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Some (noncommutative) geometrical aspects of the Sierpisnki gasket

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If you have a question about this talk, please contact Mustapha Amrani.

Analysis on Graphs and its Applications

Abstract: We present here a 2-parameter family of spectral triples for the Sierpinski gasket, based on spectral triples for the circle. Any hole (lacuna) of the gasket is suitably identified with a circle, and the triple for the gasket is defined as the direct sum of the triples for the lacunas. The first parameter is a scaling parameter for the correspondence between circles and lacunas, the second describes the metric on the circle, which is, roughly, a power of the euclidean metric. We study for which parameters the following features of the gasket can be recovered by the corresponding triple: the integration on the gasket (w.r.t. the Hausdorff measure), a non-trivial distance on the gasket, a non-trivial Dirichlet form (the Kigami energy).

This talk is part of the Isaac Newton Institute Seminar Series series.

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