Mathematics

 The existence of so called abnormal curves is one of the features distinguishing sub-Riemannian geometry from Riemannian geometry. The need to understand (or avoid) abnormal curves appears in many sub-Riemannian problems, such as the regularity of length-minimizing curves and the Sard problem. Some recent progress in both of these problems has been obtained by studying abnormal curves as trajectories of dynamical systems. In this talk, I will present some of the story of abnormal dynamics in the setting of Carnot groups. In particular, I will cover how to lift an arbitrary trajectory of an arbitrary polynomial ODE to an abnormal curve in some Carnot group. This series of seminars focuses on Real Geometry, touching topics from real algebraic geometry, control theory, convex geometry, nodal sets, random topology and subriemannian geometry. More information can be found here: https://sites.google.com/view/geometric-structures/.