中国科大学位与研究生教育
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主讲教师:王成 人气:252 更新时间: 2017年08月31日
摘要:Afewpreconditionedsteepestdescent(PSD)solversarepresentedforthecertainoptimizationproblems,inwhichthesolutioncorrespondstoaconvexenergyfunctional.Thehighestandlowestordertermsareconstant-coefficient,positivelinearoperators.Byusingtheenergydissipationproperty,wederiveadiscreteboundforthesolution,aswellasanupper-boundforthesecondderivativeoftheenergy.Theseboundsallowustoinvestigatetheconvergencepropertiesofourmethod.Inparticular,ageometricconvergencerateisshownforthenonlinearPSDiterationappliedtotheregularizedequation,whichprovidesamuchsharpertheoreticalresultovertheexistingworks.Somenumericalsimulationresultsarealsopresentedinthetalk.
主讲教师:Fred Van Oystaeyen 人气:473 更新时间: 2017年08月26日
摘要:Ifyouwantnoncommutativegeometrytoapplytorealityyouhavetomakeanoncommutativeversionofspace-time.Sinceinrelativitytheorythecurvatureofspaceisinfluencedbygravitythatgeometryhastobedynamical,ie.changeintime.SoIstartfromanaxiomaticdefinitionofnoncommutativegeometryandmakeitvaryovertime.Thereisanotionofcommutativeshadowofanoncommutativegeometrydefinedbyplaceswithtrivialself-intersection(inthenoncommutativespacetherearemanyplaceswithnon-trivialself-intersection.Undersomeminimal"continuity"assumptionsonecanconstructadynamicalcommutativegeometry(inphysicsyoucanassumethisisateachmomentanalyticallyisomorphictousualspace-time!)Iconstructtemporalpointsanda"momentspace"ateachmomentwhichturnsoutalsotobeacommutativegeometry.Fromthedynamicalsheaftheoryonmynotionofnoncommutativespaceoneobtainsadescriptionofthestalkatsometemporalpointofthenoncommutativesheafintermsofthestalkatthecorrespondingpointinthemomentspace.Thisstatesthatthenoncommutativesheafonthenoncommutativespaceisdeterminedbythecommutativetheoryonthemomentspace(butthatisaspaceofhigherdimension!).Themodelobtainedallowssomeelegantexplanationofquantumphenomena,thetalkwillendwithsomeremarksaboutthemeaningoftheassumptionthatourrealityisinadynamicalnoncommutativegeometry,includingsomePhysicsegthedoubleslitexperiment.报告人简介:ProfVanOystaeyenisemeritusattheuniversityofAntwerp.HestartedlonglastingprojectontheBrauergroup,thenoncommutativeschemetheoryofassociativealgebras,gradedringsandprojectivegeometry.Hepublishedover300scientificpublicationsincludingoneonBotanyandaproceedingsonRobotics.HealsopioneeredatheoryofnoncommutativespacewithsomenewideasforPhysics.ManyEuropeanresearchprojectsoftheECandtheESFwereorganizedbyhimbutalsoeducationprojectsinMathematicslikeErasmus,Tempus,....Healsoorganizedorco-organizedMorethan50internationalmeetingsinmanycountriesandguidedabout40Ph.D.students.HewashonoraryprofessoratBeijingNormalUniversity,andobtainedtheDoctorHonorisCausadegreeattheuniversityofAlmeria(Spain).
主讲教师: 人气:2013 更新时间: 2017年08月14日
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主讲教师:Yongqiang Liu 人气:443 更新时间: 2017年08月10日
摘要:Weusethenon-properMorsetheoryofPalais-Smaletoinvestigatethetopologyofsmoothclosedsubvarietiesofcomplexsemi-abelianvarieties,andthatoftheirinfinitecycliccovers.Asmainapplications,weobtainthefinitegeneration(exceptinthemiddledegree)ofthecorrespondingintegralAlexandermodules,aswellasthesignedEulercharacteristicpropertyandgenericvanishingforrank-onelocalsystemsonsuchsubvarieties.Furthermore,wegiveamoreconceptual(topological)interpretationofthesignedEulercharacteristicpropertyintermsofvanishingofNovikovhomology.Asabyproduct,weproveagenericvanishingresultfortheL2-Bettinumbersofveryaffinemanifolds.OurmethodsalsorecastJunHuh\'sextensionofVarchenko\'sconjecturetoveryaffinemanifolds,andprovideageneralizationofthisresultinthecontextofsmoothclosedsubvarietiesofsemi-abelianvarieties.ThisisajointworkwithLaurentiuMaximandBotongWang.
