Analysis and geometry. This field aims to develop calculus on non-smooth spaces, which lack any linear or smooth structure that is typical of smooth manifolds. Its success has been immense. There is now a rich theory of first-order calculus and Sobolev functions on metric spaces that has allowed the development of non-linear potential theory in that setting.

The theory was motivated by, and has found applications to, geometric function theory (quasiconformal and quasisymmetric mappings) in metric spaces and geometric group theory.

I share parts of my work through YouTube: YoungMeasures.