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In the context of symplectic dynamics, pseudo-rotations are Hamiltoniandiffeomorphisms with finite and minimal possible number of periodic orbits.These maps are of interest in both dynamics and symplectic topology. We showthat a closed, monotone symplectic manifold, which admits a non-degeneratepseudo-rotation, must have a deformed quantum Steenrod square of the top degreeelement, and hence non-trivial holomorphic spheres. This result (partially)generalizes a recent work by Shelukhin and complements the results by theauthors on non-vanishing Gromov-Witten invariants of manifolds admittingpseudo-rotations.

From pseudo-rotations to holomorphic curves via quantum Steenrod squares