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主讲教师:苏中根 人气:1152 更新时间: 2020年12月31日 摘要:Normalapproximationisarguablyrecognizedasoneofthemostwidelyusedtoolsintheoreticalprobabilityandappliedstatistics.AlotofpowerfulmethodsandtrickshavebeensuccessfullydevelopedinestablishingnormalapproximationsforvariousstatisticssincetheclassicdeMoivreandLaplacecentrallimittheoremwasprovedintheearly19thcentury.InthistalkIshallbrieflyreviewsomerecentadvancesonnormalapproximationsforlineareigenvaluestatisticsinrandommatrixtheory.Incontrasttotheclassiccentrallimittheoremsforsumsofi.i.d.r.v.’s,oneusuallyrequiresthetestfunctionfsatisfiesacertainstrongregularity(smoothness)conditioninthestudyoflineareigenvaluestatistics,sayPni=1f(λi),wheretheλiareeigenvaluesofarandommatrix.Whattestfunctionisgoodseemstodependheavilyonthetricksusedintheargument. 主讲教师:邱宇 人气:941 更新时间: 2020年12月31日 摘要:WediscusstherelationsbetweenvariousCalabi-Yaucategoriesofgentletypeandtheirtopologicalrealizations.ThisisajointworkwithIkedaandZhou. 主讲教师:徐国义 人气:4264 更新时间: 2020年12月19日 摘要:Intheseriesoftalks,onageodesicballwithnon-negativeRiccicurvatureandalmostmaximalvolume,weconstructthealmostlinearharmonicmaponaconcentricgeodesicballwithuniformlysmallradius.Weusethedistanceestimateformulaonthegeodesicballandinductionmethodtoproducetheharmonicmap.Andthisintrinsicmethodgivestheintegralgradientestimateofharmonicmapintermofthevolumeexplicitly.Asoneapplication,weestablishthequantitativedifferenceestimateoftworelatedharmonicfunctionsdefinedongeodesicballandEuclideanballrespectively.ThetalkwillrequireonesemesterRiemanniangeometryandonesemesterPDEcoursebackground.Thedetailswillbegiven.ThisisajointworkwithJieZhouinMathDepartmentofTsinghua. 主讲教师:江智 人气:1002 更新时间: 2020年12月09日 12-07【江 智】五教5507教室华罗庚讨论班特邀报告报告题目:霍奇猜想报告人:江智,复旦大学时间:2020年12月7日(星期一)19:00-21:00地点:东区第五教学楼5507教室摘要:霍奇猜想科普。 主讲教师:余讯 宋雷 江智 沈洋 周明铄 曹阳 申屠钧超 人气:2491 更新时间: 2020年12月09日 【12月5日-12月7日】天元代数几何讨论班天元代数几何线下活动系列:12月5-7日,地点:科大东区5教5301,5206邀请报告人:短课程系列:余讯(天津大学):Calabi-Yauvarietiesandautomorphismsgroups宋雷(中山大学):QuotientScheme江智(复旦大学):Syzygiesofabelianvarieties沈洋(南京大学):CanonicalsectionsofHodgebundles学术报告:周明铄(天津大学):Frobeniussplittingandmoduliofvectorbundles曹阳(中科大):Arithemeticpurityoflocal-globalprinciple申屠钧超(中科大)*会议安排:周六(12-05):东区五教530109:00-10:30:宋雷QuotSchemes(I-II)10:45-11:45:余讯AutomorphismgroupsofCalabi-Yaumanifolds(I)14:00-15:30:余讯AutomorphismgroupsofCalabi-Yaumanifolds(II,III)16:00-17:00:曹阳Arithemeticpurityoflocal-globalprinciple周日(12-06):东区五教530109:00-10:30:沈洋CanonicalsectionsofHodgebundles(I,II)10:45-11:45:宋雷QuotSchemes(III)14:00-15:30:江智Syzygiesofabelianvarieties16:00-17:30:沈洋CanonicalsectionsofHodgebundles(III,IV)周一(12-07):东区五教520609:00-10:00:周明铄Frobeniussplittingandmoduliofvectorbundles10:15-11:15:申屠钧超OnlineSeries:InvitedSpeakers:OsamuFujino(OsakaUniversity),LeiWu(UniversityofUtah),Talkinformation:OsamuFujino(OsakaUniversity):Onmixed-$omega$-sheavesZoomMeetingid:63193349493;Time2020-12-0209:40(ChineseZone)=10:40(JapaneseZone);Password:341282ZoomMeetingid:64635264757;Time2020-12-0909:40(ChineseZone)=10:40(JapaneseZone);Password:178142ZoomMeetingid:68285908628;Time:2020-12-1609:40(ChineseZone)=10:40(JapaneseZone);Password:900562吴磊(UniversityofUtah:V-filtrations,nearbyandvanishingcycles,Hodgemodulesandvanishingtheorems会议时间:2020/12/13(周日)09:30-12:00腾讯会议ID:49996820391会议密码:2020会议主页:staff.ustc.edu.cn/~zhlei18/tianyuan-welcome.html 主讲教师:袁日荣 人气:991 更新时间: 2020年12月05日 报告摘要:Inthistalk,wewillconsidertheproblemoffindingcompleteconformalmetricswithprescribedcurvaturefunctionsofEinsteintensorandmoregeneralmodifiedSchoutentensorsonmanifoldswithboundary.Theasymptoticbehaviorofcompleteconformalmetricsnearboundaryisalsoformulated.Ourmethodisbasedonpartialuniformellipticity.Interestingly,atopologicalobstructionshowsthatthestrategyandassumptionsimposedthereareratherappropriateanddelicate.Finally,wefurtherdiscussHessianandWeingartenequationsbyconfirmingakeyassumption. 