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Lipschitz learning and the infinity-Laplacian

Speaker: Miguel Urbano (KAUST, Saudi Arabia) Abstract: Infinity-harmonic functions have recently found application in Semi-Supervised Learning in the context of the so-called Lipschitz Learning. With this application in mind, 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 address the equivalence between being absolutely minimising Lipschitz, enjoying comparison with cones and solving the infinity-Laplace equation in the viscosity sense. We will present a few regularity results and discuss open problems if time permits