Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2 Killip, Rowan Visan, Monica Zhang, Xiaoyi We prove that solutions of the cubic nonlinear Schr\"odinger equation on $\Bbb{R}^2$ can be approximated by a finite-dimensional Hamiltonian system, uniformly on bounded sets of initial data. This is despite the wealth of non-compact symmetries: scaling, translation, and Galilei boosts. Complementing this approximation result, we show that all solutions of the finite-dimensional Hamiltonian system we use can be approximated by the full PDE. A key ingredient in these results is the development of a general methodology for transfering uniform global space-time bounds to suitable Fourier truncations of dispersive PDE models. As an application, we prove symplectic non-squeezing (in the sense of Gromov) for the cubic NLS on $\Bbb{R}^2$. This is the first symplectic non-squeezing result for a Hamiltonian PDE in infinite volume. It is also the first unconditional symplectic non-squeezing result in a scaling-critical setting. Finally, we discuss implications of non-squeezing on the nature of scattering. Johns Hopkins University Press 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22035 Killip R, Vişan M, Zhang X. Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrödinger equation on ℝ2. <i>American Journal of Mathematics</i>. 2021;143(2):613-680. doi:<a href="https://doi.org/10.1353/ajm.2021.0014">10.1353/ajm.2021.0014</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1353/ajm.2021.0014 info:eu-repo/semantics/altIdentifier/e-issn/1080-6377 info:eu-repo/semantics/altIdentifier/arxiv/1606.07738 info:eu-repo/semantics/openAccess