PIMS/ IAM Distinguished Lecture: Darren Crowdy

Motivated by problems arising in the applied sciences, I will tell the story of what might reasonably be called a "forgotten function". It was discovered in the late 1800s, but has hardly ever been used in the physical sciences even though, as I will show, its applications in science and engineering turn out to be many and varied.

In particular, I will survey a new theoretical approach to solving problems in what mathematicians call "multiply connected" domains. These are ubiquitous in applications; whenever two or more objects or entities (airfoils, bacteria, vortices, inhomogeneities in an elastic medium, black holes!...) interact in some ambient medium the analysis may call for the methods I will discuss.

Some illustrative example problems from applications, especially in fluid dynamics, will be described and their solutions explicitly constructed. I will also describe freely available numerical codes that we have developed for the computation of this "forgotten function" in order to promote its use.

We hope to demonstrate that the new methods are sufficiently general that they provide broad scope for tackling a variety of problems.