Is it always possible to park a car in a parking space whose size is exactly the same as the car? Can we do the same with a multi-trailer truck? In this talk, we will show the relationship between these two questions and the theory of distributions on differentiable manifolds. We will review this theory and focus our attention on bracket-generating distributions. Typical examples of this class of distributions are Contact and Engel structures. We will motivate these objects by showing other examples and establish several results about their tangent curves. In particular, we will show that the spaces of regular tangent knots are flexible if the dimension of the manifold is greater than $3$. These results are part of a joint work with Álvaro del Pino (Utrecht University).

In this talk we will introduce Gromov's $h$-principle theory from a basic and accessible perspective. We will motivate it through visual examples with special emphasis on the method of Convex Integration. Many problems in Differential Topology involve differential relations (differential equations, inequalities, etc.). In many contexts, it can be proven that there exists an $h$-principle: this means that the resolution of certain geometric problems can be reduced to studying the underlying Algebraic Topology. We will show how these techniques can be applied to the study of maximal growth distributions on smooth manifolds. Prototypical examples of these objects are Contact and Engel structures.