Introduction to variational models for dislocations

I will present a general introduction to some variational approaches for the analysis of line defects in crystals, the dislocations. In its generality the problem can be very complex. These defects may be relevant at different scales (in space and time) and interact creating complicated structures and patterns. The aim of the talk is to provide an overview of some of the models that can be mathematically treated, pointing some of the most interesting features of them (as for instance the formation of microstructure), as well as some of the main difficulties and open problems.