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Nalini Anantharaman

Nalini Anantharaman is a French mathematician and professor at the University Paris-Sud, Orsay, France. Her research interests are concentrated in Analysis and Mathematical Physics, including Quantum Mechanics (such as the Schrödinger equation) and wave propagation. She received the Henri Poincaré Prize in 2012. She is Vice-President of the Société Mathématique de France.

 Nalini Anantharaman

 

"Spectral geometry": The vibration of a membrane can be described by a simple partial differential equation: the 2-dimensional D'Alembert equation. The acoustic vibrations of a membrane is a superposition of harmonics, which mathematically correspond to eigenvalues and eigenfunctions of the laplacian. The relation between the geometry of the membrane and its spectrum of vibration is still not fully understood, and I will present a few classical results, but also recent research, on the subject. The talks will focus on the geometry of nodal lines and on the question asked by Mark Kac in the 60s: "Can you hear the shape of a drum?" (that is, can 2 membranes with different shapes produce the same sound?).