article epub_ahead yes Benjamin Harrop-Griffiths author Rowan Killip author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca We consider the cubic defocusing nonlinear Schrödinger equation in one dimension with the nonlinearity concentrated at a single point. We prove global well-posedness in the scaling-critical space L^2(R) and scattering for all such solutions. Moreover, we demonstrate that the same phenomenology holds whenever nonlinear effects are sufficiently concentrated in space. American Mathematical Society2026 eng 0002-9939 1088-6826 2507.1457110.1090/proc/17760 yes Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “Scattering for the Nonlinear Schrödinger Equation with Concentrated Nonlinearity.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2026. <a href="https://doi.org/10.1090/proc/17760">https://doi.org/10.1090/proc/17760</a>. B. Harrop-Griffiths, R. Killip, M. Vişan, Proceedings of the American Mathematical Society (2026). Harrop-Griffiths B, Killip R, Vişan M. 2026. Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. Proceedings of the American Mathematical Society. Harrop-Griffiths, B., Killip, R., &#38; Vişan, M. (2026). Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/17760">https://doi.org/10.1090/proc/17760</a> Harrop-Griffiths B, Killip R, Vişan M. Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity. <i>Proceedings of the American Mathematical Society</i>. 2026. doi:<a href="https://doi.org/10.1090/proc/17760">10.1090/proc/17760</a> B. Harrop-Griffiths, R. Killip, and M. Vişan, “Scattering for the nonlinear Schrödinger equation with concentrated nonlinearity,” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2026. Harrop-Griffiths, Benjamin, et al. “Scattering for the Nonlinear Schrödinger Equation with Concentrated Nonlinearity.” <i>Proceedings of the American Mathematical Society</i>, American Mathematical Society, 2026, doi:<a href="https://doi.org/10.1090/proc/17760">10.1090/proc/17760</a>. 220972026-06-19T08:59:17Z2026-06-30T11:13:33Z