Explore a concise video presentation by Francisco Torres De Lizaur from the University of Toronto, introducing the paper 'A characterization of 3D steady Euler flows using commuting zero-flux homologies'. Delve into the authors' characterization of volume-preserving vector fields on 3-manifolds that are steady solutions of the Euler equations for some Riemannian metric, using commuting zero-flux homologies. Discover how this work extends Sullivan's homological characterization of geodesible flows in the volume-preserving case. Learn about the application demonstrating that steady Euler flows cannot be constructed using plugs, as in Wilson's or Kuperberg's constructions. Gain insights into analogous results proven in higher dimensions. Additionally, examine the Helmholtz equation in unbounded wave guides with periodic coefficients, understanding the existence of solutions for non-singular frequencies using energy methods rather than traditional analyticity arguments within operator theory. Read more