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This lecture by Pierre Pansu explores the complex mathematical question of whether normal currents can be expressed as averages of integral currents. Learn about the dimensions where this is possible (0, 1, top-1 and top) and why it fails in general cases. Discover Pansu's strategy for proving that every closed current is the boundary of a mass-decomposed current that is also calibrated—an approach inspired by Kantorovitch and Beckmann's formulations of optimal transportation problems. The 50-minute presentation acknowledges that while the current focus is on Riemannian and subRiemannian manifolds, this mathematical challenge deserves future exploration in more general metric spaces.
