In the past two decades there has been intense interest in products of subsets in finite groups. Aner Shalev, Hebrew University of Jerusalem
In my talk, I will discuss some background, some of the ideas behind the proof as well as some related open problems. We also provide `stability versions' of this result, which confirm a prediction of Kahn. In joint work with Dong-yeap Kang, Tom Kelly, Abhishek Methuku and Deryk Osthus, we prove this conjecture for every large $n$. S considered this to be one of his three most favorite combinatorial problems and offered \$500 for the solution of the problem. This presentation will address some of these issues and a few representative applications of clinical interest.\\ This is a classical environment where multi-physics and multi-scale processes have to be addressed.\\Īppropriate systems of nonlinear differential equations (either ordinary and partial) and efficient numerical strategies must be devised to allow for the analysis of both heart function and dysfunction, and the simulation, control, and optimization of therapy and surgery.\\ Mathematical models based on first principles are devised for the description of the blood motion in the human circulatory system, as well as for the simulation of the interaction between electrical, mechanical, and fluid-dynamical processes occurring in the heart. Alfio Quarteroni, Politecnico di Milano and EPFL