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Geometric and Hamiltonian hydrodynamics via Madelung transform

Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018

November 27, 2018 (11:30 AM PST - 12:30 PM PST)
Speaker(s): Boris Khesin (University of Toronto)
Location: MSRI: Simons Auditorium
  • hydrodynamics

  • infinite-dimensional geometry

  • quantum information

  • Fisher–Rao metric

  • Newton’s equations

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification



We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the so-called Madelung transform between the Schrödinger-type equations on wave functions and Newton's equations on densities turns out to be a Kähler map between the corresponding phase spaces, equipped with the Fubini-Study and Fisher-Rao information metrics. This is a joint work with G.Misiolek and K.Modin.

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