El proper dimecres, 6 dabril, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).
Speaker: Robert Cardona
Universitat: Université de Strasbourg
Data: Wednesday, April 20th, 2022.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: UPC (FME aula 002) and Zoom
Títol: Undecidability in dynamical systems: from Turing machines to hydrodynamics
Resum: 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.
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