Proceedings of the International Congress of Mathematicians : Rio de Janeiro 2018 (ICM 2018), volume 1

Cover......Page 1
Title......Page 4
Contents......Page 6
Preface......Page 10
Winners of the IMU Prizes......Page 14
Organizing Committee......Page 16
Opening Ceremony......Page 18
Award Ceremonies for Gauß Prize and ChernMedal Award......Page 34
Closing Ceremony......Page 38
ALESSIO FIGALLI: HIS CONTRIBUTIONS TO GEOMETRYAND ANALYSIS......Page 54
ALI NESIN AND THE NESIN MATHEMATICS VILLAGE......Page 58
CAUCHER BIRKAR’S WORK IN BIRATIONAL ALGEBRAICGEOMETRY......Page 72
THE WORK OF PETER SCHOLZE......Page 82
ON THE WORK OF AKSHAY VENKATESH......Page 98
FIFTY YEARS OF MATHEMATICS WITH MASAKIKASHIWARA......Page 108
ARITHMETIC PHYSICS – ABEL LECTURE......Page 122
CONFORMAL GEOMETRY ON FOUR MANIFOLDS –NOETHER LECTURE......Page 130
EQUILIBRIA, FIXED POINTS, AND COMPUTATIONALCOMPLEXITY – NEVANLINNA PRIZE LECTURE......Page 158
FROM BLACKBOARD TO BEDSIDE – GAUß PRIZELECTURE......Page 220
REGULARITY OF INTERFACES IN PHASE TRANSITIONSVIA OBSTACLE PROBLEMS – FIELDS MEDAL LECTURE......Page 234
CRYSTAL BASES AND CATEGORIFICATIONS – CHERNMEDAL LECTURE......Page 258
SIMPLE MEMORIES FROM A SIMPLE MATHEMATICSLECTURER – LEELAVATI PRIZE LECTURE......Page 268
COHOMOLOGY OF ARITHMETIC GROUPS – FIELDSMEDAL LECTURE......Page 276
CALCULUS, HEAT FLOW AND CURVATURE-DIMENSIONBOUNDS IN METRIC MEASURE SPACES......Page 310
DELOCALIZATION OF SCHRÖDINGER EIGENFUNCTIONS......Page 350
MATHEMATICS OF MACHINE LEARNING: ANINTRODUCTION......Page 384
HARMONIC ANALYTIC GEOMETRY ON SUBSETS IN HIGHDIMENSIONS – EMPIRICAL MODELS......Page 398
SOME RECENT DEVELOPMENTS IN KÄHLER GEOMETRYAND EXCEPTIONAL HOLONOMY......Page 432
DYNAMICS, NUMERICAL ANALYSIS, AND SOMEGEOMETRY......Page 458
LONG-TERM HISTORY AND EPHEMERALCONFIGURATIONS......Page 490
DYNAMICAL, SYMPLECTIC AND STOCHASTICPERSPECTIVES ON GRADIENT-BASED OPTIMIZATION......Page 526
THREE PUZZLES ON MATHEMATICS, COMPUTATION,AND GAMES......Page 554
KNOTS, THREE-MANIFOLDS AND INSTANTONS......Page 608
SHTUKAS FOR REDUCTIVE GROUPS AND LANGLANDSCORRESPONDENCE FOR FUNCTION FIELDS......Page 636
CONFORMALLY INVARIANT LOOP MEASURES......Page 670
HIGH DIMENSIONAL EXPANDERS......Page 704
DYNAMICAL SYSTEMS, FRACTAL GEOMETRY ANDDIOPHANTINE APPROXIMATIONS......Page 730
METRIC DIMENSION REDUCTION: A SNAPSHOT OF THERIBE PROGRAM......Page 758
ON THE CROSSROADS OF ENUMERATIVE GEOMETRYAND GEOMETRIC REPRESENTATION THEORY......Page 836
COHOMOLOGICAL FIELD THEORY CALCULATIONS......Page 866
p-ADIC GEOMETRY......Page 896
SYSTEMS OF POINTS WITH COULOMB INTERACTIONS......Page 930
PARITY SHEAVES AND THE HECKE CATEGORY......Page 972
DYNAMICAL SYSTEMS EVOLVING......Page 1008
STRENGTHENING MATHEMATICS IN THE DEVELOPINGWORLD......Page 1040
THE GENDER GAP IN MATHEMATICAL AND NATURALSCIENCES FROM A HISTORICAL PERSPECTIVE......Page 1056
MACHINE-ASSISTED PROOFS......Page 1076
MATHEMATICIANS AND PLANETARY CHALLENGES......Page 1102
LESSON STUDY IN MATHEMATICS: CURRENT STATUSAND FURTHER DIRECTIONS......Page 1114
INTERNATIONAL MATHEMATICAL KNOWLEDGE TRUSTIMKT: AN UPDATE ON THE GLOBAL DIGITALMATHEMATICS LIBRARY......Page 1146
List of Participants......Page 1164
Back......Page 1196