This talk covers two separate topics. One, we identify a class of closed Riemannian manifolds for which there exists a rank-$infty$ quasi-flat in the metric space of the Hamiltonian deformations of a fiber in the unit codisk bundle with respect to the Lagrangian spectral norm. Two, we prove that for $ngeq 2$ any subbundle of $T^*T^n$ with bounded fibers symplectically embeds into a trivial subbundle where the fiber is an irrational cylinder.


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