Vladimir Sharafutdinov: Local audibility of a hyperbolic metric

A compact Riemannian manifold (M,g) is said to be locally audible if the following statement holds for every metric g' on M which is sufficiently close to g: if the metrics g and g' are isospectral, then they are isometric. We prove local audibility of a compact locally symmetric Riemannian manifold of negative sectional curvature. Alongwise with the proof, I will try to give you some flavour of spectral geometry.