ICM-2018, Rio de Janeiro: Proceedings, Vol.4 PDF
Preview ICM-2018, Rio de Janeiro: Proceedings, Vol.4
Proceedings of the International Congress of V M I P O n r L a t o Mathematicians U e c M th r e E n e IV em a d Rio de Janeiro 2018 t in i a o g t n s i c a o VOLUME IV ia l C f th n Invited Lectures o e s n g r e Boyan Sirakov s s Paulo Ney de Souza o f Marcelo Viana Editors ISBN 978-981-3272-87-3 (set) ISBN 978-981-3272-93-4 (v4) Proceedings of the International Congress of Mathematicians Rio de Janeiro 2018 Editors BoyanSirakov,PUC–RiodeJaneiro PauloNeydeSouza,UniversityofCalifornia,Berkeley MarceloViana,IMPA–RiodeJaneiro TechnicalEditors: BooksinBytes ProceedingsoftheInternationalCongressofMathematicians August1–9,2018,RiodeJaneiro,Brazil Copyright©2018bySociedadeBrasileiradeMatemáticaandInternationalMathemat- icalUnion. PrintedinSingapore Allrightsreserved. Nopartofthematerialprotectedbythecopyrighthereinmaybe reproducedortransmittedinanyformorbyanymeans, electronicormechanical, in- cluding,butnotlimitedtophotocopying,recording,orbyanyinformationstorageand retrievalsystem,withoutexpresspermissionfromthecopyrightowner. PublishedandDistributedby WorldScientificPublishingCoPteLtd Tel: 65-6466-5775 5TohTuckLink Fax: 65-6467-7667 Singapore596224 www.wspc.com [email protected] ISBN:978-981-3272-93-4(volumeprint) ISBN:978-981-3272-87-3(setprint) ISBN:978-981-3272-88-0(setebook) Proceedings of the International Congress of Mathematicians Rio de Janeiro 2018 VOLUME IV Invited Lectures Boyan Sirakov Paulo Ney de Souza Marcelo Viana Editors a A SBM World Scientific Contents 1 LogicandFoundations MatthiasAschenbrenner,LouvandenDriesandJorisvanderHoeven Onnumbers,germs,andtransseries 19 StephenJackson Towardsatheoryofdefinablesets 43 JochenKoenigsmann Decidabilityinlocalandglobalfields 63 UlrichKohlenbach Proof-theoreticmethodsinnonlinearanalysis 79 MaryantheMalliaris Modeltheoryandultraproducts 101 2 Algebra ChristofGeiß QuiverswithrelationsforsymmetrizableCartanmatricesand algebraicLietheory 117 OsamuIyama TiltingCohen–Macaulayrepresentations 143 MoritzKerz OnnegativealgebraicK-groups 181 SoniaNatale Ontheclassificationoffusioncategories 191 IvanPanin OnGrothendieck–Serreconjectureconcerningprincipalbundles 219 PhamHuuTiep Representationsoffinitegroupsandapplications 241 v vi 3 NumberTheory FabrizioAndreatta,AdrianIovitaandVincentPilloni p-adicvariationofautomorphicsheaves 267 YvesAndré Perfectoidspacesandthehomologicalconjectures 295 LaurentFargues Lacourbe 309 KaisaMatomäkiandMaksymRadziwiłł Multiplicativefunctionsinshortintervals,andcorrelationsof multiplicativefunctions 339 JamesMaynard Gapsbetweenprimes 363 RitabrataMunshi ThesubconvexityproblemforL-functions 381 GeorgiosPappas ArithmeticmodelsforShimuravarieties 395 BjornPoonen Heuristicsforthearithmeticofellipticcurves 417 JackThorne PotentialautomorphyofG-localsystems 433 b JacobTsimerman Functionaltranscendenceandarithmeticapplications 453 MarynaViazovska Sharpspherepackings 473 MiguelN.Walsh Characteristicsubsetsandthepolynomialmethod 485 WeiZhang Periods,cycles,andL-functions: Arelativetraceformulaapproach 505 vii 4 AlgebraicandComplexGeometry DanAbramovich Resolutionofsingularitiesofcomplexalgebraicvarietiesand theirfamilies 541 CarolinaAraujo Positivityandalgebraicintegrabilityofholomorphicfoliations 565 CaucherBirkar Birationalgeometryofalgebraicvarieties 583 SébastienBoucksom Variationalandnon-ArchimedeanaspectsoftheYau–Tian–Donaldson conjecture 609 SergeCantat Automorphismsanddynamics: Alistofopenproblems 637 LuciaCaporaso Recursivecombinatorialaspectsofcompactifiedmodulispaces 653 JungkaiA.ChenandMengChen Onexplicitaspectofpluricanonicalmapsofprojectivevarieties 671 PaulHackingandSeanKeel Mirrorsymmetryandclusteralgebras 689 JongHaeKeum AlgebraicsurfaceswithminimalBettinumbers 717 WojciechKucharzandKrzysztofKurdyka Fromcontinuousrationaltoregulousfunctions 737 AndrásNémethi Pairsofinvariantsofsurfacesingularities 767 MihneaPopa D-modulesinbirationalgeometry 799 ChenyangXu Interactionbetweensingularitytheoryandtheminimalmodelprogram 825 viii 5 Geometry NicolasBergeron Hodgetheoryandcycletheoryoflocallysymmetricspaces 849 BoBerndtsson ComplexBrunn–Minkowskitheoryandpositivityofvectorbundles 877 MahanMj Cannon–Thurstonmaps 903 EmmyMurphy (Noarticleprovidedforpublication) DenisV.Osin Groupsactingacylindricallyonhyperbolicspaces 937 PedroA.S.SalomãoandUmbertoL.Hryniewicz GlobalsurfacesofsectionforReebflowsindimensionthreeandbeyond 959 IvanSmith Stabilityconditionsinsymplectictopology 987 SongSun DegenerationsandmodulispacesinKählergeometry 1011 AnnaWienhard AninvitationtohigherTeichmüllertheory 1031 6 Topology ArthurBartels K-theoryandactionsonEuclideanretracts 1059 TobiasEkholm KnotcontacthomologyandopenGromov–Wittentheory 1081 KojiFujiwara Constructinggroupactionsonquasi-trees 1105 ix FannyKassel Geometricstructuresandrepresentationsofdiscretegroups 1133 RobertLipshitzandSucharitSarkar SpatialrefinementsandKhovanovhomology 1171 CiprianManolescu Homologycobordismandtriangulations 1193 JohnPardon (Noarticleprovidedforpublication) AlanW.Reid Profiniterigidity 1211 BernardoUribe Theevennessconjectureinequivariantunitarybordism 1235 ThomasWillwacher LittledisksoperadsandFeynmandiagrams 1259 7 LieTheoryandGeneralizations TomoyukiArakawa RepresentationtheoryofW-algebrasandHiggsbranchconjecture 1281 MichaelFinkelberg DoubleaffineGrassmanniansandCoulombbranchesof3dN=4 quivergaugetheories 1301 VyacheslavFutorny RepresentationsofGaloisalgebras 1321 TsachikGelander Aviewoninvariantrandomsubgroupsandlattices 1339 XuhuaHe SomeresultsonaffineDeligne–Lusztigvarieties 1363 DipendraPrasad Ext-analoguesofBranchinglaws 1385
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