UPC Universitat Politècnica de Catalunya
Day 1 (April 11) @ 10:10 – 11:00 Keynote
Where will the 29000 rubber ducks wash up? From Turing machines to Fluid Dynamics
What kind of physics might be non-computational? (Penrose) Is hydrodynamics capable of performing computations? (Moore). Can a mechanical system (including a fluid flow) simulate a universal Turing machine? (Tao).
In 1992, 29000 rubber ducks were lost in the Pacific ocean during a storm. Some of the rubber ducks landed in Hawaii while others reached the east coast of the US and the British shores fifteen years later. These emblematic rubber ducks are known as the “friendly floatees” and their erratic trajectories were made famous by the work of an oceanographer, Ebbesmeyer, who models ocean currents on the basis of flotsam movements.
In this talk, I will use the friendly floatees as a metaphor for complexity and undecidability in Fluid dynamics. The existence of undecidable fluid paths is a consequence of the design of a Turing complete Euler flow. The proof combines techniques from Alan Turing with modern Geometry to construct a “Fluid computer” in dimension 3. Tao’s question was motivated by a research program to address the Navier–Stokes existence and smoothness problem. Could such a Fluid computer be used to address the Millennium prize problem?
Eva Miranda is a Full Professor at Universitat Politècnica de Catalunya in Barcelona and member of the Centre de recerca Matemàtica-CRM. She is the director of the Laboratory of Geometry and Dynamical Systems. Distinguished with two consecutive ICREA Academia Prizes in 2016 and 2021, she was awarded a Chaire d’Excellence de la Fondation Sciences Mathématiques de Paris in 2017 and a Friedrich Wilhelm Bessel Prize by the Alexander Von Humboldt Foundation in 2022. Miranda is the recipient of the quadrennial François Deruyts Prize in 2022, a prize awarded by the Royal Academy of Belgium. She has been named the 2023 London Mathematical Society Hardy Lecturer.
Miranda’s research is at the crossroad of Differential Geometry, Mathematical Physics and Dynamical Systems. More than a decade ago she pioneered the investigation of b-Poisson manifolds. These structures appear naturally in physical systems on manifolds with boundary and on problems in Celestial mechanics such as the 3-body problem. More recently, she added to her research agenda some mathematical aspects of theoretical computer science in connection to Fluid Dynamics building new bridges between these areas and contact geometry. Miranda’s research strives to decipher the several levels of complexity in Geometry and Dynamics and to investigate new facets of their interaction.
Miranda is an active member of the mathematical community, a member of several international scientific panels and prize committees. She created an important school by supervising 10 Ph.D. theses and several postdocs. She has been chercheur affiliée at Observatoire de Paris and honorary doctor at CSIC. Among others, she served on the CRM Scientific Advisory Board. She is a member of the scientific committee at the Spanish Mathematical Society, a member of the Conseil d’Administration de l’Institut Henri Poincaré in Paris, and a member of the Mathematics Panel at the Spanish State Agency. She is also a member of the Scientific Commission Sciences Exactes et Naturelles of the Fund for Scientific Research FNRS.