Conferència: Undecidability in dynamical systems: from Turing machines to hydrodynamics

Abstract:

Logical and computational undecidability are notions that date back to the foundational works of Gödel and Turing developed during the first half of the 20th century. Since then, several questions in mathematics have been shown to be undecidable. In this talk, we first introduce Turing machines and explain how they can be related to the theory of dynamical systems to prove that some of their properties can be undecidable. In the context of hydrodynamics, we will be interested in the Euler equations for ideal fluids, and the undecidability properties of its solutions. We will discuss informally some recent results establishing the existence of undecidability phenomena in hydrodynamics. These results are based on several joint works with Eva Miranda, Daniel Peralta-Salas, and some of them also with Francisco Presas.

El SIMBa és un seminari jove organitzat per estudiants de doctorat i màster en Matemàtiques de l'àrea de Barcelona. Està dirigit a estudiants de doctorat, de màster i, fins i tot, dels darrers cursos de grau. Els nostres objectius són divulgar coneixements de diferents branques de les matemàtiques per tothom qui hi estigui interessat, a la vegada que fomentar la interacció entre els participants. Podeu trobar tota la informació sobre sessions passades i futures a https://www.ub.edu/simba/.

Data d'inici: 20/04/2022 12:00

Data finalització: 20/04/2022 14:00

Lloc: Aula 002 de la FME i Zoom.