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February 11, 2016
Thursday, February 11
Noncommutative Geometry
Time: 12:30
Speaker: Shahab Azarfar (Western)
Title: "Volume Quantization from Spin Geometry (III)"
Room: MC 106

Abstract: We try to investigate a generalization of the Heisenberg commutation relation [p,q]=i, introduced by Chamseddine, Connes and Mukhanov as the one-sided and the two-sided quantization equations'', which captures the geometry. The momentum variable p is encoded by the Dirac operator and the analogue of the position variable q is the Feynman slash of real scalar fields over a closed even-dimensional spin manifold. Existence of a solution of the one-sided equation implies that the manifold decomposes into a disconnected sum of spheres of unit volume which represent quanta of geometry. The two-sided equation, as the refined version of the one-sided equation by involving the real structure on a spin manifold, implies the quantization of the volume of the spin manifold.