Sub-Riemannian geometry is a flourishing subject of research that appears in many different areas of pure and applied mathematics. It is a generalisation of Riemannian geometry that provides models in robotics, aerospace engineering, medical imaging, and neurobiology. Applications in pure mathematics include metric geometry, PDEs, harmonic analysis, and geometric control theory.
In this presentation I will introduce sub-Riemannian geometry by examples, and I will briefly describe a couple of models: a special car and the primary visual cortex. The latter model has applications to image reconstruction.
The talk is tailored to a non-expert audience.