#### Optimal transportation and the quasiconformal Jacobian problem

**Leonid Kovalev** (Washington University, St. Louis)

**Abstract:** The quasiconformal Jacobian problem, which originated in a 1990 paper of David and Semmes, asks for an analytic description of the Jacobian determinants of quasiconformal mappings. A part of this difficult problem is to characterize the singular sets of such Jacobians. We prove that every set of Hausdorff dimension less than 1 is a singular set for some quasiconformal mapping. The proof involves some ideas from the theory of optimal transportation, such as the Wasserstein metric. This is joint work with Diego Maldonado.