中国科大学位与研究生教育
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主讲教师:屈长征 人气:527 更新时间: 2017年09月29日
主讲教师:李换换 人气:737 更新时间: 2017年09月28日
摘要:WeconsiderthegradedSteinbergalgebraofagradedampleHausdorffgroupoid.WeshowthatthiscategoryisisomorphictothecategoryofunitalleftmodulesovertheSteinbergalgebraoftheskew-productgroupoidarisingfromthegrading.Todothis,weshowthattheSteinbergalgebraoftheskewproductisgradedisomorphictoanaturalgeneralisationofthetheCohen-MontgomerysmashproductoftheSteinbergalgebraoftheunderlyinggroupoidwiththegradinggroup.Specialisingtothesettingofdirectedgraphs,weproducearepresentationofthemonoidofgradedfinitelygeneratedprojectivemodulesoveraLeavittpathalgebra.
主讲教师:胥世成 人气:649 更新时间: 2017年09月25日
Abstract:WewilltalkaboutarecentworkonthestabilityofnilpotentstructuresonacollapsedmanifoldwithboundedsectionalorRiccicurvature.Amanifoldofboundedsectionalcurvatureiscalledepsilon-collapsed,iftheinjectivityradius,orequivalentlythevolumeofunitball,ateverypointsislessthanepsilon.Thegeometry/topologyofacollapsedmanifoldcanbetotallydescribedbyCheeger-Fukaya-Gromov\'snilpotentstructure.SimilarresultshadbeenextendedtomanifoldsofboundedRiccicurvatureundersomeadditionalassumptions.ThestabilityoflocallydefinednilpotentstructureswereessentialintheworkofCheeger-Fukaya-Gromovtoconstructaglobalnilpotentstructureononefixedmetric.Nilpotentstructuresalsodependonthechoiceofepsilon,thecollapsedlengthscaleoneinspects.WeprovethatiftwometricsonamanifoldareL_0-bi-Lipchitzequivalentandsufficientcollapsed(dependingonL_0)underbounded(Ricci)curvature,thentheunderlyingnilpotentstructuresareisomorphictoeachother.Asapplications,weestablishalinkbetweenthecomponentsofthemodulispaceofallcollapsedRiemannianmetricsandthesetofisomorphismclassesofnilpotentstructures,andderiveanewparametrizedversionofGromov\'sflatmanifoldtheoremunderboundedRiccicurvatureandconjugateradius.
主讲教师:鲍建海 人气:334 更新时间: 2017年09月25日
摘要:Inthistalk,weshallestablishtheasymptoticlog-Harnackinequalityforarangeofpath-dependentSDEs,whichallowthelengthofmemorytobeinfiniteandthediffusiontermstobedependentfullyonthepasthistory.Werevealthattheasymptoticlog-Harnackinequalityimplies(i)theasymptoticheatkernelestimate,(ii)theabsolutecontinuityofthetransitionkernelw.r.t.theinvariantprobabilitymeasureand(iii)theuniquenessofinvariantprobabilitymeasure(ifitexists).Asanotherbyproductoftheasymptoticlog-Harnackinequality,wealsoderivetheasymptoticgradientestimate,whichfurtherimpliesthatthesemigroupgeneratedbythesegmentprocessenjoystheasymptoticstrongFellerproperty.
主讲教师:Freddy Delbaen 人气:368 更新时间: 2017年09月21日
Abstract:In1947MarkKacprovedthatforacentredHoeldercontinuousfunction$f$definedon$[0,1]$andextendedperiodicallytothewholerealline,thesequence$f(2^kt)$satisfiesaCentralLimitTheorem.Weextendtheresulttomeasurable$L^2$functionssatisfyingafastapproximationproperty.TheresultnaturallyextendstosimilarfunctionsdefinedonBernoullishifts.
