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SUMMARY:Bihamiltonian Structures of the Genus-Zero Whitham Hierarchy
DTSTART:20260519T140000Z
DTEND:20260519T150000Z
DTSTAMP:20260523T230800Z
UID:indico-event-16598@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dimitris Makris (IMB)\n\nThe genus-zero Whitham hier
 archy\, introduced in the 1990s by I. M. Krichever\, is a family of evolut
 ionary quasi-linear PDEs describing the slow modulation of nonlinear waves
 . It includes\, as special cases\, many well-known dispersionless integrab
 le systems\, such as the dispersionless KP hierarchy and the two-dimension
 al Toda hierarchy. In this talk\, we explain how to derive a bihamiltonia
 n formulation of the hierarchy using the method of R-matrices. More precis
 ely\, we construct a Poisson pencil on the loop space of holomorphic funct
 ions defined on disjoint circles in the Riemann sphere\, and then apply Di
 rac reduction to obtain a bihamiltonian structure for the genus-zero Whith
 am hierarchy. Time permitting\, we will also discuss the relationship bet
 ween this work and the theory of Frobenius manifolds\, and propose a conje
 ctural definition of a dispersive deformation of the Whitham hierarchy.\n\
 nhttps://indico.math.cnrs.fr/event/16598/
LOCATION:318
URL:https://indico.math.cnrs.fr/event/16598/
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