Noncommutative geometry and physics: a review of selected recent results

Abstract

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.

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