Abstract：Inthistalkwewillintroducealearningtheoryapproachtothetopicofestimatingtransferfunctionsinsystemidentification.Afrequencydomainidentificationproblemisformulatedasanatomicnormregularizationschemeinarandomdesignframeworkoflearningtheory.Suchaformulationmakesitpossibletoobtainsparsityandprovidefinitesampleestimatesforlearningthetransferfunctioninalearningtheoryframework.Erroranalysisisdoneforthelearningalgorithmbyapplyingalocalpolynomialreproductionformula,concentrationinequalitiesanditerationtechniques.Theconvergencerateobtainedhereisthebestintheliterature.Itishopedthatthelearningtheoryapproachtothefrequencydomainidentificationproblemwouldbringnewideasandleadtomoreinteractionsamongtheareasofsystemidentification,learningtheoryandfrequencyanalysis.

摘要：Multigridmethodscanprovideveryefficientiterativemethodsforthesolutionoflargesystemsof(non)linearalgebraicequations,resultingforinstancefromthediscretizationofpartialdifferentialequations.Inamultigridmethodseveralcoarsenedapproximationsofthealgebraicsystemandwell-designedsmoothersareusedtoacceleratetheconvergenceoftheiterativemethod.Thiscanresultinveryefficientiterativemethods,butifonewantstodevelopnewmultigridalgorithmsorunderstandtheperformanceofexistingalgorithms,thenmultilevelanalysisisindispensible.Inthisclassanoutlineofbasicmultigridanditerativemethodswillbegivenandmathematicaltechniquestounderstandandpredicttheirperformancewillbediscussed.Nopriorknowledgeofmultigridoriterativemethodswillberequired.Afterthisclassyoushouldbeabletousebasiciterativeandmultigridmethods,analyzeand(approximately)predictmultigridperformanceusingmultilevelanalysisandapplythesetechniquestoimproveandtestmultigridalgorithms.Themainapplicationswillbefromnumericaldiscretizationsofpartialdifferentialequations.Reference:U.Trottenberg,C.W.Oosterlee,A.Schüller,Multigrid,AcademicPress,ISBN0-12-701070-X,2001

【报告内容简介】:Advanced(scanning)transmissionelectronmicroscopy((S)TEM)techniqueshavebeenintensivelyappliedtostudythematerialsforenergystorage.With/CombiningdifferentTEMtechniques(includingin-situTEManddiffraction,HAADF-STEM,andSTEM-electronenergy-lossspectroscopy(EELS)),researchersareabletoprobelocalstructuralandchemicalinformationofelectrodematerials,ataresolutionofnanoscale.Thistalkwillfocusonmyrecentworkonusingin-situandanalyticalTEMtocharacterizetheconversion-reactionoxidematerial(Fe3O4)forelectrodeoflithiumionbatteries(Fe3O4)[1-2],andPtbasednanocatalystsforfuelcell[3,4].ThedynamicalprocessoftheredoxreactionofFe3O4revealedbyin-situTEMmayhelpustounderstandhowreactionpathwaysaffectthebatteries’kineticproperties.ForPtbasedelectrocatalystforfuelcell,thestraincouplingatinterfacesishighlightedforitscrucialroleindeterminingboththerateofelectrochemicalreactionandthecatalyticactivity.Reference:[1]VisualizingNon-EquilibriumLithiationofSpinelOxideviaInSituTransmissionElectronMicroscopy,He,etal.,NatureCommunications,7,11441(2016)[2]StrainCouplingofConversion-typeFe3O4ThinFilmforLithiumIonBattery,Hwang,etal.AngewandteChemie,56,7813,(2017)[3]BiaxiallystrainedPtPb/Ptcore/shellnanoplateboostsoxygenreductioncatalysis,Buetal.,Science,354,1410(2016)[4]OrderedPt3CoIntermetallicNanoparticlesDerivedfromMetal-organicFrameworksforOxygenReduction,Wangetal.NanoLett,18,4163(2018)【报告人简介】:Dr.DongSuisaProfessoratInstituteofPhysics,CAS.HewasthegroupleaderofelectronmicroscopyinCenterforFunctionalNanomaterialsatBookhavenNationalLaboratoryuntilAugust2019.HeisalsoanadjunctprofessorintheDepartmentofMaterialsScienceandEngineeringatStonyBrookUniversity.HegothisB.S.in1998fromNanjinguniversity.HegothisPh.Dincondensedmatterphysicsin2003,fromNanjinguniversityandInstituteofPhysics,CAS(advisors:Prof.YeningWang,andProf.KehsinKuo).AfterdoingpostdocinEPFL,Switzerland,UniversityofIllinoisatUrbana-Champaign,andArizonaStateUniversity,hejoinedBrookhavenNationalLaboratoryin2008asanassistantscientist.Hehasbeenthroughtherankandwaspromotedtoscientistwithcontinuingappointmentin2015.Dr.DongSuhaspublishedmorethan300papersinpeer-reviewedjournalswithcitation>18,000(Google,Hfactor~62).HisworkhavebeenhighlightedmultipletimesinDepartmentofEnergy(DOE)website,includingoneofthe40researchmilestonesinDOE40thanniversary.HehasbeenareviewerforDOE,NSF,andACSgrantsandjournalsofNature,NatureMaterials,NatureCommunications,ScienceAdvances,PRL,JACS,etc,andanorganizerofsymposiumsinnationalconferencesandworkshops.Hehasgivenmorethan30invitedtalksininternationalconferencesanduniversityseminars.

