原文由 MessiArg 发表在 SMS 版
课程名称:非交换几何引论(3学分,研本)授课教员:徐平(美国宾州州立大学)时间:周二,四晚6:00-8:30,4月14日开始上课地点:理科一号楼1303课程简介:Noncommutativegeometryaimstocarryoutgeometricalconceptstoanewclassofspaceswhosealgebrasoffunctionsarenolongercommutative.Thecentralideagoesbacktoquantummechanics,whereobservablessuchaspositionandmomentadonotcommute.Thesubjecthasundergonetremendousexplorationrecentlyduetoitscloseconnectionwithanumberareasofmathematicsandmathematicalphysics,includingfoliationtheory,indextheory,epresentationtheory,algebraicgeometry,quantumfieldtheory,quantizationtheoryandstringtheory.Inthiscourse,wewillexplainthebasicideaofnoncommutativegeometryofAlainConnes.ThenwewilldiscussKontsevich'snoncommutativealgebraicgeometry,whichiscloselyrelatedtomirrorsymmetry.Onlybasicknowledgeofdifferentialgeometryisrequired.
Ref.Connes,AlainNoncommutativegeometry.AcademicPress,Inc.,SanDiego,CA,1994.Griffiths,Phillip;Harris,JosephPrinciplesofalgebraicgeometry.Reprintofthe1978original.WileyClassicsLibrary.JohnWileySons,Inc.,NewYork,1994.PierreSchapira,Categoriesandhomologicalalgebra(anintroductiontoderivedcategories)LectureNotes |
