Homogenisation is a powerful tool from applied mathematics which can be used to probe the boundary of the space of parameters for which a problem is defined. In this talk, I will discuss some of the ways in which this tool has been applied to spectral geometry in the last 5 years, in particular how the behaviour of one eigenvalue problem can mimick that of a different one. Examples include optimal bounds for Steklov eigenvalues, flexibility of the Schrödinger and Steklov eigenvalue optimisation problem, approximation of minimal surfaces, etc.
