Geometry, Mechanics and Control Seminar

Undecidability and universal computation in Euler and Reeb flows

Speaker:  Robert Cardona (IRMA - Université de Strasbourg)
Date:  Friday, 20 May 2022 - 15:30
Online: (ID: 755 546 3367)


Is hydrodynamics capable of universal computation? This question was formulated by Moore in 1991 and has been recently revisited by Tao. In this talk, we will formalize what it means for a dynamical system to be "Turing complete" and show how to construct a Turing complete stationary solution to the Euler equations on a (non-standard) Riemannian sphere of dimension 3. This is based on joint work with E. Miranda, D. Peralta-Salas, and F. Presas, and exploits the connection between hydrodynamics and contact geometry established by Etnyre and Ghrist. Our construction shows that orbits of Reeb and stationary Euler flows can have different undecidable properties, thus unveiling a complexity different from classical sensitivity to initial conditions. Time permitting, we will discuss other related results obtained with E. Miranda and D. Peralta-Salas.