Tuesday, February 1, 2022
Elena Kudryavtseva (Moscow State University)
"Symplectic invariants of structurally stable singularities of
integrable systems."

16:00-17:00 GMT
(08:00 Los Angeles, 10:00 Mexico City, 11:00 New York, 13:00 Rio de
Janeiro, 16:00 London, 17:00 Rome, 19:00 Moscow, 21:30 Delhi, 00:00
Beijing, 03:00 Sydney)

Zoom ID: 814 7824 4988
Zoom Password: 199634

Abstract:  We study singularities of the Lagrangian fibration given by a
completely integrable system. We prove that a non-degenerate singular
fibre satisfying the so-called connectedness condition is structurally
stable under (small enough) real-analytic integrable perturbations of
the system. In other words, the topology of the fibration in a
neighbourhood of such a fibre is preserved after any such perturbation.
We also give a classification, up to real-analytic symplectic
equivalence, of the Lagrangian fibrations in a neighbourhood of such a
fibre.

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