Abstract

Did you know that when you parallel-park your car, you’re actually invoking the Chow-Rashevskii Theorem, a cornerstone of sub-Riemannian geometry? The non-commutativity of the car’s “allowed directions” not only lets you move orthogonally to the road (and thus pull into a parking space) but also gives rise to striking phenomena in more “theoretical” settings: submanifolds that are perfectly regular from the intrinsic viewpoint of sub-Riemannian Heisenberg groups yet look fractal when seen through Euclidean lenses. Such subtleties make it difficult, in the sub-Riemannian setting, to prove classical results like Stokes’ Theorem and Stepanov’s Theorem, to establish fine properties of SBV functions, or even to tackle the seemingly simple task of computing the diameter of a ball.

After an introduction to sub-Riemannian geometry and Heisenberg groups, I will outline some of the key ideas behind the proofs of the aforementioned results.

Talk based on joint works with S. Don, A. Julia, S. Nicolussi Golo, A. Pinamonti, G. Somma, D. Vittone, and K. Zambanini.

The video of the seminar will appear shortly afterwards in this Mediaspace channel.

Seminario Dottorato