Recently, a series of unprecedented leaks by Edward Snowden had made it possible for the first time to get a glimpse into the actual capabilities and limitations of the techniques used by the NSA and GCHQ to eavesdrop to computers and other communication devices. In this talk, I will survey some of the things we have learned, and discuss possible countermeasures against these capabilities.

I will discuss a recent joint work with A. Malchiodi (Pisa) and M. Micallef (Warwick) in which we show that not every harmonic map can be approximated by a sequence of $\alpha$-harmonic maps.