Abstract：Inthistalk,wefirsttalkabouttheSobolevspacetheoryandharmonicanalysistoolsfortheLaplacianopeartorassociatedwithHardypotential.Andthenweconsidertheenergy-criticalnonlinearwaveequationinthepresenceofanHardypotential.Inthedefocusingcase,weprovethatarbitraryinitialdataintheenergyspaceleadtoglobalsolutionsthatscatter.Inthefocusingcase,weprovescatteringbelowthegroundstatethreshold.ThispartisjointedwithChangxingMiaoandJasonMurphy.Finally,westudythelowregularityproblemfor3dcubicwaveequationwiththeHardypotential.ThispartisjointedwithChangxingMiaoandJunyongZhang.

Abstract：Inthistalk,wewilldiscussaSchrodingeroperatorinaconicsingularspaceandtheStrichartzestimateforthedispersiveequationassociatedwiththisoperator.Themaintechniquesarethemicrolocalanalysismethodandspectralanalysisargument.ThisisajointworkwithJiqiangZheng.

施阳教授2005年于加拿大阿尔伯特大学获得电子与计算机工程博士学位，现为加拿大维多利亚大学机械工程系终身教授。研究领域包括网络与分布式系统、模型预测控制、信息物理系统、机器人与机电一体化、自主系统导航与控制、能源系统应用等。目前担任IEEETIE共同主编，Automatica、IEEETCST、IEEETMECH、IEEETCYB等国际著名期刊编委，并入选2014年—2017年科睿唯安（前汤森路透）全球高被引科学家。施阳教授现为加拿大工程研究院院士，IEEEFellow、ASMEFellow和CSMEFellow。Thistalkwillreportarecentworkonintegral-typeevent-triggeredmodelpredictivecontrol(MPC)ofcontinuous-timenonlinearsystems.Anintegral-typeevent-triggeredmechanismisproposedbyincorporatingtheintegraloftheerrorbetweentheactualandpredictedstate.Besides,alessconservativerobustnessconstraintisintroducedtohandletheadditivedisturbance,renderingtheMPCproblemwitharelativelylargerinitialfeasibleregion.Furthermore,thefeasibilityoftheintegral-typeevent-triggeredMPCschemeandthestabilityoftheclosed-loopsystemarerigorouslyinvestigated.Sufficientconditionsforguaranteeingbothofthesepropertiesareestablished,showingthattherecursivefeasibilityandstabilitydependonthepredictionhorizon,thedisturbancebound,thetriggeringlevel,andthecontractionratefortherobustnessconstraint.Simulationandcomparisonstudiesdemonstratetheeffectivenessoftheproposedscheme.

摘要：Inthistalk,IwillpresentrecentprogressinthestudyofheatkernelsandparabolicHarnackinequalitiesforsymmetricMarkovprocessesthathavebothdiffusiveandjumpingpartsongeneralmetricmeasurespaces.Undergeneralvolumedoublingconditionandsomemildassumptionsonthescalingfunctions,weestablishstabilityresultsfortwo-sidedestimatesforheatkernelsintermsofthejumpingkernels,thegeneralizedcapacityinequalities,andPoincareinequalities.StablecharacterizationsoftheassociatedparabolicHarnackinequalitieswillalsobegiven.Ourresultsholdonspacesevenwhentheunderlyingspaceshavewalkdimensionsarelargerthan2.JointworkwithTakashiKumagaiandJianWang.

2019流形上的整体分析研讨会会议时间：2019年7月28日（报到）－8月3日（离会）会议地点：管理科研楼数学科学学院7月30日（周二）下午、8月1日（周四）下午1318教室，其余时间1308教室会议报告题目：刘冰萧马普所(波恩)Anintroductiontosymmetricspaces申述巴黎第六大学IntroductiontothetraceformualforGL(2)伊泽霖南开大学Thetangentgroupoidandrescaledbundle张鑫武汉理工大学Hopfcycliccohomologyfornon-compact$G$-manifolds戴先哲加州大学（圣芭芭拉）、华东师范大学TBA王相生北京大学Weylgroupactionsongeometricobjects卢文华中科技大学BergmankernelforsequenceoflinebundlesonK"{a}hlermanifolds张野平日本京都大学BCOVinvariantandramifiedcover史鹏帅北京大学TheAPSindexproblemforCallias-typeoperatorsandtherelativeetainvariant余世霖厦门大学Deformationquantizationofcoadjointorbits宋言理华盛顿大学（圣路易斯）Ageometricformulafor$K$-typeoftemperedrepresentations刘宇航北京大学Onpositivelycurved6-manifolds苏广想南开大学Positivescalarcurvatureonnoncompactfoliations

