Robert Jerrard (University of Toronto) will present "Weak solutions of an equation describing vortex filaments." Abstract: An old conjecture, dating back to the early 20th century, holds that vortex filaments in ideal fluids in certain limits can be described by a geometric evolution equation called the binormal curvature flow. Smooth solutions of the binormal curvature flow are mostly well-understood. However, it is interesting and possibly useful to study rough solutions as well, for a couple of (probably orthogonal) reasons: because non-smooth vortex filaments may occur in physical fluids, and because some rough solutions of the binormal curvature flow are conjectured to exhibit very rich, peculiar (and probably nonphysical) behavior. This talk will describe the history of some of these conjectures, which remain completely open, as well as a recent proposal for a notion of very weak solutions of the binormal curvature flow which reveals some previously unexpected stability properties.