摘要:MeasureDifferentialEquations(MDE)canbeconsideredasthelimitingcaseoftheusualDifferentialEquations.Inthistalk,bytakingthespatialoscillationofstringsasanexample,wewilldiscusshowsolutionsandeigenvaluesofMDEdependonmeasuresinMDE.Asaconsequenceoftheso-calledcompletelycontinuousdependence,wewillshowthatODEsandAlgebraicEquations(AEs)canbemutuallyapproximated,includingtheirsolutions,eigenvalues,etc.

摘要：Scientificcomputingisarelativelynewresearcharea,whicharosebecauseoftheadvancesincomputerresources.Itaddressesthecriticalissueofthedevelopment,analysisandapplicationofalgorithmsforsolvingproblemsinengineeringandappliedsciences.Mathematicsplaysacentralroleinthedevelopmentofscientificcomputing,andisresponsibleforthesuccessofcomputersimulationtogetherwiththeincreaseofcomputerpowers.InthistalkIwillgiveanintroductiontoscientificcomputinganduseseveralexamplestodemonstratetherolemathematicsisplayinginitsdevelopment.报告人简介：舒其望，美国布朗大学教授，中国科学技术大学“长江学者奖励计划”讲座教授，海外高层次人才引进计划B类入选者。2008年起担任美国布朗大学TheodoreB.Stowell应用数学讲座教授，曾担任计算数学领域国际著名期刊MathematicsofComputation执行主编，现任JournalofScientificComputing主编。曾获得美国NASA科研奖（1992年）、冯康科学计算奖（1995年）和SIAM/ACM计算科学与工程奖（2007年）。舒其望教授2009年当选为首届美国工业与数学应用协会会士，2012年当选为首届美国数学会会士，2014年世界数学家大会45分钟邀请报告人。舒其望教授主要的研究领域是双曲型问题的高阶数值方法的设计、分析与应用。他在科学计算领域的重要贡献包括TVD时间离散、ENO和WENO差分离散、间断Galerkin有限元方法和谱方法等。他的大量开拓性工作在计算数学、科学计算和应用领域产生了深远的影响，他的研究工作被国内外同行多次引用。2004年起被ISI列为数学科学高引用率作者。

摘要:InthistalkwedescribeacombinatorialcriterionforshowingthelocallyNoetherianpropertyofthecategoryalgebraofaninfinitecategoryoverafieldofcharacteristic0.Thiscriterioncanuniformlyapplytoquiteafewinfinitecombinatorialcategorieswhichareofparticularimportanceinrepresentationstabilitytheory,anewandactiveareaconcerningasymptoticbehaviorofhomologygroupsoftopologicalspaces.

摘要:Atherosclerosisisaleadingcauseofdeathworldwide;itoriginatesfromaplaquewhichbuildsupintheartery.WeconsideredasimplifiedmodelofplaquegrowthinvolvingLDLandHDLcholesterols,macrophagesandfoamcells,whichsatisfyacoupledsystemofPDEswithafreeboundary,theinterfacebetweentheplaqueandthebloodflow.Weprovedthatthereexistsmallradiallysymmetricstationaryplaquesandestablishedasharpconditionthatensurestheirstability.Wealsodeterminednecessaryandsufficientconditionsunderwhichasmallinitialplaquewillshrinkanddisappear,orpersistforalltimes.

摘要:Foremergingandreemergingmosquitoes,itisimportanttostudytheconditionsandmechanismstriggeringanoutbreakandrecurrenceofanendemic.Inthistalk,Iwillpresentbifurcationanalysisforcompartmentalmodelstoexplainthethresholdconditionsandmechanismsforthedynamicsforsomemodelsofgeneralmosquito-bornediseases.Thebifurcationsincludebackwardbifurcations,HopfbifurcationsandBogdanov-Takensbifurcationsofcodimensiontwoandthree.报告人简介：ZhuHuaipingistheprofessorandresearchchairofYorkUniversity.Hisresearchinterestincludesdynamicalsystem,bifurcationtheoryandapplicationsandmathematicalbiology.

摘要:Inthispaper,thenecessaryandsufficientconditionsfortheexistenceoftravelingwavesolutionsarederivedforaclassofdiffusivedisease-transmissionmodelswithnetworkstructures.Theexistenceoftravelingsemi-frontsisobtainedbySchauder\'sfixed-pointtheoremandthesetravelingsemi-frontsareshowntobeboundedbytransformingtheboundednessproblemintotheclassificationproblemofnon-negativesolutionstoalinearellipticsystemonmathbb{R}.Toovercomethereducibilityproblemarisingintheproofs,aHarnack\'sinequalityforpositivesupersolutionsonmathbb{R}isproved.ThisisajointworkwithXueyingWangandTianranZhang.

摘要：Givenasuper-criticalbranchingrandomwalkon$mathbbR$startedfromtheorigin,let$Z_n(cdot)$bethecountingmeasurewhichcountsthenumberofindividualsatthe$n$-thgenerationlocatedinagivenset.Undersomemildconditions,itisknownthatforanyinterval$Asubset{mathbbR}$,$frac{Z_n(sqrt{n}A)}{Z_n({mathbbR})}$convergesa.s.to$nu(A)$,where$nu$isthestandardGaussianmeasure.Inthiswork,weinvestigatetheconvergenceratesof$${mathbbP}left(frac{Z_n(sqrt{n}A)}{Z_n({mathbbR})}-nu(A)>Deltaright),$$for$Deltain(0,1-nu(A))$,inbothSchr"{o}dercaseandB"{o}ttchercase.ThisisajointworkwithXinxinChen.

摘要：Inthiswork,weconsidertheEulerandYosidaapproximationsofmultivaluedstochasticdifferentialequationswithnon-Lipschitzcoefficientsandestablishvariouslimittheoremresults.

Abstract：Analmostcomplexmanifoldisasmoothmanifoldequippedwithasmoothlinearcomplexstructureoneachtangentspace.Everycomplexorsymplecticmanifoldisanalmostcomplexmanifold,butnotviceversa.Transversalityisthenotionofgeneralpositioninmanifoldtopology.Itcouldbeusedtodefinethemultiplicityofazeroforasmoothfunctionwithmorethanonevariables.Wewilldiscussdifferentialtopologyofalmostcomplexmanifolds,explainhowtousetransversalitystatementsforsmoothmanifoldstoformulateandprovecorrespondingresultsforanarbitraryalmostcomplexmanifold.Theexamplesincludeintersectionofalmostcomplexmanifolds,pseudoholomorphicmapsandzerolocusofcertainharmonicforms.Usingtheseresults,weareabletodefineandstudyKodairadimensionforalmostcomplexmanifolds(jointwithHaojieChen).ItcouldalsobeappliedtogetupperboundsforeigenvaluesofLaplacianonalmostcomplexmanifolds(workofmystudentLouisBonthrone).AnundergraduatestudentwhohastakenProf.ZuoqinWang\'sManifoldclassshouldbeabletounderstandalargeportionofthetalk.

摘要:IthasbeenagreatchallengetoconstructnewquantumMDScodes.Inparticular,itisveryhardtoconstructquantumMDScodeswithrelativelylargeminimumdistance.Inthistalk,IwillshowaconstructionofnewquantumMDScodeswithminimumdistancebiggerthanq/2+1throughHermitianself-orthogonalcodes.Inaddition,Iwillintroducetheconstructionofmultipartiteentangledstatewhichisrealtedtoquantumcodes.