Michele Bartuccelli visited the Department of Mathematics at Imperial College London yesterday (Thursday 12 March) and gave a seminar in the AMMP series on “Explicit and accurate estimates of the sup-norm and length scales for Navier-Stokes in 2D“.  The seminar was given on a whiteboard and received high praise from the audience, extending the seminar to 95 minutes and generating a plethora of questions.  An abstract for the talk follows: one has obtained explicit and accurate estimates of the sup-norm for solutions of the Navier-Stokes Equations (NSE) in two space dimensions. By using the best (so far) available estimates of the embedding constants which appear in the classical functional interpolation inequalities used in the study of solutions of dissipative partial differential equations, one has evaluated in an explicit manner the values of the sup-norm of the solutions of the NSE. In addition one has calculated the so-called time-averaged dissipative length scale associated to the above solutions.