Online Talk 

 Zoom link: https://princeton.zoom.us/j/99576580357

The Beurling transform is a singular integral operator closely related to fine properties of quasiconformal mappings in the plane. Determining the L^p norms of this operator is a well-known open problem. In this talk we present some partial progress towards this problem and in particular we establish a series of new sharp integral estimates for quasiconformal maps, joint work with Astala, Faraco, Koski and Kristensen. Our approach is motivated by methods and questions arising in the Calculus of Variations.