Europe/Lisbon
Amphitheatre Fa2, IST — Online

José Miguel Urbano

José Miguel Urbano, KAUST
Semi-Supervised Learning and the $\infty$-Laplacian I

Motivated by a recent application in Semi-Supervised Learning (SSL), the minicourse 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.

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