SINGSTAR Conference 2017 : Index theory and Singular Structures

Spectral triples and non-commutative fractals

2 juin 2017, 11:45

45m

Amphi Schwartz IMT building 1R3 (TOULOUSE)

Orateur

M. Daniele Guido

Description

Self-similar nested fractals are studied from a functional point of view, and this provides a way to quantize them, namely to produce a self-similar noncommutative C*-algebra containing the continuous functions on the fractal as a sub-algebra. For the noncommutative C\*-algebra associated with the Sierpinski gasket, the representations are studied, it is shown that a noncommutative Dirichlet form can be defined, which restricts to the classical energy form on the gasket, and a spectral triple is proposed. Such triple reconstructs in particular the Dirichlet form via the formula $a\to re{s}_{s=\delta }tr(|D{|}^{-s/2}|[D,a]{|}^2|D{|}^{-s/2})$, for a suitable $\delta$. Work in progress with F.Cipriani, T.Isola and J-L.Sauvageot.

Documents de présentation

Slides

guidoTolosaBeamer.pdf