Nalini Anantharaman
Spectral stories
" One of the raisons d'être of Spectral Geometry is this need we have to retain a sense-based intuition, and therefore to establish links between our geometric vision and spectral objects . "
In the years 1920, a mathematical theory (thediagonalization 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 ". The latter is involved in any linear evolution equation , whose solutions it decomposes into a superposition ofstationary solutions known as " eigenmodes ", which vibrate at " eigenfrequencies " : these frequencies constitute the " spectrum ".
Situated at the intersection of severalmathematical communities , Spectral Geometry aims to understand the link between the initial geometry of an object and its vibration spectrum . The author traces the history of this very active fieldthrough some major past and present research themes .
Anantharaman N., Histoires de spectres, Paris, Collège de France/Fayard, coll. " Leçons inaugurales ",no 314, avril 2023, 96 p.
ISBN : 978-2-213-72552-9
Price : 12 €
Publication : 19 April 2023
