| Résume | The main focus of this talk will be to describe recent work (joint with Braverman) on the Lipschitz extension problem that obtains solutions to various natural quantitative questions by thinking about its (known) dual formulation as a question about randomly rounding an ambient metric space to its subset while preserving certain natural guarantees that are measured in terms of transportation cost. We will start by discussing the classical formulation of these old questions as well as some background and earlier results, before passing to examples of how one could reason quantitatively using the dual perspective. |
