Abstract:

What do vibrating membranes, heat diffusion in a body and the evolution of quantum particles have in common? The mathematics behind them leads to eigenvalue problems for the Laplacian or other differential operators. The mathematical field of spectral geometry is concerned with the question how these eigenvalues are influenced by the underlying geometry (of, e.g., the membrane or the body). This talk is intended to be a gentle introduction to this field. We will pass by famous questions such as “Can one hear the shape of a drum?”.