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{\bf
Alexey Bolsinov} (Loughborough University and Moscow State University)
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{\bf Symplectic invariants of integrable Hamiltonian systems: the case of degenerate singularities}
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Abstract.
The nature of symplectic invariants for non-degenerate singularities of integrable Hamiltonian systems has been studied and clarified (both in the local and semi-local setting) in fundamentally important papers by Vey, Eliasson, Dufour, Toulet, Miranda, Zung and San Vu Ngoc. The talk is devoted to some new ideas and techniques that can be used for studying symplectic invariants of degenerate singularities.
As an example, I would like to discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities.
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