​04-10【Stéphane NONNENMACHER】五教5207 中法班讨论班系列报告026


题目:Some questions of spectral geometry

报告人:Stéphane NONNENMACHER, Université Paris-Saclay(巴黎-萨克雷大学)




Probably the most popular differential operator in physics and mathematicsis the Laplacian: it appears in wave propagation, in thermodynamics, in quantum mechanics, fluid dynamics, Riemannian geometry..

When restricted to a bounded region (in 2 dimensions a drum, in 3 dimensions a box), the Laplacian admits a discrete sequence of eigenvalues (eigenfrequencies), associated with eigenfunctions (stationary vibration modes), both making up the spectrum of the Laplacian.

Spectral geometry studies the relations between this spectrum and the geometry (shape) of the box. I will review some questions and results pertaining to this topic, among which Weyl's asymptotic formula for counting eigenvalues.