主讲教师:王宏玉 人气:983 更新时间: 2020年12月05日 摘要:Inthistalk,wediscusstheChern-Hopfconjecture.LetMbeaclosedsymplecticmanifoldofdimension2nwithnon-ellipticity.WecandeneanalmostKahlerstructureonMbyusingthegivensymplecticform.UsingDarbouxcoordinatecharts,wedeformthegivenalmostKahlerstructuretoobtainahomotopyequivalentmeasurableKahlerstructureontheuniversalcoveringofM.AnalogoustoTeleman\'sL2-HodgedecompositiononPLmanifoldsorLipschitzRiemannianmanifolds,wegiveaL2-HodgedecompositiontheoremontheuniversalcoveringofMw.r.t.themeasurableKahlermetric. 主讲教师:Zhou ZHANG 人气:1290 更新时间: 2020年11月26日 Abstract:Inthepasttenyearsorso,thestudyofKahler-Ricciflowhasbeenreformedquiteessentially.ByallowingtheKahlerclasstoevolvewithtime,werevealitsnaturalrelationwiththeMinimalModelPrograminalgebraicgeometryasoutlinedinTian’sProgram.ThisalsobringsthesubjectalotclosertothestudyofRicciflow,andtightenstherelationwithpluripotentialtheoryinseveralcomplexvariables.Withmoretoolsandconceptsintroducedintothisresearchfieldfromothermajorbranchesofpuremathematics,wehavegotmanyanswerswithevenmoreproblemsforfuturework.Inthistalk,weaimatadescriptionofthewholestory,accessibleforthegeneralaudience. 主讲教师:陶琪 人气:1371 更新时间: 2020年11月23日 摘要:Inthispaper,westudysuperconvergencepropertiesoftheultraweak-localdiscontinuousGalerkin(UWLDG)methodforanone-dimensionallinearfourth-orderequation.Withspecialinitialdiscretizations,weprovethenumericalsolutionofthesemi-discreteUWLDGschemesuperconvergestoaspecialprojectionoftheexactsolution.Theorderofthissuperconvergenceisprovedtobek+min(3,k)whenpiecewiseP^kpolynomialswithk≥2areused.Wealsoprovea2k-thordersuperconvergencerateforthecellaveragesandforthefunctionvaluesandderivativesoftheUWLDGapproximationatcellboundaries.Moreover,weprovesuperconvergenceof(k+2)-thand(k+1)-thorderofthefunctionvaluesandthefirstorderderivativesoftheUWLDGsolutionataclassofspecialquadraturepoints,respectively.Ourproofisvalidforarbitrarynon-uniformregularmeshesandforarbitraryk≥2.Numericalexperimentsverifythatalltheoreticalfindingsaresharp. 主讲教师:李芳 人气:1142 更新时间: 2020年11月23日 摘要:Weintroduceandstudyaclassoffreeboundarymodelswith``nonlocaldiffusion\'\',whicharenaturalextensionsofthefreeboundarymodelsin[1]andelsewhere,where``localdiffusion\'\'isusedtodescribethepopulationdispersal,withthefreeboundaryrepresentingthespreadingfrontofthespecies.Weshowthatthisnonlocalproblemhasauniquesolutiondefinedforalltime,andthenexamineitslong-timedynamicalbehaviorwhenthegrowthfunctionisofFisher-KPPtype.Weprovethataspreading-vanishingdichotomyholds,thoughforthespreading-vanishingcriteriasignificantdifferencesarisefromthewellknownlocaldiffusionmodelin[1].Furthermore,weestablishathresholdconditiononthekernelfunctionsuchthatspreadinggrowslinearlyintimeexactlywhenthisconditionholds,whilewhenthekernelfunctionviolatesthiscondition,acceleratingspreadinghappens.[1]Y.Du,Z.Lin,Spreading-Vanishingdichotomyinthediffusivelogisticmodelwithafreeboundary,SIAMJ.Math.Anal.,42(2010)377-405. |
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