Guillaume Carlier. Barycenters in the Wasserstein Space. In the first part of the talk, after recalling some basic facts from optimal transport theory, we will explain how some matching problems arising in mathematical economics are intimately related to optimal transport problems. In the second part of the talk, focusing on the quadratic case, we will relate the problem to a notion of barycenters that generalizes the McCann interpolation to the case of more than two marginals. We will give existence, characterization,uniqueness and regularity results for these barycenters and will consider some examples. This talk will be based on joint works with Martial Agueh and Ivar Ekeland.