Can one hear a singularity?

The topic of the talk is spectral geometry. In 1966 Mark Kac asked in his paper "Can one hear
the shape of a drum?". Mathematically the question is formulated as follows. A drum is a domain
in Euclidean space that is held along its boundary. When we play a drum we hear an infinite
sequence of frequencies. The question is if one can determine geometry of a domain using only information on this sequence. Nowadays the question is generalised to Riemannian manifolds and
even to spaces with singularities. I will conclude the talk with my results on spaces with conic singularities.