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SUMMARY:Elmar Schrohe (University of Hannover)
DTSTART:20200909T121500Z
DTEND:20200909T140000Z
DTSTAMP:20260423T022921Z
UID:NCG-CPH/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCG-CPH/1/">
 The local index formula of Connes and Moscovici and equivariant zeta funct
 ions for the affine metaplectic group.</a>\nby Elmar Schrohe (University o
 f Hannover) as part of NCG Learning Seminar Copenhagen\n\n\nAbstract\nWe c
 onsider the algebra $A$ of bounded operators on $L^2(\\mathbb{R}^n)$ gener
 ated by quantizations of isometric affine canonical transformations.\nThis
  algebra includes as subalgebras the noncommutative tori and toric orbifol
 ds.\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 triple 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 and decay
 s rapidly along vertical lines.\nOur main result then is an explicit algeb
 raic expression for the Connes-Moscovici cyclic cocycle.\nAs a corollary w
 e obtain local index formulae for noncommutative tori and toric orbifolds.
 \n\n(Joint work with Anton Savin\, RUDN\, Moscow)\n
LOCATION:https://researchseminars.org/talk/NCG-CPH/1/
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