FAU MoD Lecture: From Alan Turing to contact Geometry: Towards a “Fluid computer”

Date: Wed. April 19, 2023
Event: FAU MoD Lecture
Organized by: FAU MoD, Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)

Title: From Alan Turing to contact Geometry: Towards a “Fluid computer”
Speaker: Prof. Dr. Eva Miranda
Affiliation: UPC, Universitat Politècnica de Catalunya · BarcelonaTech

Abstract. Is hydrodynamics capable of performing computations? (Moore, 1991). Can a mechanical system (including a fluid flow) simulate a universal Turing machine? (Tao, 2016). Etnyre and Ghrist unveiled a mirror between contact geometry and fluid dynamics reflecting Reeb vector fields as Beltrami vector fields. With the aid of this mirror, we can answer in the positive the questions raised by Moore and Tao. This is done by combining techniques from Alan Turing with modern Geometry (contact geometry) to construct a “Fluid computer” in dimension 3.

This construction shows, in particular, the existence of undecidable fluid paths. 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 this Millennium prize problem? We will end up the talk with some speculative ideas of a Fluid computer construction à la Feynman.

WHERE?

On-site / Online
Room H13. Johann-Radon-Hörsaal
Department Mathematik. Friedrich-Alexander-Universität Erlangen-Nürnberg
Cauerstraße 11, 91058 Erlangen
GPS-Koord. Raum: 49.573764N, 11.030028E

Online:
Zoom meeting link
Meeting ID: 614 4658 1599 | PIN code: 914397

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You might like:
• FAU MoD Lecture Series
• FAU MoD Lecture: Applications of AAA Rational Approximation by Prof. Dr. Nick Trefethen
• FAU MoD Lecture: Learning-Based Optimization and PDE Control in User-Assignable Finite Time by Prof. Dr. Miroslav Krstic

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