中国科大学位与研究生教育
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主讲教师:Kailiang Wu 人气:2422 更新时间: 2018年01月02日
摘要:Inthenumericalsimulationofrelativisticmagnetohydrodynamics(RMHD),awell-knownmajorcauseofproblemsiswhenthenumericalsolutionsviolatethephysicalboundconstraints,i.e.,thepositivityofthedensityandpressureaswellasthesubluminalconstraintonthefluidvelocity.Designofprovablybound-preserving(BP)schemesforRMHDishighlydesiredbutchallenging.ThedifficultiesmainlycomefromtheintrinsiccomplexityoftheRMHDequationsaswellastheindeterminaterelationbetweentheBPpropertyandthedivergence-freeconditiononthemagneticfield.Inthistalk,IamgoingtointroduceourrecenteffortonthedesignandanalysisoftheBPschemesforRMHD,whicharebasedondeeplystudyingseveralmathematicalpropertiesoftheadmissiblestateset.Itwillbeshownthatadiscretedivergence-freeconditioniscrucialforachievingtheBPproperty.Severalnumericalexampleswillbeprovidedtofurtherdemonstratethetheoreticalfindings.
主讲教师:刘会立 人气:2432 更新时间: 2018年01月02日
Abstract:在三维欧氏空间中利用直纹面的标准方程与球曲线标架定义直纹曲面的一种微分不变量;讨论这些不变量的几何意义与运动学特征;这些不变量与空间曲线的切线曲面,主法线曲面,副法线曲面的关系;在三维Minkowski空间中的一些应用等。
主讲教师:Liangming Shen 人气:2373 更新时间: 2018年01月02日
Abstract:WegeneralizedLott-Zhang\'smaximaltimeexistenceofcuspKahler-RicciflowwithsuperspatialinitialdatatoarbitraryinitialdatawithzeroLelongnumber.Firstweconstructthesolutionwithsmoothandboundedinitialbyperturbations.ThenbyDemailly\'sdecreasingapproximationmethodwhichwasdevelopedbyGuedj-Zeriahi,wecanconstructthesolutionwitharbitraryzerolelongnumberdata.Iftimepermits,wewilltalkabouttheapplicationsontheminimalmodelprogram,especiallyonlogcanonicalvarieties.ThisworkisjointwithAlbertChauandKa-FaiLi.
主讲教师:刘勇 人气:2287 更新时间: 2018年01月02日
Abstract:TheKP-Iequationisanimportantdispersiveequationappearinginmanyphysicalcontexts.Itisalsoaclassical2+1dimensionalintegrablesystem.Itsonedimensionalreductionisthewell-knownKdVequation.Inthistalk,wediscussthenonlinearstabilityoftheclassicallumpsolutiontotheKP-Iequation.WeinvestigatetheBacklundtransformationassociatedtothislump.Basedonthis,weshowthatthelumpsolutionisnondegeneratedinthesensethatthecorrespondinglinearizedKP-Ioperatordoesnothavenontrivialkernel.Generalizingthisargument,wealsoprovethataparticularfamilyof$y$-periodicsolitonsolutionsconnectedtolumpisnondegeneratedinsuitablesense.Finally,usingtheseresults,weprovethattheMorseindexofthelumpsolutionisequaltooneandthelumpisorbitallystable.Thequestionofasymptoticalstabilityremainsopen.ThisisjointworkwithJunchengWeifromUBC.
主讲教师:黄佳 人气:2347 更新时间: 2018年01月02日
摘要:The0-Heckealgebraisadeformationofthegroupalgebraofthesymmetricgroup.InthistalkIwillreviewsomeinterestingresultsregardingsymmetricgroupactionsoncertainquotientsofpolynomialringsandpresentanalogousresultsthatIhaveobtainedfor0-Heckealgebraactionsonsimilarquotients.SomeofmynewresultsarefromjointworkwithBrendonRhoades(UCSanDiego).
主讲教师:袁原 人气:2440 更新时间: 2018年01月02日
Abstract:ItfollowsfromthecomparisontheoremthatiftheKahlermanifoldhasbisectionalcurvatureatleast1,thenthediameterisnogreaterthanthediameterofthestandardprojectivespace.IwilldiscussarecentjointresultwithG.Liuregardingtherigiditywhenthediameterreachesthemaximum.
