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Viterbo has conjectured that any Lagrangian in the unit co-disc bundle of atorus which is Hamiltonian isotopic to the zero-section satisfies a uniformbound on its spectral norm; a recent result by Shelukhin showed that this isindeed the case. The modest goal of this note is to explore two naturalgeneralisations of the above geometric setting in which the bound of thespectral norm fails: first, passing to Legendrian isotopies in thecontactisation of the unit co-disc bundle (Hamiltonian isotopies lift toLegendrian isotopies) and, second, considering Hamiltonian isotopies but aftermodifying the co-disc bundle by attaching a critical Weinstein one-handle.

Families of Legendrians and Lagrangians with unbounded spectral norm