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January 13, 2023 By GeometryAdmin

Eva Miranda to talk in geometry seminar 15/12/2022

Eva Miranda will speak in the geometry seminar at 2pm on 15/12/2022. Eva’s title is “Two sides of a mirror” and her abstract is below.

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 affirmatively the questions raised by Moore and Tao in a geometrical manner by combining techniques from Alan Turing with contact geometry to construct a “Fluid computer” in dimension 3. This construction shows, in particular, the existence of undecidable fluid paths. 

Furthermore, the application of the h-principle to the contact side of the mirror discloses the universal nature of Euler flows on the other side: Any dynamical system can be presented as an Euler flow (indeed as a Beltrami field) in higher dimensions. As contact geometry provides a natural language for many problems in Celestial mechanics, this mirror allows us to construct a “tunnel” connecting problems in Celestial mechanics to Fluid Dynamics.

Time permitting, I will also briefly explain applications of this mirror to the detection of escape trajectories in Celestial mechanics. 

Filed Under: geometry seminar news

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Département de mathématiques
Université libre de Bruxelles CP 218
Boulevard du Triomphe, Bruxelles 1050,
Belgium

Getting here

The department of mathematics is in building NO, on the Campus de la Plaine, of the Université libre de Bruxelles. The geometry group is on the 7th floor. This page has a map of the campus as well as information on how to reach it via public transport. See the STIB website for more information on public transport in Brussels.

Image credits

Polished ammonite fossil, by Kara Stenberg, Creative Commons licence CC BY-NC 2.0.

Model of 3D projection of a 120-cell, by Edmund Harriss.

The root system of the exceptional Lie algebra E8. By Jared Tarbell, Creative Commons Licence CC BY 2.0.

Getting here

The department of mathematics is in building NO, on the Campus de la Plaine, of the Université libre de Bruxelles. The geometry group is on the 7th floor. This map shows NO, as well as the metro station Delta and entrance 2, which is right by the stop for the number 71 and 72 buses. The number 95 also stops a short walk from the department. See the STIB website for more information on public transport in Brussels.

Image credits

Polished ammonite fossil, by Kara Stenberg, Creative Commons licence CC BY-NC 2.0.

Model of 3D projection of a 120-cell, by Edmund Harriss.

The root system of the exceptional Lie algebra E8. By Jared Tarbell, Creative Commons Licence CC BY 2.0.

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