摘要：标签s-t割问题是在信息安全和计算机网络等领域中提出的一个组合优化问题。给一个图，边上有标签，该问题询问最少数目的标签，使得在图上把具有这些标签的边去掉后，能够将给定的源点s和目标点t断开。容易看出，标签s-t割问题是经典的最小s-t割问题的推广。在本报告中，我们主要介绍标签s-t割问题的两个纯组合算法。这两个算法的近似比分别为O(m1/2)和O(n2/3)，其中m和n分别为图上的边数和点数。这是标签s-t割问题当前已知最好的近似比。报告人简介：张鹏，山东大学软件学院副教授。2007年7月于中科院软件所取得博士学位，长期以来从事组合优化和近似算法的研究工作。在Algorithmica、ToCS、TCS、DAM等主流国际期刊，以及LATIN、ISAAC、COCOON等主流国际会议发表论文40多篇，其中第一作者SCI论文13篇，通讯作者SCI论文3篇。主持国家自然科学基金面上项目两项。

纽约州立大学宾汉姆顿分校助理教授张世奇学术报告会题目:Knowledge-basedRobotSequentialDecision-MakingunderUncertainty时间:2019年7月29日16:00地点:西区电三楼632学术报告厅

摘要：Inthegyrokineticmodelandsimulations,whenthedouble-gyroaveragetermincorporatesthecombiningeffectcontributedbythefiniteLarmorradius,shortscalesoftheperturbation,andsteepgradientoftheequilibriumprofile,thelow-orderapproximationofthistermcouldgeneratenonnegligibleerror.Thispaperimplementsaninterpolationalgorithmtocomputethedouble-gyroaveragetermwithoutlow-orderapproximationtoavoidthiserror.Forasteepequilibriumdensity,theobviousdifferencebetweenthedensityonthegyrocentercoordinateframeandtheoneontheparticlecoordinateframeshouldbeaccountedforinthequasi-neutralityequation.AnEuler–Maclaurin-basedquadratureintegratingalgorithmisdevelopedtocomputethequadratureintegralforthedistributionofthemagneticmoment.Theapplicationoftheinterpolationalgorithmtocomputingthedouble-gyroaveragetermandtosolvingthequasi-neutralityequationisbenchmarkedbycomparingthenumericalresultswiththeknownanalyticalsolutions.Finally,tomakeadvantageoftheinterpolationsolvermoreclearly,thenumericalcomparisonbetweentheinterpolationsolverandaclassicalsecondordersolveriscarriedoutinaconstanttheta-pinchmagneticfieldconfigurationBasedonSELALIBcode.Whentheequilibriumprofileisnotsteepandtheperturbationonlyhasthenon-zeromodenumberalongtheparallelspatialdimension,theresultscomputedbythetwosolversmatcheachotherwell.Whenthegradientoftheequilibriumprofileissteep,theinterpolationsolverprovidesabiggerdrivingeffectfortheion-temperature-gradientmodes,whichpossesslargepolarmodenumbers.

Abstract：WestudythequestionofwhetherthereexistdoublepointsontheboundariesofclustersinplanarBrownianloop-soups-anobjectintroducedbyLawlerandWernerin2004.Thisquestionismotivatedbyourearlierworks(withWerner)onthedecompositionofBrownianloop-soupclusters.Moreconcretely,weintroduceanotionofdisconnectionexponentswhichgeneralizestheBrowniandisconnectionexponentsderivedbyLawler,SchrammandWernerin2001.Bycomputingthegeneralizeddisconnectionexponents,wecanpredictthedimensionofmultiplepointsontheclusterboundariesinBrownianloop-soups-theirdimensionshavenotbeenconjecturedbefore.Weplantorigorouslyconfirmthepredictioninafuturework.Accordingtoourprediction,thereexistdoublepointsontheclusterboundariesofBrownianloop-soupswithanysubcriticalintensity.Interestingly,forthecriticalintensity,thedimensionofdoublepointsontheclusterboundariesbecomeszero,leavinganopenquestionofwhethersuchpointsexistforthecriticalloop-soup.

Abstract：In1987,FukayaprovedthecontinuityofeigenvaluesofRiemannianmanifoldswithuniformlyboundedcurvatureanddiameterwithrespecttothemeasuredGromov-Hausdorfftopology.WiththemajorconcernbeingasequenceofcollapsingRiemannianmanifolds,hisresultwasbasedonaso-calledkeyestimate,assertingthattheeigenfunctionsarealmostconstantalongthosecollapsingdirections.Inthistalk,wediscussageneralizationofFukaya\'skeylemmatothesettingofcollapsingEinsteinmanifolds,withoutassumingauniformcurvaturebound.