Cheeger inequality in sub-Riemannian geometry

We explore extending the classical Cheeger inequality to sub-Riemannian manifolds, which are manifolds
in which shortest paths can only take velocities confined to a subbundle of the tangent bundle. During the talk, I will
discuss the basis properties of sub-Riemannian structures, as well as the key geometric and analytic concepts used in
the proof of Cheeger's inequality.
If time permits, I will sketch future applications to magnetic systems.