From Alan Turing to Contact Geometry: Towards a Fluid Computer

Explore the fascinating intersection of hydrodynamics, computation, and geometry in this conference talk. Delve into the questions posed by Moore and Tao regarding the computational capabilities of fluid systems and mechanical simulations of universal Turing machines. Discover the groundbreaking mirror between contact geometry and fluid dynamics, unveiled by Etnyre and Ghrist, which connects Reeb vector fields to Beltrami vector fields. Learn how this mirror enables the construction of a "Fluid computer" in three dimensions, demonstrating the existence of undecidable fluid paths. Examine the applications of this geometric approach to detecting escape trajectories in celestial mechanics, and understand how it bridges problems in celestial mechanics and fluid dynamics. Gain insights into the fusion of Alan Turing's techniques with modern contact geometry, opening new avenues for understanding computation in physical systems.