The music of shapes

Alain Connes

5 November 2020 - 18:30

Professor at the Collège de France, at the Institut des hautes études scientifiques at the University of Paris-Saclay and at Ohio State University, Columbus Fields medal in 1982

Quantum physics, especially matrix mechanics, has had a profound influence on mathematical notions of geometric space. This lecture will explain this link by dealing, among other things, with «spectra» and «the music of shapes». Indeed, if the geometrical characteristics of an instrument, for example, determine the sounds it can produce, then conversely, knowledge of the scale and chords produced by an object is sufficient to reconstruct its shape. This property makes it possible to characterize geometrical shapes from invariants that do not refer to a coordinate system. The resulting new geometry, illustrating the mathematical link between visual and auditory perception, has a wealth of applications in physics, in particular for gravitation and quantum physics. This lecture will also be an opportunity to discuss the meaning of the notions of variability and the emergence of time.