主讲教师:徐任远 人气:2268 更新时间: 2017年12月27日
摘要:Ingeneral,findingaNashequilibrium(NE)orprovingParetooptimality(PO)forcontinuous-timestochasticgamewithmultipleplayersishard,evenwhenthereareonlytwoplayersinthegame.MeanFieldGame(MFG)providesapowerfultoolandanalyticallyfeasibleframeworktoapproximatetheNEandthePOoftheN-playerstochasticgames.Inthistalk,wewillfirstpresentthestochasticgamefortheclassicalfinitefuelfollowerproblemintheseminalpaperbyBenes,Shepp,andWitsenhausen(1980).WewillthensolveandcomparewithexplicitsolutionsfortheNEandthePOoftheN-playergame,andthecorrespondingMFGwhenthenumberofplayersgoestoinfinity.ThisisajointworkwithProfessorXinGuofromUCBerkeley.Bio:RenyuanXuisafourth-yearPh.D.candidateinIndustrialEngineeringandOperationsResearch(IEOR)DepartmentatUCBerkeleywheresheworksunderthesupervisionofProfessorXinGuo.Herresearchfocusesontheinterfacebetweenmachinelearning,andstochasticoptimizationandcontrol,withapplicationsonbigdataespeciallyhighfrequencytrading.Shereceivedabachelor’sdegreeinMathematicsfromUniversityofScienceandTechnologyofChina(USTC)in2014.
主讲教师:黄佳 人气:2289 更新时间: 2018年01月02日
摘要:AninfinitecirculantdigraphistheCayleygraphoftheadditivegroupZofallintegerswithrespecttosomefinitesubsetSofZ.Theminimumdensityofadominatingsetinthisgraphiscalleditsdominationratio.WeestablishsomebasicresultsonthedominationratioofthisgraphandpreciselydetermineitwhenSconsistsoftwointegerssandtwithtdividings.ThisisjointworkwithJamesCarraher.
主讲教师:吴云辉 人气:2902 更新时间: 2017年12月26日
Abstract:WestudythesystolefunctionalongWeil-Peterssongeodesics.WeshowthatthesquarerootofthesystolefunctionisuniformLipschitzontheTeichmullerspaceendowedwiththeWeil-Peterssonmetric.Asanapplication,westudythegrowthoftheWeil-PeterssoninradiusofthemodulispaceofRiemannsurfacesofgenusgwithnpuncturesasafunctionofgandn.WeshowthattheWeil-Peterssoninradiusiscomparableto$sqrt{ln{g}}$withrespecttog,andiscomparableto1withrespectton.
主讲教师:何维勇 人气:2566 更新时间: 2017年12月26日
Abstract:WediscusscompactnessresultsofKahlermetricsinafixedKahlerclass,undergeometricassumptionssuchasRiccicurvatureboundand/orlog-volumeratiobound.TheclassicalresultinthisdirectionisYau’ssolutionoftheCalabiconjectureandcomplexMonge-Ampereequation.Ourmaininterestistodeducetheestimateofthemetric(estimatesofsecondorder),underthecertainminimalassumptions.Wesummarizesomeofouroldresults,andprovesomenewresultsinthisdirection.ThetalkisbasedonjointworkwithXiuxiongChenformanyyears,andrecentjointworkwithXiuxiongChenandTamasDarvas.
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Aranda Pino
Profesor of Department of Algebra, Geometry and Topology Science Faculty, University of Málaga, Spain. Research Interests: Leavitt path
Nikos Hadjichristidis
Prof. Nikos Hadjichristidis, Department of Chemistry, University of Athens.
蔡荣根
中国科学院理论物理所研究员,博士生导师。中国引力和相对论天体物理学会副理事长(2008-) 中国科学技术大学交叉学科理论研究中心兼职教授
欧阳钟灿
欧阳钟灿,中国科学院院士。1968年清华大学自控系毕业,1981年清华大学物理系固体物理专业获硕士学位,1984年获光学专业理学博士学位。1985-1986年在理论物理所
Manuela M. Veloso
Manuela M. Veloso教授是国际人工智能和自主机器人领域的主要学界领导人和学术带头人之一,取得了一系列杰出成就,其中部分成果产生了深远的影响。
庄小威
庄小威,华裔美籍生物物理学家,美国国家科学院院士, 哈佛大学化学与化学生物、物理学教授,创办有庄小威实验室。
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