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