From Drinfeld-Sokolov bihamiltonian structures to Dubrovin-Frobenius manifolds

Add to your list(s) Download to your calendar using vCal

• Yassir Dinar (Sultan Qaboos University)
• Thursday 11 August 2022, 11:00-12:00
• Seminar Room 2, Newton Institute.

If you have a question about this talk, please contact nobody.

HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

It is well known that local  bihamiltonian structure (compatible  Poisson structures) of hydrodynamic  type on a loop space is  the leading term of a local bihamiltonian structure admitting a dispersionless limit and under certain conditions it defines Dubrovin-Frobenius manifold. We consider Drinfeld-Sokolov bihamiltonian structure associated with a distinguished nilpotent element of semisimple type in a simple Lie algebra which does not always  admit a dispersionless limit.  We show that its  leading term defines a finite dimensional polynomial completely integrable system. Moreover, its reduction to the space of common equilibrium points of this integrable system leads to a local algebraic bihamiltonian structure admitting a dispersionless limit.  In addition, the leading term of the new local bihamiltonian structure leads to an algebraic Dubrovin-Frobenius manifold which  supports a conjecture due to Dubrovin about their classification.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 2, Newton Institute
• bld31

Note that ex-directory lists are not shown.