Universita di Roma Tor Vergata and CMTP
26 Pages
English
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Universita di Roma Tor Vergata and CMTP

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26 Pages
English

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Distances in Noncommutative Geometry Pierre Martinetti Universita di Roma Tor Vergata and CMTP Seminaire CALIN, LIPN PARIS 13, 8th February 2011

  • d?1 ??

  • commutative algebra

  • metric space

  • topological aspect

  • noncommutative geometry

  • sup f?c∞0

  • sub- riemannian geometry

  • ?? ds


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DistancesinNoncommutativeGeometryPierreMartinettiUniversita`diRomaTorVergataandCMTPSe´minaireCALIN,LIPNPARIS13,8thFebruary1102
Metricaspectofnoncommutativegeometry00ds=D100DistancebetweenstatesofanalgebraAinterestinglinkswithotherdistances:.Nto(siLozzim&au;lciDhamsikst,uMdu¨lliee-rdoHsbne;uoIthcmmu,aKnaryejswik,.P.M)-distanceongraph(Anitedimensional),-horizontaldistanceinsubriemanniangeometry(A=C0(M)Mn(C))(P.M.),-Wassersteindistanceinoptimaltransporttheory(commutativeA)(D’Andrea,P.M.),-distanceinsomemodelofquantumspacetime(A=K=(S,?))(Cagnache,-distanceinsomD’Andrea,P.M.,Wallet);alsoyieldsametricinterpretationoftheHiggsfieldinConnesdescriptionofthestandardmodel(Wulkenhaar,P.M.).TopologicalaspectmostlystudiedbyRieffel,Latre´molie`reandarecentpaperofBe´lissard,MarcolliandReihani.