Carlos Matheus (École Polytechnique, Paris, France)

Brazilian mathematician working in dynamical systems, analysis and geometry. He earned his Ph.D. from the Instituto de Matemática Pura e Aplicada (IMPA) in 2004 under the supervision of Marcelo Viana, at the age of 19. Matheus had become a frequent co-author of Jean-Christophe Yoccoz after a post-doctorate at the Collège de France under his supervision (between 2007 and 2010). Currently, Matheus is CNRS research director assigned to the Laurent Schwartz Mathematics Center of the Ecole Polytechnique and responsible for the mathematical archives of Jean-Christophe Yoccoz.

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ENSPM 2021 Presentation

Title: Billiards

Abstract: Dynamical billiards were designed to serve as simpler models for intricate phenomena in Statistical Mechanics. Nevertheless, the body of research developed over the last 100 years taught us that the family of dynamical billiards is rich enough to exhibit all  complicated behaviours (elliptic, parabolic and hyperbolic) described  by the modern theory of Dynamical Systems.

In this talk, after briefly recalling the link between dynamical billiards and Lorentz ideal gases in Statistical Mechanics, we will discuss billiards on ellipses, billiards on rational polygons, and Sinai billiards as an excuse to make a tour around the theories of elliptic, parabolic and hyperbolic systems.