Geometry & Topology

The $2n+1$–dimensional Heisenberg groups $\mathbb H_n$ are some of the simplest examples of subriemannian manifolds, and the subriemannian structure has distinctive effects on surfaces in $\mathbb H_n$. In this talk, we explore the geometry of surfaces in the Heisenberg group. We will describe some techniques for visualizing, constructing, and analyzing surfaces, and use these to explain how the geometry and analysis of surfaces in $\mathbb H_n$ depends on $n$. Parts of this talk are joint with Naor and Chousionis–Li.