Alvaro Carballeira will give a talk on 10/06/2026.

In the first lecture, we saw that energy supercritical defocusing NLS equations can form finite-time self-similar singularities. The proof has two steps: first, construct a self-similar profile and then find a perturbation to construct compactly supported, smooth initial data that blows up in finite time. This talk will focus on the second part, the global stability argument. I will present the analysis of the spectrum of the linearized operator and the construction of a finite-codimension manifold of smooth initial data that gives rise to the self-similar blow-up. This talk is based on joint work with Kevin Buck, Javier Gómez-Serrano, and Jia Shi.