Abstract：InSpace-TimeDiscontinuousGalerkinfiniteelementmethodsfortime-dependentpartialdifferentialequationstimeisconsideredasanadditionaldimension.Byformulatingtheprobleminspace-time,thespatialandtemporalvariablescanbesimultaneouslydiscretizedusingbasisfunctionsthatarediscontinuousbothinspaceandintime.Space-timeDGmethodsarewellsuitedtosolvealargeclassofpartialdifferentialequationson(time-dependent)domainsandprovideaccurateandconservativenumericaldiscretizationsthataresuitableforhp-meshadaptation.Inthisseriesoflectures,wewillfirstconsiderspace-timeDGdiscretizationsforsimplehyperbolicandparabolicequationsinordertoexplainthemainconceptofthespace-timeDGmethod.Inthesecondpartsomeexamplesfromfluidmechanicswillbediscussed,suchasthecompressibleEulerandNavier-Stokesequations,theincompressibleNavier-Stokesequations,andiftimepermits,dispersedmultiphaseflowsmodeledbynon-conservativehyperbolicpartialdifferentialequations.

http://www.smartchair.org/conference/program/session_list/?conf_id=ICCA2020The12thInternationalConferenceonCliffordAlgebrasandTheirApplicationsinMathematicalPhysics3-7August,2020,Hefei

【7月27日-8月14日】LecturesSeriesonHigh-OrderNumericalMethodsTherehavebeensignificantprogressesonhighordernumericalmethods.Weinviteleadingexpertstogivearelativelydetailedintroductiontothetopicssurroundingthisconstruction.ThelectureswillbeheldonlinefromJuly27thtoAugust14th,2020.ItissupportedbySchoolofMathematicalSciences,UniversityofScienceandTechnologyofChina.OrganizingCommitteeChi-WangShu(BrownUniversity,USA)YinhuaXia(UniversityofScienceandTechnologyofChina,China)YanXu(UniversityofScienceandTechnologyofChina,China)IntendedAudience:Youngresearchers,postdocs,graduatestudentsLocation（Online）ZOOMID：68939394543ZOOMAPP(Downloadtheapphttps://zoom.com.cn/download）LecturesLecture1:DiscontinuousGalerkinmethods,stabilityanderrorestimatesLecturer:QiangZhang(NanjingUniversity)Time:9:30-11:30,July27,and9:30-11:30,July28,2020(Beijingtime)Lecture2:KrylovimplicitintegrationfactormethodsLecturer:YongtaoZhang(UniversityofNotreDame)Time:8:30-10:30,July29,2020(Beijingtime)Lecture3:Semi-LagrangianmethodsLecturer:JingmeiQiu(UniversityofDelaware)Time:8:30-10:30,July30,2020(Beijingtime)Lecture4:AsymptoticpreservingmethodsLecturer:FengyanLi(RensselaerPolytechnicInstitute)Time:8:30-10:30,July31,2020(Beijingtime)Lecture5:WENOmethodsLecturer:ZhengfuXu(MichiganTechnologicalUniversity)Time:9:00-11:00,August1,2020(Beijingtime)Lecture6:DirectdiscontinuousGalerkinmethodsLecturer:JueYan(IowaStateUniversity)Time:8:30-10:30,August3,2020(Beijingtime)Lecture7:HybridizablediscontinuousGalerkinmethodsLecturer:GuoshengFu(UniversityofNotreDame)Time:8:30-10:30,August4,2020(Beijingtime)Lecture8:SparsegridmethodsLecturer:YingdaCheng(MichiganStateUniversity)Time:8:30-10:30,August5,2020(Beijingtime)Lecture9:Well-balancedschemesLecturer:YulongXing(OhioStateUniversity)Time:9:30-11:30,August6,and9:30-11:30,August7,2020(Beijingtime)Lecture10:ReducedbasismethodsLecturer:YanlaiChen(UniversityofMassachusettsDartmouth)Time:9:30-11:30,August12,and9:30-11:30,August13,2020(Beijingtime)Lecture11:PositivitypreservingschemesLecturer:XiangxiongZhang(PurdueUniversity)Time:8:30-10:30,August14,2020(Beijingtime)

课程摘要：TheincompressibleNavier-StokesEquation(NSE)isthefundamentalequationtodescribethemotionoftheincompressible,viscousfluidfromphysics.Itisusedtomodeltheweather,oceancurrents,waterflowinapipeandairflowaroundawing.CoupledwithMaxwell\'sequationandFokker-Planckequation,itcanbeusedtostudymagnetohydrodynamics(MHD)andcomplexfluidflowsincludingviscoelasticfluidsrespectively.NSEsarealsoofgreatinterestsfrommathematicalviewpoints,inwhichmanyfundamentalquestionsareyettobeunderstood.Theoutlineofthecoursemayconsistof:ThelinearStokesequation:Basictheorybehindbothsteadyanddynamiccases.ThesteadyNavier-Stokesequation:Existence,regularity,andstability.ThedynamicNavier-Stokesequation:Ladyzhenskya\'stheoryindimensiontwo,LerayandHopf\'stheoryindimensionthree,Serrin-Prodi\'sregularityanduniquenesstheorem,andCaffarelli-Kohn-NirenbergandEscauriaza-Seregin-Sverak\'sregularitytheories.

