Leon Poladian University of Sydney Wave equations with eigenvalue-dependent boundary conditions (and why they come up in modern optical fibre design) Wednesday 7th Oct 14:05-14:55pm, Eastern Avenue Lecture Theatre. The propagating modes of conventional optical fibres correspond to eigenfunctions of wave equations that decay "exponentially" in the transverse direction. In the last decade a new type of fibre has become popular: one that does not completely confine the light and thus the transverse fields no longer decay. These modes (called leaky modes) can be obtained by applying, instead, an outward radiation condition. The theoretical and numerical investigation of these modes on a finite domain requires the manipulation of eigenvalue-dependent boundary conditions. I will discuss various approaches (of more or less utility) from the literature and some that I have explored over the last few years.