On the mimimal rank Sard Conjecture in sub-Riemannian geometry

After recalling the notion of singular horizontal curve in sub-Riemannian geometry, we will discuss various versions of the so-called Sard conjecture and present a result dealing with singular curves whose rank is minimal. The proof of our result that will be sketch relies on several tools from sub-analytic and symplectic geometry. This is a joint work with André Belotto and Adam Parusinski.