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SUMMARY:Some (noncommutative) geometrical aspects of the Sierpisnki gasket
  - Guido\, D (Roma)
DTSTART:20100727T150000Z
DTEND:20100727T154500Z
UID:TALK25646@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Abstract: We present here a 2-parameter family of spectral tri
 ples for the Sierpinski gasket\, based on  spectral triples for the circle
 . Any hole (lacuna) of the gasket is suitably identified with a circle\, a
 nd the triple for the gasket is defined as the direct sum of the triples f
 or the lacunas.    The first parameter is a scaling parameter for the corr
 espondence between circles and lacunas\, the second describes the metric o
 n the circle\, which is\, roughly\, a power of the euclidean metric. We st
 udy for which parameters the following features of the gasket can be recov
 ered by the corresponding triple: the integration on the gasket (w.r.t. th
 e Hausdorff measure)\, a non-trivial distance on the gasket\, a non-trivia
 l Dirichlet form (the Kigami energy).
LOCATION:Seminar Room 1\, Newton Institute
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