Superoscillations is the phenomenon that a function with compact support in Fourier domain can oscillate faster than its largest Fourier component, for an arbitrarily long period. I will go through a couple of examples of this phenomenon, all due to Michael Berry.
I will then discuss the recent paper by Aharonov, Popescu and Rohrlich where superoscillations are put into relation to conservation laws in quantum mechanics.
Reference: Y. Aharonov, S. Popescu, D. Rohrlich, "On conservation laws in quantum mechanics", PNAS 118 (1) e1921529118 (2021)