# 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 matterpp. v–xvi Contentspp. 5034–5055 Mathematical analysis and numerical methods for inverse scattering problemsGang Bao

DOI 10.4171/ICM2022/5pp. 5056–5071 Towards adaptive simulations of dispersive tsunami propagation from an asteroid impactMarsha J. BergerRandall J. LeVeque

DOI 10.4171/ICM2022/73pp. 5072–5097 Structure-preserving model order reduction of Hamiltonian systemsJan S. HesthavenCecilia PagliantiniNicolò Ripamonti

DOI 10.4171/ICM2022/100pp. 5098–5117 Numerical stability of algorithms at extreme scale and low precisionsNicholas J. Higham

DOI 10.4171/ICM2022/74pp. 5118–5139 The mathematics of artificial intelligenceGitta Kutyniok

DOI 10.4171/ICM2022/141pp. 5140–5153 Stochastic gradient descent: where optimization meets machine learningRachel Ward

DOI 10.4171/ICM2022/171pp. 5154–5175 Solving inverse problems with deep learningLexing Ying

DOI 10.4171/ICM2022/49pp. 5178–5210 Discrepancy theory and related algorithmsNikhil Bansal

DOI 10.4171/ICM2022/169pp. 5212–5233 Enlargements: a bridge between maximal monotonicity and convexityRegina S. Burachik

DOI 10.4171/ICM2022/107pp. 5234–5255 Nonlinear eigenvalue problems for seminorms and applicationsMartin Burger

DOI 10.4171/ICM2022/140pp. 5256–5289 The evaluation complexity of finding high-order minimizers of nonconvex optimizationCoralia CartisNicholas I. M. GouldPhilippe L. Toint

DOI 10.4171/ICM2022/95pp. 5290–5313 An overview of nonlinear optimizationYu-Hong Dai

DOI 10.4171/ICM2022/72pp. 5314–5338 Control theory of stochastic distributed parameter systems: recent progress and open problemsQi Lü

DOI 10.4171/ICM2022/57pp. 5340–5373 Independent learning in stochastic gamesAsuman OzdaglarMuhammed O. SayinKaiqing Zhang

DOI 10.4171/ICM2022/152pp. 5374–5395 Reachable states for infinite-dimensional linear systems: old and newMarius Tucsnak

DOI 10.4171/ICM2022/12pp. 5398–5419 Gradient descent on infinitely wide neural networks: global convergence and generalizationFrancis BachLénaïc Chizat

DOI 10.4171/ICM2022/121pp. 5420–5449 On mathematical modeling in image reconstruction and beyondBin Dong

DOI 10.4171/ICM2022/2pp. 5450–5476 Theory of graph neural networks: representation and learningStefanie Jegelka

DOI 10.4171/ICM2022/162pp. 5478–5498 Theory of adaptive estimationOleg V. Lepski

DOI 10.4171/ICM2022/15pp. 5500–5514 Mean estimation in high dimensionGábor Lugosi

DOI 10.4171/ICM2022/75pp. 5516–5538 On some information-theoretic aspects of non-linear statistical inverse problemsRichard NicklGabriel P. Paternain

DOI 10.4171/ICM2022/18pp. 5540–5593 From statistical to causal learningBernhard SchölkopfJulius von Kügelgen

DOI 10.4171/ICM2022/173pp. 5594–5615 Second- and higher-order Gaussian anticoncentration inequalities and error bounds in Slepian’s comparison theoremCun-Hui Zhang

DOI 10.4171/ICM2022/186pp. 5618–5654 Lower bounds on the Lyapunov exponents of stochastic differential equationsJacob BedrossianAlex BlumenthalSam Punshon-Smith

DOI 10.4171/ICM2022/44pp. 5656–5678 Multiscale eco-evolutionary models: from individuals to populationsNicolas ChampagnatSylvie MéléardViet Chi Tran

DOI 10.4171/ICM2022/24pp. 5680–5699 Quantitative analysis of field concentration in presence of closely located inclusions of high contrastHyeonbae Kang

DOI 10.4171/ICM2022/83pp. 5702–5714 The hug of the scutoidClara I. Grima

DOI 10.4171/ICM2022/38pp. 5716–5745 The long way from mathematics to mathematics education: how educational research may change one’s vision of mathematics and of its learning and teachingAnna Sfard

DOI 10.4171/ICM2022/90pp. 5748–5770 George Birkhoff’s forgotten manuscript and his programme for dynamicsJune Barrow-Green

DOI 10.4171/ICM2022/119pp. 5772–5782 Some uses and associations of mathematics, as seen from a distant historical perspectiveAnnette Imhausen

DOI 10.4171/ICM2022/170pp. 5784–5812 The history and historiography of the discovery of calculus in IndiaK. Ramasubramanian

DOI 10.4171/ICM2022/77pp. 5813–5817 List of contributors