Dr Alexey Bolsinov - Frobenius pencils and compatible non-homogeneous Poisson structures

  • 13 October 2021
  • 15:00-16:00
  • SCH.105 Schofield Building

Presented by Dr Alexey Bolsinov (Loughborough University)

This work, joint with A. Konyaev and V. Matveev, is another application of Nijenhuis geometry in the theory of integrable systems.  Our goal is to study compatible (differential geometric) non-homogeneous Poisson structures of the form B + A, where B and A are homogeneous Darboux-Poisson structures of order 3 and 1 respectively. The problem reduces to classification of pairs of compatible Frobenius algebras and we solve it completely by geometric methods under some minor genericity conditions.

Some interesting examples of multicomponent integrable PDE systems will be demonstrated too.

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