Francesca Tripaldi (University of Leeds) – An overview of subRiemannian geometry

SubRiemannian geometry represents a vast generalisation of Riemannian geometry and it is meant to model motions that are permitted only along a limited set of directions at any point. The aim of this talk is to give an intuition of how subRiemannian geometry naturally arises from modelling different mathematical and physical problems (e.g. optimal control, image processing, thermodynamics). Surprisingly, for such a setting many fundamental mathematical objects are not yet defined or understood. If time allows, I will present what obstacles appear when trying to extend the most basic tools of geometric analysis and differential geometry to subRiemannian manifolds.