Knots, Flows and Fluids

In the year 1858, Herman Ludwig Ferdinand von Helmholtz published in Crelle's Journal a deep and pioneering paper on vortex motions where the topological properties of vortex lines in a fluid motion were emphasised. This work has been a strong source of inspiration for P G Tait who settled down the foundation of knot theory and for H Poincare, the father of geometric theory of dynamical systems. As a matter of fact, by the end of the 19^th century, three topics, knots, flows and fluids were closely related. In the last decades, the topic has been boosted by a series of new appealing problems and interesting results gathered under the name Topological Methods in Hydrodynamics. Our talk will start with a short trip around the pioneering works. Then we will focus on two essential recent topics: