Drowning by numbers: topology and physics in fluid dynamics

Abstract : Since its very beginnings, topology has forged strong links with physics and the last Nobel prize in physics, awarded in 2016 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, hydrodynamics provides a natural domain through the common theme offered by the notion of vortex, relevant both in classical (§ 2) and in quantum fluids (§ 3). Before getting into the details, I will sketch in § 1 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.
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Contributeur : Amaury Mouchet <>
Soumis le : samedi 10 juin 2017 - 08:59:38
Dernière modification le : samedi 13 janvier 2018 - 01:22:34
Document(s) archivé(s) le : mercredi 13 décembre 2017 - 02:42:02

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  • HAL Id : hal-01530467, version 1
  • ARXIV : 1706.09454

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Amaury Mouchet. Drowning by numbers: topology and physics in fluid dynamics. Imagine maths 6, Between culture and mathematics,, 2018. 〈hal-01530467〉

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