【1月4日】WorkshoponGeometryandPhysicsDate:January4,2020(Saturday)Place:Room1418,ManagementR&DBuilding,USTC8:40-8:50OpeningRemarks8:50-9:40QiDingLiouvilleTheoremsandHessianEstimatesforSpecialLagrangianEquations9:55-10:45ShibingChen$L_p$-Brunn-MInkowskiinequalityfor$p<1.$10:55-11:45GuoyiXuThegrowthrateofharmonicfunctions14:30-15:20XuezhangChenConformalcurvatureflowsoncompactmanifolds15:35-16:25SongShaoNilpotentsystemsintopologicalandergodicdynamics16:35-17:25DiYangOnHodge-GUEcorrespondenceOrganizers:BingWang(USTC)BinXu(USTC)

Abstract：ThisisapartialworkofanongoingprojectwithJianxunHuandBai-LingWang.ThegoaloftheprojecttoconstructageneralschemeforKtheory,complex(co)bordismtheoryandetc.formodulispaces.Inthistalk,IwillfocusontheKtheorycaseandexplainhowtoconstructtherelatedtheoryonvirtualorbifoldsintroducedbyTianandmyself.

Abstract：WewilltalkaboutourrecentworkontheproofofthegluingformulaofBismut-Lottanalytictorsionforms.ThegluingformulawillplayanimportantroleinestablishingahigherversionofCheeger-Mllertheorem.ThisisajointworkwithMartinPucholandYepingZhang.

南京大学刘佳副研究员学术报告会题目:RFID标记识别与空间感知时间:2020年1月3日10:00地点:西区电三楼632学术报告厅

摘要：WeproposeaninexactproximalaugmentedLagrangianframeworkwithexplicitinnerproblemterminationruleforcompositeconvexoptimizationproblems.Weconsiderarbitrarylinearlyconvergentinnersolverincludinginparticularstochasticalgorithms,makingtheresultingframeworkmorescalablefacingtheever-increasingproblemdimension.Eachsubproblemissolvedinexactlywithanexplicitandself-adaptivestoppingcriterion,withoutrequiringtosetanaprioritargetaccuracy.Whentheprimalanddualdomainarebounded,ourmethodachievesthebestknowncomplexityboundsintermsofnumberofinnersolveriterations,respectivelyforthestronglyconvexandnon-stronglyconvexcase.Withouttheboundednessassumption,onlylogarithmtermsneedtobeadded.Withinthegeneralframeworkthatwepropose,wealsoobtainthefirstiterationcomplexityboundsunderrelativesmoothnessassumptiononthedifferentiablecomponentoftheobjectivefunction.Weshowthroughtheoreticalanalysisaswellasnumericalexperimentsthecomputationalspeedupachievedbytheuseofrandomizedinnersolversforlarge-scaleproblems.

报告人简介：谢凡，男1981年生，副研究员，2011年获博士学位。目前担任中国地震局地球物理研究所先导技术研究室岩石物理学科组组长。主要从事多重散射波传播机制及应用方面工作，重点是发展基于多重散射波的介质变化三维动态成像方法及其跨尺度的监测应用。主持国家级基金3项，发表论文10余篇，其中包括JGR，SHM，Ultrasonics等杂志。

摘要：Intheyear1970,Kobayashiintroducedanintrinsiccanonicalmetricforeverycomplexmanifold$X$,andwhenthisobtainedmetriciseverywherenon-degenerated,$X$issaidtobecomplexhyperbolic.Heconjecturedthat,inalldimensions,mostmanifoldsshouldbecomplexhyperbolic.Inthistalkweshallpresentthehistoryandsomerecentdevelopmentsinthissubject,includingtheGreen-Griffiths-Langconjecture.

摘要:Iwillsurveysomerecentprogressondifferentialcalculusofquiverswithpotentialsandgivesomeapplicationsofittoalgebraicgeometryandrepresentationtheory.

摘要:OnebasicphilosophyinDiophantineGeometryislocal-globalprinciple(Hasseprinciple)forrationalpointsandintegralpoints.Inthistalk,Iwillfocusonhowtouselinearalgebraicgrouptostudythelocal-globalprincipleforintegralpointsandtalkabout:(1)thedescentobstructionanditerateddescenteobstruction;(2)invariantBrauersubgroupandstrongapproximationofhomogeneousspaces;(3)arithmeticpurityofstrongapproximationforhomogeneousspaces.

摘要:WereportrecentprogressonajointprojectwithYangCao.Ifanalgebraicvarietyoveranumberfieldverifiesstrongapproximationoffafinitesetofplaces,ithasbeenfirstconjecturedbyWittenbergthatthispropertyismaintainedundertheremovalofanysubvarietyofcodimensiontwo.Ifthisisthecase,thenwesaythatthevarietysatisfiesarithmeticpurity.Acloselyrelatedquestionisthedensityofintegralpointswhosemultivariablepolynomialvalueshavenocommongcd\'s.Weconfirmthearithmeticpurityforsemi-simplesimplyconnectedk-simpleisotropiclinearalgebraicgroups,andforaffinequadratichypersurfaces,usingdifferentmethods.Theyshowhowthefibrationmethodforrationalpointsandvarioussievemethods(e.g.affinealmostprimelinearsieve,Ekedahl’sgeometricsieve,Iwaniec’shalf-dimensionalsieve)matchtogether.