6 mai 2019

Rodolfo Gutierrez (IMJ)
Lower bounds on the Hausdorff dimension of the Rauzy gasket

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Lieu : salle 3L8

Résumé : The Rauzy gasket is an important fractal object arising in several dynamical constructions, such as Novikov’s problem and some renormalization schemes for certain families of interval exchange maps. It was conjectured by Novikov and Maltsev in 2003 that the Hausdorff dimension D of the Rauzy gasket is strictly comprised between 1 and 2. In 2016, Avila, Hubert and Skripchenko confirmed the upper bound D<2. In this talk, I will explain how to use the thermodynamical results of Cao, Pesin and Zhao to show that D>1.19. This is joint work with Carlos Matheus.

Lower bounds on the Hausdorff dimension of the Rauzy gasket  Version PDF

Pawel Nurowski (Center for Theoretical Physics, Polish Academy of Sciences)
Parabolic geometry of a car

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Lieu : IMO ; salle 3L8.

Résumé : 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 can not 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.

Parabolic geometry of a car  Version PDF