Séminaire de topologie, géométrie et algèbre

More than twenty years ago, Etnyre and Ghrist established a connection between Reeb fields in contact geometry and a class of stationary solutions to the 3D Euler equations for ideal fluids. In this talk, we present a new framework that allows assigning contact/symplectic invariants to large sets of time-dependent solutions to the Euler equations on any three-manifold with an arbitrary fixed Riemannian metric, thus broadening the scope of contact topological methods in hydrodynamics. We use it to prove a general non-mixing result for the infinite-dimensional dynamical system defined by the equation and to construct new conserved quantities obtained from spectral invariants in embedded contact homology. This is joint work with Francisco Torres de Lizaur.