Symplectic geometry seminar

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21 September 2026
15:15-16:45

Ibrahim Trifa
ETHZ

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Title	A multidimensional Birkhoff Theorem for some $C^0$ Lagrangians
Speaker, Affiliation	Ibrahim Trifa, ETHZ
Date, Time	21 September 2026, 15:15-16:45
Location	HG G 43
Abstract	In 1922, Birkhoff proved that an essential embedded closed curve that is invariant under a symplectic twist map of the cylinder is a Lipschitz graph over the zero section. There has been several works extending this theorem in higher dimension (Herman, Katznelson–Ornstein, Siburg, Bialy–Polterovich...). In 2010, Arnaud proved that a closed exact Lagrangian in the cotangent bundle of a closed manifold that is invariant under the flow of a Tonelli Hamiltonian is a graph over the base. Some improvements on this theorem have been made on one hand by Bernard-dos Santos and Amorim-Oh-dos Santos, who showed a version of this theorem for Lipschitz Lagrangian submanifolds, and on the other hand by Charfi who replaced the invariance assumption with a recurrence assumption (for a topology he defined and called "reduced complexity convergence"). In this talk, I will explain how to define a new class of "$C^0$ Lagrangians" for which the multidimensional Birkhoff theorem holds, using a new variant of the reduced complexity convergence topology. In particular, this class contains all images of continuous graphs by $C^1$ exact symplectomorphisms, which can be less regular than Lipschitz. This is based on a work in progress with Skander Charfi.

A multidimensional Birkhoff Theorem for some $C^0$ Lagrangiansread_more

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