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Multidimensional Poisson Vertex Algebras and Poisson brackets of hydrodynamic type

Speaker: 
Matteo Casati
Institution: 
SISSA
Schedule: 
Wednesday, January 22, 2014 - 11:00 to 12:30
Location: 
A-136
Abstract: 

We extend the definition of Poisson Vertex Algebras, whose relation with Integrable Systems has been investigated by De Sole and  Kac, in order to deal with evolutionary equations with more than one spatial degree of freedom. We get a powerful computational technique that is applied to the study of deformations of Poisson brackets of hydrodynamic type: in particular, we prove that the all the first order deformations of a 2-dimensional Poisson bracket of such class are trivial. Reference: preprint arXiv:1312.1878 [math.DG]

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