Mathematics

In this talk I will present two concepts of tangent bundle, an 'analytic' one and a 'geometric' one, which can be constructed on metric measure spaces satisfying suitable rectifiability properties. The former is based upon the notion of L²-normed module, while the latter is related to the Gromov-Hausdorff limits of the rescaled space. Finally, I will prove that the two approaches are in fact equivalent.