主讲教师:蒋继发 人气:351 更新时间: 2017年09月19日
摘要:Thistalkfocusesonexploringtheglobalstabilityofnonlinearstochasticfeedbacksystemsonthenonnegativeorthantdrivenbymultiplicativewhitenoiseandpresentingacoupleofsmall-gainresults.Weinvestigatethedynamicalbehaviorofpull-backtrajectoriesforstochasticcontrolsystemsandprovethatthereexistsauniquegloballyattractingpositiverandomequilibriumforthosesystemswhoseoutputfunctionseitherpossessboundedderivativesorareuniformlyboundedawayfromzero.Ourresultscanbeappliedtowell-knownstochasticGoodwinnegativefeedbacksystem,Othmer-TysonpositivefeedbacksystemandGriffithpositivefeedbacksystemaswellasotherstochasticcooperative,competitiveandpredator-preysystems.ThisisajointworkwithDr.LvXiang.
主讲教师:董昭 人气:382 更新时间: 2017年09月19日
摘要:通过两类具体方程,浅谈有关随机微分方程和随机偏微分方程渐进稳定性的研究感想。
主讲教师:殷浩 人气:525 更新时间: 2017年09月19日
Abstract:Inthistalk,weuse2-Dharmonicmapasanexampletoillustratethebasictheoryofneckanalysis.Theproofswillbealmostself-contained.WealsocomparewiththeYang-Millstheoryandoutlinesomegeneralizationoftheargument.
主讲教师:Jani Virtanen 人气:379 更新时间: 2017年09月19日
摘要:Idiscusssomerecentresultsonboundednessandcompactnessof(generalized)ToeplitzoperatorsactingonBergmanspacesoftheunitdiskandonFockspacesofthecomplexplane,andstatesomerelatedopenproblems;inparticular,thereisstillnocompletecharacterizationofboundedToeplitzoperatorsonBergmanspaces.WhilespectraltheoryofToeplitzoperatorsonHardyspacesiswellunderstood,muchlessisknownabouttheminBergmanandFockspaces.Inparticular,thereareveryfewresultsonFredholmnessofToeplitzoperatorsonFockspaces.IdiscusssomerecentgeneralizationsoftheresultsintheHilbert-Fockspacetotheother(generalized)Fockspaces,andlistrelatedopenproblems.
主讲教师:Jaap van der Vegt 人气:397 更新时间: 2017年09月14日
摘要:Inthenumericalsolutionofpartialdifferentialequations,itisfrequentlynecessarytoensurethatcertainvariablesremainpositive;otherwiseunphysicalsolutionswillbeobtainedthatmightresultinthefailureofthenumeralalgorithm.Positivityofcertainvariablesisgenerallyensuredusingpositivitypreservinglimiters,whichlocallymodifythesolutiontoensurethattheconstraintsaresatisfied.Thecombinationof(positivitypreserving)limitersandimplicittimeintegrationmethodsresults,however,inseriousproblems.Manylimitershaveacomplicated,non-smoothformulationthatisdifficulttolinearize,whichseriouslyhamperstheuseofstandardNewtonmethodstosolvethenonlinearalgebraicequationsoftheimplicittimediscretization.Inthispresentation,wewilldiscussadifferentapproachtoensurethatthenumericalsolutionsatisfiesthepositivityconstraints.Insteadofusingalimiter,weimposethepositivityconstraintsdirectlyonthealgebraicequationsresultingfromadiscontinuousGalerkinmethodbyreformulatingtheDGequationswithconstraintsusingtechniquesfrommathematicaloptimizationtheory.Theresultingalgebraicequationsarethensolvedusingasemi-smoothNewtonmethodthatiswellsuitedtodealwiththeresultingnonlinearcomplementarityproblem.ThisapproachallowsthedirectimpositionofconstraintsinimplicitdiscontinuousGalerkindiscretizations,withouttheconstructionofcomplicatedlimiters,andresultsinmoreefficientsolversfortheimplicitdiscretization.
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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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