ERC Advanced Grant · 2019
Spectral rigidity and integrability for billiards and geodesic flows
In 1911, Hermann Weyl proved the remarkable asymptotic formula describing distribution of (large) eigenvalues of the Dirichlet Laplacian in a bounded domain Ω ⊂ Rd N (λ) = (2π)−d ωd Vol(Ω) λd/2(1 + o(1)) as λ → +∞. where N (λ) is the number of eigenvalues of the Laplacian spectrum, which are less than λ, ωd is a volume of the unit ball in Rd, Vol(Ω) is the volume of Ω, and the Laplace spectrum of a domain Ω is defined as the set of positive real numbers λ (with multiplicities) that satisfy the eigenvalue problem in Ω with Dirichlet boundary conditions. This result motivated the title of a famous paper by M. Kac “Can you hear the shape of a drum?”. The question is: can the shape of a bounded…
From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.