Resumen de Distance geometry, algebra and drones
Is it always possible to reconstruct a point configuration in the plane from the unlabeled set of mutual distances between the points? This and other questions translate to invariant theory and ultimately into problems about polynomial ideals. As it turns out, the following question is related: can a drone detect the walls of a room from hearing the echoes of a sound? What if the time at which the sound was emitted is unknown? Attacking these questions again leads to ideal theory and requires massive computer algebra computations. The talk presents results by Mireille Boutin and the speaker, some of which are old and some very recent.
