摘要：Normalapproximationisarguablyrecognizedasoneofthemostwidelyusedtoolsintheoreticalprobabilityandappliedstatistics.AlotofpowerfulmethodsandtrickshavebeensuccessfullydevelopedinestablishingnormalapproximationsforvariousstatisticssincetheclassicdeMoivreandLaplacecentrallimittheoremwasprovedintheearly19thcentury.InthistalkIshallbrieflyreviewsomerecentadvancesonnormalapproximationsforlineareigenvaluestatisticsinrandommatrixtheory.Incontrasttotheclassiccentrallimittheoremsforsumsofi.i.d.r.v.’s,oneusuallyrequiresthetestfunctionfsatisfiesacertainstrongregularity(smoothness)conditioninthestudyoflineareigenvaluestatistics,sayPni=1f(λi),wheretheλiareeigenvaluesofarandommatrix.Whattestfunctionisgoodseemstodependheavilyonthetricksusedintheargument.

摘要：WediscusstherelationsbetweenvariousCalabi-Yaucategoriesofgentletypeandtheirtopologicalrealizations.ThisisajointworkwithIkedaandZhou.

摘要:Intheseriesoftalks,onageodesicballwithnon-negativeRiccicurvatureandalmostmaximalvolume,weconstructthealmostlinearharmonicmaponaconcentricgeodesicballwithuniformlysmallradius.Weusethedistanceestimateformulaonthegeodesicballandinductionmethodtoproducetheharmonicmap.Andthisintrinsicmethodgivestheintegralgradientestimateofharmonicmapintermofthevolumeexplicitly.Asoneapplication,weestablishthequantitativedifferenceestimateoftworelatedharmonicfunctionsdefinedongeodesicballandEuclideanballrespectively.ThetalkwillrequireonesemesterRiemanniangeometryandonesemesterPDEcoursebackground.Thedetailswillbegiven.ThisisajointworkwithJieZhouinMathDepartmentofTsinghua.

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。

【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

报告摘要：Inthistalk,wewillconsidertheproblemoffindingcompleteconformalmetricswithprescribedcurvaturefunctionsofEinsteintensorandmoregeneralmodifiedSchoutentensorsonmanifoldswithboundary.Theasymptoticbehaviorofcompleteconformalmetricsnearboundaryisalsoformulated.Ourmethodisbasedonpartialuniformellipticity.Interestingly,atopologicalobstructionshowsthatthestrategyandassumptionsimposedthereareratherappropriateanddelicate.Finally,wefurtherdiscussHessianandWeingartenequationsbyconfirmingakeyassumption.

摘要：Inthistalk,wediscusstheChern-Hopfconjecture.LetMbeaclosedsymplecticmanifoldofdimension2nwithnon-ellipticity.WecandeneanalmostKahlerstructureonMbyusingthegivensymplecticform.UsingDarbouxcoordinatecharts,wedeformthegivenalmostKahlerstructuretoobtainahomotopyequivalentmeasurableKahlerstructureontheuniversalcoveringofM.AnalogoustoTeleman\'sL2-HodgedecompositiononPLmanifoldsorLipschitzRiemannianmanifolds,wegiveaL2-HodgedecompositiontheoremontheuniversalcoveringofMw.r.t.themeasurableKahlermetric.

Abstract:Inthepasttenyearsorso,thestudyofKahler-Ricciflowhasbeenreformedquiteessentially.ByallowingtheKahlerclasstoevolvewithtime,werevealitsnaturalrelationwiththeMinimalModelPrograminalgebraicgeometryasoutlinedinTian’sProgram.ThisalsobringsthesubjectalotclosertothestudyofRicciflow,andtightenstherelationwithpluripotentialtheoryinseveralcomplexvariables.Withmoretoolsandconceptsintroducedintothisresearchfieldfromothermajorbranchesofpuremathematics,wehavegotmanyanswerswithevenmoreproblemsforfuturework.Inthistalk,weaimatadescriptionofthewholestory,accessibleforthegeneralaudience.

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.

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.