SPEAKER: Therese Landry
TITLE: Spectral Triples, Quantum Compact Metric Spaces, and the Sierpinski Gasket
ABSTRACT: One of the fundamental tools of noncommutative geometry is Connes' spectral triple. Michel Lapidus and his collaborators have developed spectral triples for the Sierpinski gasket that recover the Hausdorff dimension, the geodesic metric, and the $\log_2 3$-dimensional Hausdorff measure. The space of continuous, complex-valued functions on the Sierpinski gasket can be viewed as a quantum compact metric space. The Gromov-Hausdorff distance is an important tool of Riemannian geometry, and building on the earlier work of Rieffel, Latr\'emoli\`ere introduced a generalization of the Gromov-Hausdorff distance to the quantum compact metric space. Aspects of geometry that can be recovered via the Gromov-Hausdorff propinquity will be discussed and compared with the geometric information that can be obtained from spectral triples.
Friday, October 26, 2018 at 1:10pm to 2:00pm
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