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SUMMARY:Elmar Schrohe (University of Hannover)
DTSTART;VALUE=DATE-TIME:20200909T121500Z
DTEND;VALUE=DATE-TIME:20200909T140000Z
DTSTAMP;VALUE=DATE-TIME:20201029T102108Z
UID:NCG-CPH/1
DESCRIPTION:Title: The local index formula of Connes and Moscovici and equ
ivariant zeta functions for the affine metaplectic group.\nby Elmar Schroh
e (University of Hannover) as part of NCG Learning Seminar Copenhagen\n\n\
nAbstract\nWe consider the algebra $A$ of bounded operators on $L^2(\\math
bb{R}^n)$ generated by quantizations of isometric affine canonical transfo
rmations.\nThis algebra includes as subalgebras the noncommutative tori an
d 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 spec
tral triple has simple dimension spectrum: For every operator $B$ in the a
lgebra $\\Psi(A\,H\,D)$ generated by the Shubin type pseudodifferential op
erators 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 and decays rapidly along vertical lines.\nOur main result then is an
explicit algebraic expression for the Connes-Moscovici cyclic cocycle.\nA
s a corollary we obtain local index formulae for noncommutative tori and t
oric orbifolds.\n\n(Joint work with Anton Savin\, RUDN\, Moscow)\n
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SUMMARY:Jens Kaad (SDU Odense)
DTSTART;VALUE=DATE-TIME:20200916T121500Z
DTEND;VALUE=DATE-TIME:20200916T140000Z
DTSTAMP;VALUE=DATE-TIME:20201029T102108Z
UID:NCG-CPH/2
DESCRIPTION:Title: Exterior products of compact quantum metric spaces.\nby
Jens Kaad (SDU Odense) as part of NCG Learning Seminar Copenhagen\n\n\nAb
stract\nThe theory of compact quantum metric spaces was initiated by Rieff
el in the late nineties. Important inspiration came from the fundamental o
bservation of Connes saying that the metric on a compact spin manifold can
be recovered from the Dirac operator. A compact quantum metric space is a
n operator system (e.g. a unital C*-algebra) equipped with a seminorm whic
h metrizes the weak-*-topology on the state space via the associated Monge
-Kantorovich metric. In this talk we study tensor products of compact quan
tum metric spaces with specific focus on seminorms arising from the exteri
or product of spectral triples. On our way we obtain a novel characterizat
ion of compact quantum metric spaces using finite dimensional approximatio
ns and we apply this characterization to propose a completely bounded vers
ion of the theory.\n
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SUMMARY:Juan Orendain (UNAM Mexico)
DTSTART;VALUE=DATE-TIME:20200902T121500Z
DTEND;VALUE=DATE-TIME:20200902T140000Z
DTSTAMP;VALUE=DATE-TIME:20201029T102108Z
UID:NCG-CPH/3
DESCRIPTION:Title: Double categories of factors.\nby Juan Orendain (UNAM M
exico) as part of NCG Learning Seminar Copenhagen\n\nAbstract: TBA\n
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