Tuesday, May 21, 2019 - 3:30pm
This is an introductory talk on optimal transport theory, which in the past two decades, has emerged as a fertile field of inquiry and a powerful tool for applications to problems within and beyond mathematics. The physical interpretation of the basic issue is this. We ask how we can optimally rearrange a given pile of soil or rubble (the d'eblais) with mass distribution mu_0 into an excavation or fill (the remblais), with mass distribution mu_1? Here, optimality is measured against the cost function c(x, y)=|x-y|^p. A geometric characterization of the solutions allows to describe geodesics of minimal lengths on the set of probability measures and to derive sharp functional inequalities.