SO(3) is the special orthogonal group of rotations that describe the range of motion of a free rigid body rotating about a fixed point. Whilst the N-body problems of celestial mechanics have been written about extensively, the N-vortex problem is relatively new. I'll describe what a vortex is, and what the Hamiltonian of 2-point vortices moving on the surface of the sphere tells us (the spherical model is used when considering large scale atmospheric and oceanographic flows which persist for long periods of time on the earth's surface).
I aim to also describe the connection between SO(3) and the sphere and why this is helpful for evaluating N-point vortices on a sphere for N>3.
This will be accessible to all: there is no need to look up anything before the talk as I intend to cover all of the above aspects in a lot of detail.