In this talk, I consider the existence of local-in-time strong solutions to a well established coupled system of partial differential equations arising in Fluid-Structure interactions. The system consisting of an incompressible Navier-Stokes equation and an elasticity equation with velocity and stress matching boundary conditions at the interface in between the two domains where each of the two equations is defined. I discuss new existence results for a range of regularity in the initial data and the differences in the exsitence results when domains with non-flat boundaries are considered.

The past few years have seen an incredible explosion of new (or revival of old) fast and effective algorithms for various imaging and information science applications. These include: nonlocal means, compressive sensing, graph cuts, Bregman iteration, as well as relatively old favorites such as the level set method and PDE based image restoration. I'll give my view of where we are, hopefully giving credit to all the people involved.

Light-matter interactions on the nanometer scale are at the heart of nano optics. The fact that some quantum effects begin to dominate on nanoscale makes nanostructures possess strikingly different optical properties from their bulk. This talk will consider the excitons and biexcitons confinement effects in an optically excited nanocrystal.
Modeling and computational studies will be presented.