Cornel Pintea
Babeş-Bolyai University, Cluj-Napoca, Romania

By the classical Frobenius Theorem, a distribution is completely integrable if and only if it is involutive. In this talk, we investigate the size of tangencies of submanifolds with respect to a given non-involutive distribution. We provide esti- mates for the size of the tangency set in terms of its Hausdorff dimension. This generalises earlier works by Derridj and the first author. Our results apply in the setting of contact and symplectic structures as well as of Carnot groups. We illustrate the sharpness of our estimates by a wide range of examples and round the paper off with additional comments and open questions.