Lax-Philips scattering theory is a method to solve for scattering as an expansion over the singularities of the analytic extension of the scattering problem to complex frequencies. I will show how a complete theory can be developed in the case of simple scattering problems. I will illustrate how this theory can be used to find a numerical solution and I will illustrate the method by applying it to the vibration of ice shelves.

One of the key components in the earth’s climate is the formation and melting of sea ice. Currently, we struggle to model correctly this process. One possible explanation for this shortcoming is that ocean waves play a key role and that their effect needs to be include in climate models. I will describe a series of recent experiments which seem to validate this hypothesis and discuss attempts my myself and others to model wave-ice interaction.

Linear Water Wave theory is one of the most important branches on fluid mechanics. Practically it underpins most of the engineering design of ships, offshore structures, etc. It also has a very rich history in the development of applied mathematics. In this talk I will focus on the connection between solutions in the frequency and time-domains and show how we can use various formulations to make numerical calculations and to construct approximate solutions. I will illustrate these methods with application to some simple wave scattering problems.