Friday, Nov 2: Vladimir Sverak (Minnesota), 4:00 pm On scale-invariant solutions of the Navier-Stokes equations The solutions of the Navier-Stoles equations which are invariant under the scaling symmetry of the equations provide an interesting window into non-linear regimes which are not accessible by perturbation theory. They appear to give valuable hints concerning the old question about the uniqueness of weak solutions. In the lecture we outline a recent proof of the result that for every scale-invariant initial data there is a global scale-invariant solution (smooth for positive times), and we explain connections to the uniqueness problem. This is joint work with Hao Jia