Abstract：Weshowthatany$Kappa$-soluitionofRicciflowoncompactK"ahlermanifoldsmustbequotientsofproductsofirreduciablecompactHermitiansymmetricmanifolds.Wewillalsodiscussthenoncompactcase.

Abstract：TheMinkowskiinequalitystatesthat,foraconvexbody$OmegasubsetmathbbR^{n+1}$,$int_{partialOmega}HdsigmageC_n(int_{partialOmega}dsigma)^{frac{n-1}{n}}$forsomedimensionalconstant$C_n>0$,theequalityholdsifandonlyif$Omega$isaroundball.Thisinequalityhasbeenextendedforstarshapeddomains(Guan-Li)andforareaouterminimizingdomains(Huisken).Inthistalk,thefocusisthistypeofinequalityinspaceform:hyperbolicspace$mathbbH^{n+1}$andellipticspace$mathbbS^{n+1}$.Wewilldiscusssomerecentresultsandchallengingopenproblems.

Abstract：WeusethereductionmethodtoconstructclusteredphasetransitionlayersneartheboundaryofdomainforaninhomogeneousAllen-Cahnequation.ThisisanextensionoftheresultbyA.MalchiodiandJ.WeiinJ.fixedpointtheoryappl.(2007).

摘要：Iwillgiveatourofthenotionofhamiltonianactionsfrombasicconceptstorecentdevelopments.InthefirsthourIwillgiveaselfcontainedreviewofthefollowingtopics:conservedquantitiesinclassicalmechanics;integrability;hamiltoniangroupactions;toricmanifolds,Guillemin-Sternbergconvexitytheorem,Delzantreconstrucion;symplecticreduction;Bochner-Weinsteinlinearizatonatcriticalpoints.InthelasthalfhourIwilldescribearecentgeneralizationofhamiltonianactionstoLiealgebroidsandLiegroupoids,whichismotivatedbyastudyofthesymmetriesofGeneralRelativity.ThisisjointworkwithAlanWeinstein.

摘要：Onemaintaskinsettheoryistoprovetheindependenceofstatements,e.g.,axiomofchoice(AC),continuumhypothesis(CH),Suslinhypothesis(SH).Iwillgiveabriefintroductionofseveralstatements:history,solution,ongoingopenproblems.

王贤文，2017年度教育部“青年长江学者”、大连理工大学教授、博士生导师、大连理工大学学术委员会委员、人文与社会科学学部副部长，担任JournalofInformetrics编委、FrontiersinResearchMetricsandAnalytics期刊副主编，以及十余本SSCI期刊的审稿人。主持国家及省部级课题10余项，发表学术论文100余篇，其中SSCI论文近30篇，多篇论文入选ESI高被引论文、ESI热点论文，被Nature等全球数十家媒体报道。

Abstract：Weconsiderquantitativeestimatesinthehomogenizationofsecond-orderellipticsystemswithperiodiccoefficientsthatoscillateonmultipleseparatedscales.Weestablishlarge-scaleinteriorandboundaryLipschitzestimatesdowntothefinestmicroscopicscaleviaiterationandrescalingarguments.WealsoobtainaconvergencerateintheL2spacebythereiteratedhomogenizationmethod.