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SUMMARY:Conformally mapping water waves:  top\, bottom or sides. - Andre N
 achbin (IMPA - Instituto Nacional de Matemática Pura e Aplicada\, Rio de 
 Janeiro)
DTSTART:20190909T140000Z
DTEND:20190909T143000Z
UID:TALK129256@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:I will present a brief overview of recent work showcasing conf
 ormal mapping&#39\;s important role on surface water-wave dynamics. Confor
 mal mapping can be used to flatten the free surface or a highly irregular 
 bottom topography. It has also been used along the sides of forked channel
  regions\, leading to a Boussinesq system with solitary waves on a graph. 
  Mapping a highly variable bottom topography\, among other features\,  all
 ows the construction of a Dirichlet-to-Neumann operator over a polygonal b
 ottom profile. One very recent example applies to a hydrodynamic pilot-wav
 e model\, capturing two bouncing droplets confined in cavities\, where the
 y can synchronize as nonlinearly coupled oscillators. Finally\, on another
  topic\, I will briefly present a very recent result displaying  a spectra
 lly accurate finite difference operator. This difference operator is const
 ructed by unconventional means\, having in mind complex analytic functions
 .
LOCATION:Seminar Room 1\, Newton Institute
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