EVENT DETAILS AND ABSTRACT

Title: Riemannian Geometry of Compact Metric Spaces
Speaker: Jean Bellissard
Speaker Info: Affiliation: Georgia Institute of Technology
Brief Description:
Special Note:
Abstract:

Using the tools on Noncommutative Geometry, such as the notion of spectral triple introduced by A. Connes in the eighties, a compact metric space $(X,d)$ can be described in terms of Riemannian Geometry. If the Hausdorff dimension and the corresponding Hausdorff measure are finite and non trivial, then the Hausdorff measure can be seen as the analog of a volume form. A general argument about spectral triple leads also to the definition of the analog of a Laplace Beltrami Operator acting on functions. The same approach can be used for an ultrametric Cantor sets (C,d). One of the application concerns tiling spaces. The most recent results about it will be described. (This work was done in collaboration with John Pearson, Jean Savinien, Antoine Julien and Ian Palmer.)