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. 2376–2390 Developments in 3D Ricci flow since PerelmanBruce Kleiner
DOI 10.4171/ICM2022/150pp. 2392–2429 Survey lecture on billiardsRichard Evan Schwartz
DOI 10.4171/ICM2022/66pp. 2432–2455 Some recent developments in Ricci flowRichard H. Bamler
DOI 10.4171/ICM2022/58pp. 2456–2483 Emergent complex geometryRobert J. Berman
DOI 10.4171/ICM2022/59pp. 2484–2503 SausagesDanny Calegari
DOI 10.4171/ICM2022/4pp. 2504–2528 Lagrange multiplier functionals and their applications in symplectic geometry and string topologyKai Cieliebak
DOI 10.4171/ICM2022/46pp. 2530–2550 Real Gromov–Witten theoryPenka Georgieva
DOI 10.4171/ICM2022/189pp. 2552–2574 Gamma classes and quantum cohomologyHiroshi Iritani
DOI 10.4171/ICM2022/156pp. 2576–2592 Kähler manifolds with curvature bounded belowGang Liu
DOI 10.4171/ICM2022/6pp. 2594–2614 Groups acting at infinityKathryn Mann
DOI 10.4171/ICM2022/47pp. 2616–2637 Floer cohomology, singularities, and birational geometryMark McLean
DOI 10.4171/ICM2022/13pp. 2638–2654 Surfaces via spinors and soliton equationsIskander A. Taimanov
DOI 10.4171/ICM2022/92pp. 2656–2676 Entropy in mean curvature flowLu Wang
DOI 10.4171/ICM2022/116pp. 2678–2695 Composing and decomposing surfaces and functionsRobert J. Young
DOI 10.4171/ICM2022/19pp. 2696–2717 Mean curvature and variational theoryXin Zhou
DOI 10.4171/ICM2022/27pp. 2718–2737 Kähler–Ricci flow on Fano manifoldsXiaohua Zhu
DOI 10.4171/ICM2022/63pp. 2740–2766 Homology cobordism, knot concordance, and Heegaard Floer homologyJennifer Hom
DOI 10.4171/ICM2022/45pp. 2768–2790 Stable homotopy groups of spheres and motivic homotopy theoryDaniel C. IsaksenGuozhen WangZhouli Xu
DOI 10.4171/ICM2022/32pp. 2792–2805 Surface automorphisms and finite coversYi Liu
DOI 10.4171/ICM2022/70pp. 2806–2825 Homotopy patterns in group theoryRoman Mikhailov
DOI 10.4171/ICM2022/21pp. 2826–2854 Frobenius homomorphisms in higher algebraThomas Nikolaus
DOI 10.4171/ICM2022/159pp. 2856–2878 Diffeomorphisms of discsOscar Randal-Williams
DOI 10.4171/ICM2022/16pp. 2880–2902 Floer homology of 3-manifolds with torus boundaryJacob Rasmussen
DOI 10.4171/ICM2022/103pp. 2904–2927 Homological stability: a tool for computationsNathalie Wahl
DOI 10.4171/ICM2022/137pp. 2930–2946 PBW degenerations, quiver Grassmannians, and toric varietiesEvgeny Feigin
DOI 10.4171/ICM2022/81pp. 2948–2975 Representations of reductive groups over local fieldsTasho Kaletha
DOI 10.4171/ICM2022/115pp. 2976–2996 Perfect bases in representation theory: three mountains and their springsJoel Kamnitzer
DOI 10.4171/ICM2022/132pp. 2998–3037 Spherical varieties, functoriality, and quantizationYiannis Sakellaridis
DOI 10.4171/ICM2022/88pp. 3038–3060 Categorification and applicationsPeng Shan
DOI 10.4171/ICM2022/93pp. 3062–3078 Theta correspondence and the orbit methodBinyong SunChen-Bo Zhu
DOI 10.4171/ICM2022/23pp. 3080–3102 Quantum symmetric pairsWeiqiang Wang
DOI 10.4171/ICM2022/76pp. 3104–3139 Convex geometry and its connections to harmonic analysis, functional analysis and probability theoryKeith Ball
DOI 10.4171/ICM2022/65pp. 3142–3164 Moment methods on compact groups: Weingarten calculus and its applicationsBenoît Collins
DOI 10.4171/ICM2022/114pp. 3166–3188 Analysis on simple Lie groups and latticesMikael de la Salle
DOI 10.4171/ICM2022/160pp. 3190–3201 Weighted Fourier extension estimates and applicationsXiumin Du
DOI 10.4171/ICM2022/28pp. 3202–3223 Noncommutative ergodic theory of higher rank latticesCyril Houdayer
DOI 10.4171/ICM2022/39pp. 3224–3248 On some properties of sparse sets: a surveyMalabika Pramanik
DOI 10.4171/ICM2022/153pp. 3250–3265 The number of closed ideals in the algebra of bounded operators on Lebesgue spacesGideon Schechtman
DOI 10.4171/ICM2022/7pp. 3266–3290 Slices and distances: on two problems of Furstenberg and FalconerPablo Shmerkin
DOI 10.4171/ICM2022/97pp. 3292–3313 Quantitative invertibility of non-Hermitian random matricesKonstantin Tikhomirov
DOI 10.4171/ICM2022/10pp. 3314–3338 Abstract classification theorems for amenable -algebrasStuart White
DOI 10.4171/ICM2022/183pp. 3340–3365 Asymptotic behaviors of random walks on countable groupsTianyi Zheng
DOI 10.4171/ICM2022/138pp. 3367–3371 List of contributors