# International Congress of Mathematicians

2022 July 6–14

## Editors

### Dmitry Beliaev

University of Oxford, United Kingdom### Stanislav 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 matterp. v Forewordpp. vii–xviii Contentsp. 1 International Congresses of Mathematicianspp. 3–4 Fields Medalists and IMU Award Winnerspp. 5–7 Opening greetings by the IMU Presidentpp. 9–10 Closing remarks by the IMU Presidentpp. 11–20 Status Report for the IMUpp. 21–23 Photographspp. 26–49 The work of Hugo Duminil-CopinMartin Hairer

DOI 10.4171/ICM2022/210pp. 50–65 The work of June HuhGil Kalai

DOI 10.4171/ICM2022/211pp. 66–80 The work of James MaynardKannan Soundararajan

DOI 10.4171/ICM2022/212pp. 82–105 The work of Maryna ViazovskaHenry Cohn

DOI 10.4171/ICM2022/213pp. 106–117 The work of Mark BravermanRan Raz

DOI 10.4171/ICM2022/214pp. 118–141 The work of Barry MazurHenri Darmon

DOI 10.4171/ICM2022/217pp. 142–158 The work of Elliott LiebRupert L. Frank

DOI 10.4171/ICM2022/216pp. 160–162 Nikolai Andreev and the art of mathematical animation and model-buildingTadashi Tokieda

DOI 10.4171/ICM2022/215pp. 164–210 100 years of the (critical) Ising model on the hypercubic latticeHugo Duminil-Copin

DOI 10.4171/ICM2022/204pp. 212–239 Combinatorics and Hodge theoryJune Huh

DOI 10.4171/ICM2022/205pp. 240–268 Counting primesJames Maynard

DOI 10.4171/ICM2022/206pp. 270–283 On discrete Fourier uniqueness sets in Euclidean spaceMaryna Viazovska

DOI 10.4171/ICM2022/207pp. 284–320 Communication and information complexityMark Braverman

DOI 10.4171/ICM2022/208pp. 322–330 Popularization of math: sketches of Russian projects and traditionsNikolai Andreev

DOI 10.4171/ICM2022/209pp. 332–374 Representations of $p$-adic groups over commutative ringsMarie-France Vignéras

DOI 10.4171/ICM2022/192pp. 376–413 The Ising model in our dimension and our timesAndrei Okounkov

DOI 10.4171/ICM2022/200pp. 414–458 Combinatorial geometry takes the leadAndrei Okounkov

DOI 10.4171/ICM2022/201pp. 460–490 Rhymes in primesAndrei Okounkov

DOI 10.4171/ICM2022/202pp. 492–545 The magic of 8 and 24Andrei Okounkov

DOI 10.4171/ICM2022/203pp. 548–553 2022 Abacus Medal: Mark BravermanAllyn Jackson

DOI 10.4171/ICM2022/218pp. 554–558 2022 Chern Medal: Barry MazurAllyn Jackson

DOI 10.4171/ICM2022/219pp. 560–564 2022 Gauss Prize: Elliott H. LiebAllyn Jackson

DOI 10.4171/ICM2022/220pp. 566–570 2022 Leelavati Prize: Nikolai AndreevAllyn Jackson

DOI 10.4171/ICM2022/221pp. 571–575 List of contributors