摘要：Anewnotionofgraphcoloringwillbeintroducedinthistalk:Givenasystemofgraphs$G_1,dots,G_m$onthesamevertexsetV,acooperativecoloringisapartitionofthevertexsetwithparts$I_1,dots,I_m$suchthat$I_j$isindependentin$G_j$.Heuristicallythisnewnotionisin-betweentheusualcoloringandtheexistenceofindependenttransversalssatisfyingacertain"locality"constraint.

摘要：Inthistalk,wewilldiscusstheprincipaleigenvaluetheoryforperiodicnonlocaldispersalsystemswithtimedelay.First,wewillintroduceageneralizedKrein-Rutmantheoremandsomepropertiesaboutresolventpositiveoperators.Then,wewillgivetheanalysisofessentialspectrumpointsforthecorrespondingsystem.Atlast,wewillpresentasufficientconditionfortheexistenceoftheprincipaleigenvalue.

Abstract：WeconsidertheDiracoperatorofageneralmetricinthecanonicalconformalclassonthenoncommutativetwotorus,twistedbyanidempotent(representingtheK-theoryclassofageneralnoncommutativevectorbundle),andderivealocalformulafortheFredholmindexofthetwistedDiracoperator.OurapproachisbasedontheMcKean-Singerindexformula,andexplicitheatexpansioncalculationsbymakinguseofConnes\'pseudodifferentialcalculus.Asatechnicaltool,anewrearrangementlemmaisprovedtohandlechallengesposedbythenoncommutativityofthealgebraandthepresenceofanidempotentinthecalculationsinadditiontoaconformalfactor.

2019几何分析夏季研讨会（6月15-16日）会议时间：2019年6月15日－16日（14日报到，17日离会）会议地点：中国科学技术大学东区管理科研楼1418室/第五教学楼5206室会议简介：为了提升与繁荣国内几何分析相关课题的研究工作，总结和交流近期研究成果，“2019几何分析夏季研讨会”将于2019年6月14日-17日在中国科学技术大学举行。会议议题：几何热流及其在微分几何、复几何中的应用。

第六届学术交流会数学分会场会议议程时间：2019年6月12日下午14:30-17:30地点：东区五教5107教室主持人：陈世炳会议议程：一、院领导致辞二、学术报告三、交流和评分

摘要：Weconsiderthesolutiontoatight-binding,periodicSchrödingerequationwitharandompotentialevolvingstochasticallyintime.IfthepotentialevolvesaccordingtoastationaryMarkovprocessweobtainapositive,finitediffusionconstantfortheevolutionofthesolution.Moregenerally,weshowthatthesquareamplitudeofthewavepacket,afterdiffusiverescaling,convergestoasolutionoftheheatequation.(JointworkwithJ.SchenkerandZ.TiloccoattheMichiganStateUniversity).

摘要：Duringthelasttwodecades,ithasbeenoneofthecentralproblemtocomputetheGromov-WitteninvariantsofCalabi-Yau3-foldsingeometryandphysics.Inthistalk,wewilldiscusstherecentmathematicalapproachtotheallgeneraGromov-Wittenpotentialfunctionsofthequinticthreefolds.Wewillalsodiscussaboutthepossiblegeneralizationsofthesemethods.

摘要：Inthistalk,wewillreviewourworkonsolvingsteadyEulerequations.Themotivationandimportanceoftheproblemswillbebrieflyintroduced.TowardstherobustnessandefficiencyofthefinitevolumemethodsforEulerequations,weproposedanadaptivemeshmethodsbasedontheerrorindicatorgeneratedfromtheadjointproblems,andintroducetheNURBStechniquetoimprovetheperformanceofthealgorithmoncomplexdomains.Numericalexperiemntsshowtheeffectivenessoftheproposedframework.Finally,wewillbrieflyintroducetheongoingworkontheshapeoptimization.

摘要：Inthistalk,IwillreviewtheLyapunov-Schmidtproceduretoseehowtoreduceahigh-orinfinite-dimensionalproblemtoaproblemhavingalowdimensions.Inparticular,weshallseehowthestructuralconstraints(suchasHamiltonian,reversible,symmetriesandsoon)affectthebifurcationequations.

摘要:Inthistalk,wedealwiththecomplexMonge-AmpereequationproposedbyGromovonclosedalmostKaehlermanifoldsandextendtoarbitrarydimensionanon-existenceresultprovedincomplexdimension2.AlsoweconsiderCalabi-Yauequationonclosedsymplecticmanifolds