This course focuses on analysis on metric measure spaces and their applications to metric geometry.

Analysis on metric measure spaces is a mathematical field to study metric spaces with no a priori smooth structure. One of the earliest motivations and applications of this field arose in Mostow’s celebrated rigidity work. Heinonen and Koskela later axiomatize several aspects of Euclidean quasiconformal geometry in the setting of metric measure spaces, which initiated the modern theory of analysis on metric spaces.

Today, this is an active field with far-reaching applications to areas such as geometric measure theory, geometric function theory, geometric group theory, nonlinear PDEs, dynamics of rational maps, fractal geometry, and even theoretical computer science.