On Wednesday 6 November, Michele Bartuccelli visited the Department of Mathematics at the University of Sheffield to give a talk in the Applied Mathematics Colloquium.  The title of the talk was “Obtaining estimates of the norm for solutions of dissipative partial differential equations“.  In the talk he addressed the problem of obtaining explicit and accurate estimates of the sup-norm for solutions of dissipative partial differential equations such as the Swift–Hohenberg Equation and the Navier-Stokes equations. 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 can evaluate in an explicit manner the values of the sup-norm of the solutions of the PDE under investigation. In addition (time permitting) the talk will show how to compute the so-called time-averaged dissipative length scale associated to the solutions of the PDE.