摘要：LetMbeaclosedsymplecticmanifoldofdimension2nwithnon-ellipticity.WecandefineanalmostK?hlerstructureonMbyusingthegivensymplecticform.UsingDarbouxcoordinatecharts,wedeformthegivenalmostK?hlerstructureontheuniversalcoveringofMtoobtainaLipschitzK?hlerstructureontheuniversalcoveringofMwhichishomotopyequivalenttothegivenalmostK?hlerstructure.AnalogoustoTeleman\'sL2-HodgedecompositiononPLmanifoldsorLipschitzRiemannianmanifolds,wegiveaL2-HodgedecompositiontheoremontheuniversalcoveringofMwithrespecttotheLipschitzK?hlermetric.UsinganargumentofGromov,wegiveavanishingtheoremforL2harmonicp-forms,p≠n(resp.anon-vanishingtheoremforL2harmonicn-forms)ontheuniversalcoveringofM,thenitssignedEulercharacteristicsatisfies(?1)nχ(M)≥0(resp.(?1)nχ(M)>0).Asanapplication,weshowthattheChern-HopfconjectureholdstrueinclosedevendimensionalRiemannianmanifoldswithnonpositivecurvature(resp.strictlynegativecurvature),itgivesapositiveanswertoaYau\'sproblemduetoS.S.ChernandH.Hopf.

Abstract：Inthistalk,wewillinvestigatethesolvabilityandregularityofDirichletproblemforaclassof(degenerateornon-degenerate)fullynon-linearellipticequationsundersuitableassumptions.Somenewfeaturesoftheregularityassumptionsonboundaryandboundarydataarealsodiscussed.Asanapplication,wecanapplyQunLi’sconstantranktheoremtostudythesolvabilityofDirichletproblemforhomogeneouscomplexMonge-Amp`ereequationoncertainK”ahlermanifolds.

Abstract：TheoptimaltransportationproblemwasintroducedbyMongein1781.Sincethentheproblemhasbeenextensivelystudiedandgeneralcostsareallowed.ButforMonge\'sorignalcost,verylittleisknownabouttheregularity.Inthistalk,wediscusstheregularityinMonge\'sproblem,andinparticularshowthat,intwodimensionalcase,theoptimalmappingiscontinuous.ThetalkisbasedonjointworkswithF.SantambrogioandX.-J.Wang.

摘要：Wefirstintroducetheresultsonheatkernelestimatesfornon-localDirichletformswhenjumpkernelisstable-like,whichisoneofthenon-singularcases.Forsingularnon-localDirichletforms,itwasstudiedonultrametricspaces.Recently,wegeneralizethisresultfromultrametricspacestogeneralmetricmeasurespaces.Thatis,certaintypeofheatkernelboundsongeneralmetricspacesareequivalenttothefollowingthreeconditions:thetailestimateofjumpmeasure,Poincaréinequalityandgeneralizedcapacitycondition.

2019中山大学-中科大微分几何研讨会2019SYSU-USTC,SeminaronDifferentialGeometry会议时间：2019年4月12日－14日（12日报到，14日离会）会议地点：中国科学技术大学东区第五教学楼5206会议简介：为了提升与繁荣国内微分几何相关课题的研究工作，总结和交流近期研究成果，共同研讨微分几何的新进展与新动向，进一步促进和加强学术交流，“2019中山大学-中科大微分几何研讨会”将由中山大学与中国科学技术大学联合承办，并于2019年4月12日-14日在中国科学技术大学举行。会议议题：几何中的典则结构和相关非线性偏微分方程。会议日程：4.13上午08:50-09:00开幕式主持人：李嘉禹09:00-09:45陈世炳（中国科学技术大学）主持人：朱熹平10:15-11:00梁灏（中山大学）11:05-11:50贺丹青（中山大学）4.13下午主持人：陈兵龙14:15-15:00袁伟（中山大学）15:05-15:50刘世平（中国科学技术大学）主持人：麻希南16:10-16:55柯华忠（中山大学）4.14上午主持人：张希09:00-09:45张川静（中国科学技术大学）主持人：张希10:15-11:00李超（中国科学技术大学）11:05-11:50黄立鼎（中国科学技术大学）4.14下午自由讨论会议组织者：张希（中国科学技术大学）会议主办单位：中国科学技术大学数学科学学院

报告人简介：Dr.ElitaLijoinedtheDepartmentofCivilandEnvironmentalEngineeringattheNationalUniversityofSingaporeasanassistantprofessorin2016.BeforecomingtoSingapore,Dr.LididherpostdoctoralresearchatMassachusettsInstituteofTechnology,holdingajointpositionintheEarthResourcesLaboratoryandtheDepartmentofMathematics.Dr.LireceivedherPh.D.andM.S.degreesinGeophysicsfromStanfordUniversityin2014and2010,respectively.SheobtainedherB.S.degreeinInformationandComputationalSciencefromChinaUniversityofPetroleum,Beijingin2008.Herresearchinterestsinclude,butnotlimitedto,seismicwavesimulation,seismicinversionforstructuralimaging,subsurfacecharacterizationwithdeterministicandstochasticmethods,dataintegrationwithmulti-physicaldata,seismicmonitoringforreservoirandcivilpurposes,anddigitalsignalandimageprocessing.Dr.Li’spaperonintegratedVTImodelbuildingreceived“HonorableMention”forBestPaperinGeophysicsin2016.Herpresentationswererankedamong“theTopPresentationsattheSEGAnnualMeeting”in2016and2017.Dr.LiwastherecipientoftheJ.ClarenceKarcherAwardfromSEGin2018.

