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. 1440–1461 Tameness in geometry and arithmetic: beyond o-minimalityGal BinyaminiDmitry Novikov
pp. 1462–1486 Ramsey theory of homogeneous structures: current trends and open problemsNatasha Dobrinen
pp. 1488–1502 Measurable graph combinatoricsAndrew S. Marks
pp. 1504–1528 The Paris–Harrington principle and second-order arithmetic—bridging the finite and infinite Ramsey theoremKeita Yokoyama
pp. 1530–1552 Constraint satisfaction problem: what makes the problem easyDmitriy Zhuk
pp. 1554–1576 A totally disconnected invitation to locally compact groupsPierre-Emmanuel CapraceGeorge A. Willis
pp. 1578–1598 The Zariski cancellation problem and related problems in affine algebraic geometryNeena Gupta
pp. 1600–1622 The formal model of semi-infinite flag manifoldsSyu Kato
pp. 1624–1635 Character estimates for finite simple groups and applicationsMichael J. Larsen
pp. 1636–1658 Finite approximations as a tool for studying triangulated categoriesAmnon Neeman
pp. 1660–1680 Syzygies over a polynomial ringIrena Peeva
pp. 1682–1710 Survey lecture on arithmetic dynamicsJoseph H. Silverman
pp. 1712–1743 Relative trace formulae and the Gan–Gross–Prasad conjecturesRaphaël Beuzart-Plessis
pp. 1744–1766 The cohomology of Shimura varieties with torsion coefficientsAna Caraiani
pp. 1768–1799 On the Brumer–Stark conjecture and refinementsSamit DasguptaMahesh Kakde
pp. 1800–1836 Arithmetic and dynamics on varieties of Markoff typeAlexander Gamburd
pp. 1838–1869 The number of rational points on a curve of genus at least twoPhilipp Habegger
pp. 1870–1892 Theta lifting and Langlands functorialityAtsushi Ichino
pp. 1894–1916 Rational approximations of irrational numbersDimitris Koukoulopoulos
pp. 1918–1939 Euler systems and the Bloch–Kato conjecture for automorphic Galois representationsDavid LoefflerSarah Livia Zerbes
pp. 1940–1965 Counting problems: class groups, primes, and number fieldsLillian B. Pierce
pp. 1966–1988 Points on Shimura varieties modulo primesSug Woo Shin
pp. 1990–2010 The congruent number problem and elliptic curvesYe Tian
pp. 2012–2045 Arithmetic and geometric Langlands programXinwen Zhu
pp. 2048–2106 Motivic cohomologyMarc Levine
pp. 2108–2144 Homological knot invariants from mirror symmetryMina Aganagic
pp. 2146–2170 Vector bundles on algebraic varietiesAravind AsokJean Fasel
pp. 2172–2195 The unreasonable effectiveness of wall-crossing in algebraic geometryArend BayerEmanuele Macrì
pp. 2196–2211 Counting lattice points in moduli spaces of quadratic differentialsVincent DelecroixÉlise GoujardPeter ZografAnton Zorich
pp. 2212–2226 K-theory of large categoriesAlexander I. Efimov
pp. 2228–2249 Enhanced mirror symmetry for Langlands dual Hitchin systemsTamás Hausel
pp. 2250–2284 Hodge theory, between algebraicity and transcendenceBruno Klingler
pp. 2286–2310 Canonical Kähler metrics and stability of algebraic varietiesChi Li
pp. 2312–2322 The double ramification cycle formulaAaron Pixton
pp. 2324–2345 Effective results in the three-dimensional minimal model programYuri Prokhorov
pp. 2346–2368 Some aspects of rational points and rational curvesOlivier Wittenberg
pp. 2369–2373 List of contributors