Digital publication of the opening lecture by Pr Nalini Anantharaman

Nalini Anantharaman

Spectrum stories

In the years 1920, a mathematical theory (the diagonalization of matrices) and a physical question (the determination of the spectrum of atoms), born independently, came together to give birth to quantum mechanics and the branch of mathematics known as " spectral theory ". This theory applies to any linear evolution equation, breaking down its solutions into a superposition of stationary solutions known as "eigenmodes", which vibrate at " eigenfrequencies " : these frequencies constitute the " spectrum ".

Situated at the intersection of several mathematical communities, Spectral Geometry aims to understand the link between the initial geometry of an object and its vibration spectrum. The author sets out to retrace the history of this very active field through some major past and present research themes.

Anantharaman N., Histoires de spectres, Paris, Collège de France, coll. " Leçons inaugurales ",^no 314, 2023.

Nalini Anantharaman is a mathematician, member of the French Academy of Sciences and winner of the Prix Henri Poincaré. Her work focuses on the geometric description of wave propagation. In 2022, she was appointed Professor at the Collège de France, holding the Spectral Geometry chair.