Abstract：In1980s,SpencerBlochconstructedacycle-classmapbetweenBloch\'shigherChowgroupsandDeligne-Beilinsonhomologyforsmooth,complexquasiprojectivevarieties,whichgeneralizestheclassicalGriffithsAbel-JacobimapandtheBeilinsonregulatormap.In2004,MattKerr,JamesD.LewisandStefanMüller-StachgaveanexplicitformulathatagreesrationallywithBloch\'sabstractdefinition.ArecentworkadaptedKerr,LewisandMüller-Stach\'sformula,provedtheexistenceofanintegralregulatoronhigherChowcomplexes,andgaveanexplicitexpressionforit.ThisintegralregulatorcanbeappliedtodetecttorsionphenomenainhigherChowgroups.

摘要：Inthispaper,wediscussthestabilityanderrorestimatesofthefullydiscreteschemesforlinearconservationlaws,whichconsistsofanarbitraryLagrangian-EuleriandiscontinuousGalerkinmethodinspaceandexplicittotalvariationdiminishingRunge-Kutta(TVD-RK)methodsuptothirdorderaccuracyintime.Thescalingargumentsandthestandardenergyanalysisarethekeytechniquesusedinourwork.WepresentarigorousprooftoobtainstabilityforthethreefullydiscreteschemesundersuitableCFLconditions.Withthehelpofthereferencecell,theerrorequationsareeasytoestablishandwederivethequasi-optimalerrorestimatesinspaceandoptimalconvergenceratesintime.FortheEuler-forwardschemewithpiecewiseconstantelements,thesecondorderTVD-RKmethodwithpiecewiselinearelementsandthethirdorderTVD-RKschemewithpolynomialsofanyorder,theusualCFLconditionisrequired,whileforothercases,strongertimesteprestrictionsareneededfortheresultstoholdtrue.

摘要:Inthistalk,IwillreviewsomebasicsonthearithmeticofellipticcurvesincludingtheBSDconjectureandtheTate-Shafarevichgroup.ThenIwillintroducearesultaboutfinitenessoftheelementsofTate-Shafarevichgrouptrivializedbypurelyinseparablebasechangesoverfunctionfields.

摘要：Motivatedbytheneedforanalyzingtherapidlyproducingdatastreams,suchasimages,videos,sensordata,etc,inatimelymanner,thestudyonthestreamingalgorithmstoextractrepresentativeinformationfrommassivedatatomaximizesomeobjectivefunctionisthereforeimportantandurgent.Mostofpreviousworksareassumedunderanoise-freeenvironment,whileinmanyrealisticapplicationsobtainingtheexactfunctionvalueishardorcomputingthefunctionvaluemaycostmuch,whichbringsthenoisyversion.Henceinthispaper,weaddressamoregeneralproblemtoselectasubsetofatmost$k$elementsfromthestreamtomaximizeanoisysetfunction(notnecessarilysubmodular).Tobespecific,wecastourproblemasthestreamingsubmodularmaximizationproblemwithmultiplicativeandadditivenoisemodels.Wedevelopanefficientthresholdingstreamingalgorithm,whichis$frac{1}{k+1}$-approximationforbothofnoisymodelsandhasamemoryindependentofdatasize.Inournumericalexperiments,weextensivelyevaluatetheeffectivenessofourthresholdingstreamingalgorithmonsomeapplicationsinrealdataset.报告人简介：徐大川，北京工业大学数理学院，教授，博士生导师。2002年于中国科学院数学与系统科学研究院计算数学与科学工程计算研究所获得博士学位，2004年于中国科学院数学与系统科学研究院应用数学研究所博士后出站。曾访问斯坦福大学，加拿大新布伦瑞克大学，西蒙弗雷泽大学，香港中文大学等。研究兴趣包括：组合优化，近似算法，机器学习与优化，算法博弈论，鲁棒优化，供应链管理等。中国运筹学会数学规划分会副理事长/秘书长，北京运筹学会副理事长，中国运筹学会副秘书长/理事，中国数学会理事。AppliedMathematicsandComputation、Asia-PacificJournalofOperationalResearch、JournaloftheOperationsResearchSocietyofChina、Statistics,OptimizationandInformationComputing、《运筹与管理》编委，Algorithmica、JournalofCombinatorialOptimization、《运筹学学报》特约编委。曾获得中国运筹学会青年论文奖一等奖、中国运筹学会运筹新人奖。主持国家自然科学基金六项，国家自然科学基金重点项目子课题一项。在科学出版社出版学术专著《设施选址问题的近似算法》，在MathematicalProgramming,Omega，INFORMSJournalonComputing，Algorithmica，TheoreticalComputerScience，JournalofCombinatorialOptimization，JournalofGlobalOptimization，InformationProcessLetters，OperationsResearchLetters等发表学术论文100余篇。