摘要：OpenKdV方程簇来源于对带边黎曼面模空间相交理论的研究，它刻画了靶空间为单点的情形下的OpenGromov-Witten不变量与Witten-Kontsevich配分函数之间的联系。在近期的工作中，我们从KdV方程簇的一个一般的tau函数出发，建立其与OpenKdV方程簇的tau函数之间的联系。作为应用，我们给出OpenGromov-Witten不变量的一个有效计算方法；同时，我们从KdV方程簇的广义BGWtau函数出发构造OpenKdV方程簇的一类新的tau函数，并给出其显式公式。

摘要：Inthetalk,wewillshowtoyousomeresultsontheSatotheoryofq-mKPhierarchy.Satotheory,developedbyMikioSatoandhisschoolinKyoto,containsmanyinterestingmathematicalstructuresandinparticularprovidestheconstructionofhierarchiesofsolitonequations,writtenintermsoftau-functionsdependingoninfinitenumberofindependentvariables.Inthistalk,thetaufunctionandadditionalsymmetriesofq-mKPhierarchyareintroduced.

摘要：Davey-Stewartson系统是重要的（2+1）维可积模型。在这次报告中，我主要介绍在经典的Davey-Stewartson系统研究基础上所做的一些工作，包括新定义的Davey-Stewartson可积系列，无色散Davey-Stewartson系统以及相关的无色散可积系列.

摘要：Tutte多项式是拟阵的一个重要不变量。在超平面配置理论中，Tutte多项式包含了超平面配置的组合和拓扑信息。本次报告我们回顾这些结果，并介绍Moci的算术Tutte多项式在环面配置理论中的应用，以及Liu-Tran-Yoshinaga的G-Tutte多项式及其应用。

摘要：Inthistalk,Iwilldiscusssomeorthogonality-freeapproachesforoptimizationproblemsonStiefelmanifold.Stiefelmanifoldconsistsofmatriceswithorthogonalcolumns.Optimizationproblemswithorthogonalityconstraintsappearinmanyimportantapplicationssuchasleadingeigenvaluescomputation,discretizedKohn-Shamtotalenergyminimization,andsparseprincipalcomponentanalysis.WepresentnewalgorithmsforsolvingoptimizationproblemsonStiefulmanifold.Thesealgorithmsarebasedonpenaltyfunctions,thustherearenoneedstocarryoutorthogonalizationcalculationsineachiteration.Themajorcomputationcostoforthogonality-freealgorithmsisintheformofmatrix-matrixmultiplication,whichhastheadvantageofbeingparallelizedeasily.Problemswithbothsmoothandnonsmoothobjectivefunctionsareconsidered.Theoreticalpropertiesofouralrogithmsarediscussedandnumericalexperimentsarealsopresented.报告人简介：袁亚湘现为中国科学院院士、发展中国家科学院院士、巴西科学院通讯院士，美国工业与应用数学会会士、美国数学学会首届会士、国际工业与应用数学联合会当选主席、中国数学会理事长、全国政协常委、中国科协副主席。曾获国家自然科学奖二等奖、首届冯康科学计算奖、TWAS数学奖、陈省身数学奖、苏步青应用数学奖、何梁何利基金科学与技术进步奖等。袁亚湘院士长期从事运筹学研究并取得了系统成果，在信赖域法、拟牛顿法、非线性共轭梯度法等方法方面做出了重要贡献。在信赖域法方面，给出了著名的Celis-Dennis-Tapia问题的最优性定理；提出并解决了Steihaug-Toint方法的下降估计；和导师Powell合作提出了利用光滑评价函数的约束优化信赖域法；独立提出了一个利用无穷范数罚函数的信赖域法，被国外著名学者推广到整数规划。在拟牛顿法方面，和美国优化专家合作证明了除DFP外Broyden凸簇的所有方法的全局收敛性；提出了一个改进的BFGS方法，发展了非拟牛顿方法。在共轭梯度法方面，和学生合作提出了一个新的共轭梯度法，被国际同行称为“戴袁方法”。

报告摘要：机器学习取得的突破不仅仅给人工智能带来了新的生机，也给科学和工程领域带来了前所未有的机会。传统的科学方法和机器学习方法的有机结合，给科学研究提供了一个新的、极为有效的研究方式，同时也将大大缩短科研场景和实际场景之间的距离，使科学研究和技术创新得到更深度的融合。机器学习和人工智能在实践中的成功也对其理论基础提出了迫切需求。怎样建立这个理论基础？这对数学来说，也是极大的机会和挑战。这个演讲将从科学、数学和人工智能等三个方面全面地审视机器学习带来的机会和挑战，并试图提出我们应采取的应对措施。

摘要：Representationstabilitytheory,introducedbyThomasChurchandBensonFarbin2010,explorestheasymptoticbehaviorofasequenceofrepresentationsofgroups(suchassymmetricgroups,generallineargroups,etc.),andiswidelyappliedtoinvestigatepropertiesof(co)homologygroupsofmanyimportantexampleslikeconfigurationspaces,congruencesubgroups,mappingclassgroupsingeometricgrouptheory,algebraictopologyandalgebraicgeometry.Recentlythistheorywascategorifiedviaintroducingsomeinfinitediscretecategorieswithparticularcombinatorialstructureandstuyingtheirrepresentations.InthistalkIwilldescribethemotivation,background,currentdevelopentofthistheory,aswellasmyowncontribution.

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)