Designing the sound of a cut-off drum

The spectral action in noncommutative geometry naturally implements an ultraviolet cut-off, bycounting the eigenvalues of a (generalized) Dirac operator lower than an energy of unification.Inverting the well known question “how to hear the shape of a drum”, we ask what drum can bedesigned by hearing the truncated music of the spectral action ? This makes sense because thesame Dirac operator also determines the metric, via Connes distance. The latter thus offers anoriginal way to implement the high-momentum cut-off of the spectral action as a short distancecut-off on space. This is a non-technical presentation of the results of.