Séminaires : Séminaire Géométrie et Topologie

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ

Is Hydrodynamics capable of universal computation? This question was formulated by Moore in 1991 and has been recently revisited by Tao in relation to the global regularity problem for the Euler and Navier-Stokes equations. In this introductory talk, we will present what it means for a dynamical system to be "Turing-complete". This property implies that the system has undecidable trajectories, a kind of complexity that is different from the classical sensitivity to initial conditions. We will sketch the construction of conservative systems with undecidable properties, with an eye toward recent results in hydrodynamics obtained in joint works with E. Miranda, D. Peralta-Salas, and F. Presas.