23 Sep 2019 Mon 12:15-13:00 Forskningsparken Klasserom 1 (B281)

Pawel Nurowski (Centre for Theoretical Physics in the Polish Academy of Sciences)

"The parabolic geometry of a car".

I will discuss the geometry of the configuration space of a car equipped with ideal tires. Such a physical system is nonholonomic, meaning that its velocities obey constraints that cannot be integrated to the constraints on positions. These constraints are linear, which results in equipping the configuration space of a car with the structure of a bracket generating vector distribution. Surprisingly, two kinds of very natural movements of a car define an additional structure on this distribution, whose local symmetry is SO(2,3).

My talk will try to provide elementary arguments why this simple Lie group, which in particular is a conformal symmetry group of the 3-dimensional Minkowski space, appears as one of the features of any car.