主讲教师:Chengjian Yao 人气:310 更新时间: 2017年08月10日
摘要:Atripleofsymplecticformsonadifferentiable4-manifold,spanningamaximalpositivesubspaceofLambda^2ateachpointiscalledahypersymplecticstructure.ThisnotionwasintroducedbyDonaldsoninhisprogrammeofstudyingtheadiabaticlimitsofG_2manifolds.HyperKaehlermanifoldsofdimension4giverichsourcesofhypersymplecticstructures,andwereconjecturedbyDonaldsontobethe"onlysources"inthecompactcase.Westudyageometricflow---hypersymplecticflow--ofsuchstructures,designedtodeformagivenhypersymplecticstructuretoahyperKaehleroneinthesamecohomologyclass.Thisflowisadimensionalreductionofthemorewell-knownG_2LaplacianflowintroducedbyHitchinandBryanttostudytheexistenceofmetricswithG_2holonomy.Weshowthatthehypersymplecticflowdoesnotdevelopfinitetimesingularitywithuniformlyboundedtorsion.Wealsostudytheconvergenceoftheglobalsolutionoftheflowundervariousgeometricconditions.ThisisjointworkwithJoelFine.
主讲教师:朱富海 人气:442 更新时间: 2017年08月10日
摘要:Inthistalk,wewillintroducesomebasicpropertiesofRota-BaxteroperatorsandwilldescribesomeclassofRota-BaxteroperatorsonsemisimpleLiealgebras,whichwillbeusedtoconstructleft-invariantflatconnectionsonLiegroups.
主讲教师:王冉 人气:305 更新时间: 2017年08月07日
摘要:Usingthehyper-exponentialrecurrencecriterion,alargedeviationprinciplefortheoccupationmeasureisderivedforaclassofnon-linearmonotonestochasticpartialdifferentialequations.ThemainresultsareappliedtomanyconcreteSPDEssuchasstochastic$p$-Laplaceequation,stochasticporousmediumequation,stochasticfast-diffusionequation,andevenstochasticrealGinzburg-Landauequationdrivenby$alpha$-stablenoises.JointworkwithJieXIONGandLihuXU.
主讲教师:何维勇 人气:462 更新时间: 2017年08月03日
摘要:RecentlyGurskyandStreetsintroduceaveryinterestinggeometricstructureonspaceofConformalmetricinthecontextofsigma-2problemonfourmanifold.Thegeodesicequationisafullynonlineardegenerateellipticequation.InthistalkwediscussthesolutionoftheGursky-StreetsequationwithC^1\'1regularity
主讲教师:林治武 人气:464 更新时间: 2017年08月03日
摘要:Westudythemetastabilityoftheshearflowsiny(Kolmogorovflow)for2DNavier-Stokesequationinatorus.Thisflowisnonlinearlystablefortheinviscidcase.Whentheviscosityissmallenough,itisshownthatthenon-shearpartoftheperturbationscandecayatamuchfasterratethantheviscoustimescale,foranintermediatebutlongtimeperiod.TheresultistrueforthelinearizedNSequationwithanyinitialvorticityinL2,andforthenonlinearNSequationwithinitialvorticityofthesizeofviscosity.WealsoconsidertheinvisciddampingfortwoclassesofshearflowsbyusingtheHamiltonianstructuresofthelinearizedEulerequation.ThisisajointworkwithMingXu.
主讲教师:徐方军 人气:251 更新时间: 2017年08月02日
摘要:Giventwoindependentd-dimensionalfractionalBrownianmotions(fBms)withthesameHurstindexH,weconsiderthelimittheoremsforfunctionalsofthesetwofBmsinthecasesHd<2andHd=2.
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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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