ИСТИНА

In 1966, Mark Kac formulated a celebrated question "Can one hear the shape of a drum?" It illustrates very well one of the central problems in spectral geometry: namely, to understand the relations between the geometry of a domain (or a manifold) and the spectrum of the Laplace operator with suitable boundary conditions. Nowadays, spectral geometry is a very active area of mathematics with numerous links to analysis, mathematical physics, differential geometry an other fields. In this three lecture mini-course, I will present a brief introduction to spectral geometry and discuss its connections to mathematical physics.