http://cxjh.ustc.edu.cn/show/?970.html

Complexgeometryhasbeenaveryactiveareainrecentyears.Ithasdeepinteractionswithotherareas,e.g.algebraicgeometry,Riemanniangeometryandmathphysics.Despitetherecentenormousprogress,therearestillmanyinterestingdirectionstoexplore.Thiscoursewillserveasanintroductiontocomplexgeometry.Wewillcoverthefollowingtopics:holomorphicfunctionsofseveralvariablesondomainsof$C^n$,complexmanifolds,holomorphicvectorbundlesandChernclasses,Kahlermetrics,sheafsandtheircohomology,Hodgetheory,theRiemann-Rochtheorem(proofforRiemannsurfaces),theL^2estimatesandapplications.

Complexgeometryhasbeenaveryactiveareainrecentyears.Ithasdeepinteractionswithotherareas,e.g.algebraicgeometry,Riemanniangeometryandmathphysics.Despitetherecentenormousprogress,therearestillmanyinterestingdirectionstoexplore.Thiscoursewillserveasanintroductiontocomplexgeometry.Wewillcoverthefollowingtopics:holomorphicfunctionsofseveralvariablesondomainsof$C^n$,complexmanifolds,holomorphicvectorbundlesandChernclasses,Kahlermetrics,sheafsandtheircohomology,Hodgetheory,theRiemann-Rochtheorem(proofforRiemannsurfaces),theL^2estimatesandapplications.

课程摘要：Theaimofthecourseistoexploreanumberofdifferentconstructionsofnon-compacthyperkahlermanifolds,inparticularindimension4.Hyperk?hlergeometry,inJoyce’swords,“form(s)abeautifulandrichbranchofmathematics”andthecourseisanattempttodescribesomeaspectsofthistheory.Wewillstartwiththefirstexamplesofhyperk?hlermetricsgivenbyCalabi,wewillthendiscussthehyperkahlerquotientconstructionofKronheimer’sALEspaces,theTaub–NUTmetricandtheconstructionofcompletehyperk?hlermanifoldsasmodulispacesofsolutionstotheYang–Millsanti-self-dualityequations.Onemotivationforstudyingcompletenon-compactRicci-flatmanifoldsistheunderstandingofthemodulispaceofcompactEinsteinmetricsandtheirdegenerations.Asanillustrationofthispoint,wewilldescribetheconstructionoftheCalabi-YaumetricontheKummersurfacebygluingmethods.Introductiontohyperk?hlergeometry.ThegroupSp(n)asaRiemannianholonomygroup,thecurvatureofRiemannian4–manifolds,compactexamples,Calabi’smetriconT*CPnHyperkahlerquotientconstructionandALEspaces.SymplecticandK?hlerquotients,hyperk?hlerquotients,Kronheimer’sALEspaces.Gibbons–Hawkingansatz,twistorspaces.Gibbons–Hawkingansatz,theTaub–NUTmetric,gravitationalinstantons,thetwistorspaceofahyperkahlermanifold.Infinitedimensionalhyperkahlerquotients.TheYang–Millsanti-self-dualityequationsasahyperk?hlermomentmap,Kronheimer’shyperk?hlermetricsoncoadjointorbits.TheKummerconstruction.Donaldson’sgluingconstructionoftheCalabi-YaumetricontheKummersurface.References[1]Hitchin,N.,Hyper-K?hlermanifolds,SéminaireBourbaki,Vol.1991/92,Astérisque206,1992,Exp.No.748,3,137–166.[2]Joyce,D.,Riemannianholonomygroupsandcalibratedgeometry,Chapter10,OxfordGraduateTextsinMathematics,12,OxfordUniversityPress,2007.[3]Hitchin,N.,andKarlhede,A.andLindstr?m,U.andRo?ek,M.,Hyper-K?hlermetricsandsupersymmetry,Comm.Math.Phys.,CommunicationsinMathematicalPhysics,108,1987,4,535–589.[4]Donaldson,S.,Calabi-YaumetricsonKummersurfacesasamodelgluingproblem,Advancesingeometricanalysis,Adv.Lect.Math.(ALM),21,109–118,Int.Press,Somerville,MA,2012.

课程摘要：IwillgiveintroductiontothetheoryofminimalsurfacesinRiemaniangeometry.Wewillstartwiththefirstandsecondvariationformulaoftheareafunctional.ThenwediscussminimalsurfacesinEuclideanspaceandthesphere.AfterwardwewillfocusonstableminimalhypersurfacesinRiemannianmanifolds.Iftimepermits,wewillalsotalkaboutthePlateauproblem,geometricapplicationsofminimalsurfacesandsomeotherrelatedtopics.AsaprerequisitestudentsshouldhavesomebasicknowledgeofRiemanniangeometry.