Drowning by Numbers: Topology and Physics in Fluid Dynamics

Amaury Mouchet ()
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Amaury Mouchet: Université François Rabelais de Tours, Laboratoire de Mathématiques et de Physique Théorique

A chapter in Imagine Math 6, 2018, pp 249-266 from Springer

Abstract: Abstract Since its very beginnings, topology has forged strong links with physics and the 2016 Nobel prize in physics, awarded to Thouless, Haldane and Kosterlitz “for theoretical discoveries of topological phase transitions and topological phases of matter”, confirmed that these connections have been maintained up to contemporary physics. To give some (very) selected illustrations of what is, and still will be, a cross fertilization between topology and physics, 1 hydrodynamics provides a natural domain through the common theme offered by the notion of vortex, relevant both in classical (second section) and in quantum fluids (third section). Before getting into the details, I will sketch in first section a general perspective from which this intertwining between topology and physics can be appreciated: the old dichotomy between discreteness and continuity, first dealing with antithetic thesis, eventually appears to be made of two complementary sides of a single coin.

Date: 2018
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DOI: 10.1007/978-3-319-93949-0_20

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