Abstract
In this talk, I will present some recent results on the optimal matching problem. This problem, which was much studied at the end of the last century in particular after the work of Ajtai-Komlos-Tusnady, has seen renewed interest in recent years from the PDE community thanks to the ansatz proposed by Caracciolo Lucibello, Parisi and Sicuro in 2014. I will show how this ansatz allows us to draw a parallel with a stochastic homogenization problem. This analogy has led to many advances on this problem, such as the (partial) resolution of a Barthe and Bordenave conjecture.
