Vortices are a prominent feature of both quantum and classical fluids, thought to play a crucial role in turbulence. They have been a central theme in mathematical fluid dynamics for over 150 years. Over more than 30 years, mathematicians have developed a good understanding of point vortices in 2-dimensional fluids, although many questions persist. The mathematics connected to vortex filaments in 3-dimensional fluids is much more subtle, and it remains the focus of many notable open problems, the most signicant of which is probably the conjecture that vortex filaments in solutions of the 3-d Gross-Pitaevskii and incompressible Euler equations, respectively describing certain quantum and classical fluids, are governed in a particular limit by a geometric evolution equation known as the binormal curvature flow.

Recent results suggest that these very classical questions are ripe for new developments. At the same time, the binormal curvature flow, and other reduced models for 3d vortex dynamics, exhibit very rich behavior and have emerged as the focus of important open problems in their own right.

This workshop will bring together the leading scholars approaching this timely and prominent family of questions from a variety of different perspectives, including those focussing on vortices in classical fluids or quantum fluids, as well as researchers directly studying limiting geometric models with analytic, geometric, and computational tools.