mixed characteristicBhargav Bhatt
pp. 750–795 Dynamics of dilute gases: a statistical approachThierry BodineauIsabelle GallagherLaure Saint-RaymondSergio Simonella
pp. 796–824 Automorphic functions on moduli spaces of bundles on curves over local fields: a surveyAlexander BravermanDavid Kazhdan
pp. 826–871 Evolution of form and shapeTobias Holck Colding
pp. 872–913 The regularity theory for the area functional (in geometric measure theory)Camillo De Lellis
pp. 914–954 A mathematical perspective of machine learningWeinan E
pp. 956–1006 Homomorphic encryption: a mathematical surveyCraig Gentry
pp. 1008–1052 Rare events in random matrix theoryAlice Guionnet
pp. 1054–1089 Decoupling estimates in Fourier analysisLarry Guth
pp. 1090–1120 One-dimensional quasiperiodic operators: global theory, duality, and sharp analysis of small denominatorsSvetlana Jitomirskaya
pp. 1122–1153 Abelian pole systems and Riemann–Schottky-type problemsIgor Krichever
pp. 1154–1200 Semiorthogonal decompositions in familiesAlexander Kuznetsov
pp. 1202–1258 What is a random surface?Scott Sheffield
pp. 1260–1310 The distribution of values of zeta and L-functionsKannan Soundararajan
pp. 1312–1353 Categorification: tangle invariants and TQFTsCatharina Stroppel
pp. 1354–1391 Noncommutative crepant resolutions, an overviewMichel Van den Bergh
pp. 1392–1432 Interactions of computational complexity theory and mathematicsAvi Wigderson
pp. 1433–1437 List of contributors