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 Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.Comment: Based on lectures given at the TMR School on contemporary string theory and brane physics, Jan 26- Feb 2, 2000, Torino, Italy. To be published in Class. Quant. Grav. 17 (2000). 3 ref.s added, typos corrected, formula on exterior product of n left-invariant one-forms corrected, small changes in the Sect. on integratio