The material will be relatively self-contained and accessible to undergraduate sec- ond and third year students, and graduate students (Masters and PhD). Needless to say, everyone is welcome!

Motivated by a recent application in Semi-Supervised Learning (SSL), the mini-course is a brief introduction to the analysis of infinity-harmonic functions. We will discuss the Lipschitz extension problem, its solution via MacShane-Whitney extensions and its several drawbacks, leading to the notion of AMLE (Absolutely Minimising Lipschitz Extension). We then explore the equivalence between being absolutely minimising Lipschitz, enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense.