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SUMMARY:Elmar Schrohe (University of Hannover)
DTSTART:20200909T121500Z
DTEND:20200909T140000Z
DTSTAMP:20260404T095847Z
UID:NCG-CPH/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NCG-C
 PH/1/">The local index formula of Connes and Moscovici and equivariant zet
 a functions for the affine metaplectic group.</a>\nby Elmar Schrohe (Unive
 rsity of Hannover) as part of NCG Learning Seminar Copenhagen\n\n\nAbstrac
 t\nWe consider the algebra $A$ of bounded operators on $L^2(\\mathbb{R}^n)
 $ generated by quantizations of isometric affine canonical transformations
 .\nThis algebra includes as subalgebras the noncommutative tori and toric 
 orbifolds.\nWe introduce the spectral triple $(A\, H\, D)$  with $H=L^2(\\
 mathbb R^n\, \\Lambda(\\mathbb R^n))$ and the Euler operator $D$\, a first
  order differential operator of index $1$.\nWe show that this spectral tri
 ple has simple dimension spectrum: For every operator $B$ in the algebra $
 \\Psi(A\,H\,D)$ generated by the Shubin type pseudodifferential operators 
 and the elements of $A$\, the zeta function $\\zeta_B(z) = Tr (B|D|^{-2z})
 $ has a meromorphic extension to $\\mathbb C$ with at most simple poles an
 d decays rapidly along vertical lines.\nOur main result then is an explici
 t algebraic expression for the Connes-Moscovici cyclic cocycle.\nAs a coro
 llary we obtain local index formulae for noncommutative tori and toric orb
 ifolds.\n\n(Joint work with Anton Savin\, RUDN\, Moscow)\n
LOCATION:https://stable.researchseminars.org/talk/NCG-CPH/1/
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SUMMARY:Jens Kaad (SDU Odense)
DTSTART:20200916T121500Z
DTEND:20200916T140000Z
DTSTAMP:20260404T095847Z
UID:NCG-CPH/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NCG-C
 PH/2/">Exterior products of compact quantum metric spaces.</a>\nby Jens Ka
 ad (SDU Odense) as part of NCG Learning Seminar Copenhagen\n\n\nAbstract\n
 The theory of compact quantum metric spaces was initiated by Rieffel in th
 e late nineties. Important inspiration came from the fundamental observati
 on of Connes saying that the metric on a compact spin manifold can be reco
 vered from the Dirac operator. A compact quantum metric space is an operat
 or system (e.g. a unital C*-algebra) equipped with a seminorm which metriz
 es the weak-*-topology on the state space via the associated Monge-Kantoro
 vich metric. In this talk we study tensor products of compact quantum metr
 ic spaces with specific focus on seminorms arising from the exterior produ
 ct of spectral triples. On our way we obtain a novel characterization of c
 ompact quantum metric spaces using finite dimensional approximations and w
 e apply this characterization to propose a completely bounded version of t
 he theory.\n
LOCATION:https://stable.researchseminars.org/talk/NCG-CPH/2/
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SUMMARY:Juan Orendain (UNAM Mexico)
DTSTART:20200902T121500Z
DTEND:20200902T140000Z
DTSTAMP:20260404T095847Z
UID:NCG-CPH/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NCG-C
 PH/3/">Double categories of factors.</a>\nby Juan Orendain (UNAM Mexico) a
 s part of NCG Learning Seminar Copenhagen\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/NCG-CPH/3/
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