Abstract: We give a survey on a recent algebraic approach to kinematic formulas. The two main notions are that of "valuation" and of "curvature measure". It turns out that the space of valuations is an algebra and the space of curvature measures is a module over this algebra. On isotropic spaces, these algebraic structures are closely related to kinematic formulas. The kinematic formulas on complex space forms have been worked out explicitly (joint work with Joseph Fu and Gil Solanes).

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