分析组大会报告人_3.docx

分析组大会报告人郭坤宇(复旦大学数学科学学院)Tit1e：OperatortheoryontheBergmanspaceAbstract：Inthista1k,wewi11focusonoperatortheoryontheBergmanspace,andcombinemethodsofcomp1exana1ysis,grouptheoryandthetheoryofvonNeumanna1gebrastoestab1ishafascinatingconnectionbetweenoperatortheoryandfreegroupfactors.Aninterp1ayofana1ytica1,geometrica1,operatorandgrouptheoretica1techniquesisintrinsictothiswork.(1) AbriefsurveyofvonNeumanna1gebras;(2) OperatortheoryontheBergmanspace;(3) Ho1omorphiccoveringsofp1anardomains;(4) TypeIIfactorsfromconforma1geometry;(5) Freegroupfactors;(6) Orbifo1dp1anardomainsandtypeIIfactorsprob1ems,conjecturesandresu1ts.分析组邀请报告人(1)桂贵龙(江苏大学理学院)Tit1e:Ontheg1oba1we11-posednessofthe3-DinhomogeneousNavier-StokesequationsAbstract:Inthista1k,weconsiderthe1oca1andg1oba1we11-posednessofthe3-Dincompressib1einhomogeneousNavier-Stokesequations(INS),Withoutsma11nessassumptiononthevariationoftheinitia1densityfunction,wefirstprovethe1oca1we11-posednessof3-Dincompressib1einhomogeneousNavier-Stokesequationswithinitia1datainthecritica1Besovspaces.Thenweprovetheg1oba1we11-posednessof(INS)withhigh1yosci11atoryinitia1ve1ocityfie1dandanyinitia1densityfunctionwithapositive1owerbound.Ontheotherhand,weinvestigatetheg1oba1we11-posednessto(INS)with1argeinitia1ve1ocitys1ow1yvaryinginonespacevariab1eintheframeworkofanisotropictypeBesovspaces.(2)姚磊(西北大学数学系)Tit1e:Incompressib1e1imitofviscous1iquid-gastwo-phasef1owmode1Abstract:Weinvestigatetheincompressib1e1imitoftheviscous1iquid-gastwo-phasef1owmode1withperiodicboundaryconditions.Itisshownthatthe1oca1c1assica1so1utionofthetwo-phasef1owmode1convergestothe1oca1c1assica1so1utionoftheincompressib1eNavier-Stokesequations,as$epsi1onrightarrowinfty$whichbui1dsupthere1ationshipbetweenthetwo-phasef1owmode1andtheincompressib1eNavier-Stokesequations.Inaddition,wegivetheconvergencerateestimatesinsomenorms.ThisisajointworkwithProf.ChangjiangZhuandDr.RuizhaoZi(3)邵井海(北京师范大学数学学院)题目：随机过程的耦合及与维数无关的Hamack不等式摘要：(4)夏建明(中国科学院数学与系统科学研究院)题目:风险与不确定性厌恶摘要：对风险与不确定性下的偏好理论及其在金融学中的应用做一简要回顾并介绍本人在相关问题上的最新进展。(5)张希承(武汉大学数学与统计学院)Tit1e：$1Ap$-maxima1regu1arityofnon1oca1parabo1icequationandapp1icationsAbstract：ByusingFourier'stransformandFefferman-Stein1Stheorem,weinvestigatethe$1Ap$-maxima1regu1arityofnon1oca1parabo1icande11ipticequationswithsingu1arandnon-symmetric1,evyoperators,andobtaintheuniquestrongso1vabi1ityofthecorrespondingnon1oca1parabo1icande11ipticequations,wheretheprobabi1isticrepresentationp1aysanimportantro1e.Asaconsequence,acharacterizationforthedomainofpseudo-differentia1operatorsof1Vevytypewithsingu1arkerne1sisgivenintermsoftheBesse1potentia1spaces.Asabyproduct,wea1soshowthata1argec1assofnon-symmetric1Vevyoperatorsgeneratesanana1yticsemigroupin$1AP$-SPaCes.Moreover,asapp1ications,weproveaKry1ov,sestimateforstochasticdifferentia1equationsdrivenbyCauchyprocesses(i.e.critica1diffusionprocesses),anda1soobtaintheg1oba1we11-posednesstoac1assoffu11ynon1inearparabo1icequationwithcritica1diffusions.Inparticu1ar,critica1Hami1ton-Jacobiequationsandmu1tidimensiona1critica1Burger,sequationsareunique1yso1vab1eandthesmoothso1utionsareobtained.(6)冀书关(吉林大学数学科学学院)Tit1e:Timeperiodicso1utionsofnon1inearwaveequationsincomp1exmediaAbstract:ThisisajointworkwithProf.Yong1i.Inthista1k,weareconcernedwiththetimeperiodicso1utionsofnon1inearwaveequationincomp1exmediabeginequation)Mabe1E1-I)u(x)y_U-(u(x)y_x)_x+g(x,y)=f(x,t),xin(O,pi),tinmathbbR.end(equation)Byadjustingthebasisof$1A2$functionspace,Wecancircumventthedifficu1tiescausedbythecoefficientsthatdonotmeetthestrongconvexity,andobtaintheexistenceofweaktimeperiodicso1ution,whichwasposedasanopenprob1embyBarbuetc.in1997.Furthermore,wea1sopresenttheapp1icationstotheforcedSine-Gordonequationwithvariab1eorconstantcoefficients.(7)李洪全(复旦大学数学科学学院)题目：中心极大函数范数与维数相关性的新进展摘要：在本报告中，我们给出在各种流形上心极大函数范数与维数相关性的结果。(8)王凯(复旦大学数学科学学院)Tit1e:Reducingsubspacesforana1yticmu1tip1iersoftheBergmanspaceAbstract:Severa1yearsagosomeincisiveresu1tsareobtainedonthestructuresofthereducingsubspacesforthemu1tip1icationoperator$M_phi$forafiniteB1aschkeproduct$phi$ontheBergmanspaceontheunitdisk.Inparticu1ar,the1ineardimensionofthecommutant,$mathca1A)_phi=M_phi,M_phiA*'$,isshowntoequa1$q$,thenumberofconnectedcomponentsoftheRiemannsurface,$phiA-1circphi$.Inthista1k，wewi11showthatSmathca1A)_phi$iscommutativeandhenceisomorphictomathbbC)qS,andmoreover,thattheminima1reducingsubspacesarepairwiseorthogona1andtheactionof$M_phi$onanytwoofthemarenotunitari1yequiva1ent.Further,thenumberofmutua11yorthogona1minima1reducingsubspacesis$q$.Fina11y,anana1ytic/arithmeticdescriptionoftheminima1reducingsubspacesof$M_phi$isa1soprovided,a1ongwiththetaxonomyofthepossib1estructuresofthereducingsubspacesfor$M_phi$for$phi$havingeightzeros.Theseresu1tshaveimp1icationsinbothoperatortheoryandthegeometryoffiniteB1aschkeproducts.ThisisajointworkwithRona1dGDoug1asandMihaiPutinar.(9)陈琼蕾(北京应用物理与计算数学研究所)Tit1e:Onthei11-posednessofthecompressib