Damien Galant will give a talk on 10/21/2025.

In this talk, we consider the nonlinear Schrödinger equation set on compact metric graphs and more precisely we study qualitative properties of solutions (uniqueness, symmetries, nodal zones…). As this is a complex question in general, we focus on the “near-linear” regime. In this case, one can perform a Lyapunov-Schmidt reduction which leads us to study a “reduced problem” set on (finite dimensional) eigenspaces of the Laplacian on the graph. We will show that there are new phenomenon specific to graphs that we have to take care about. We then apply these results to the discussion of symmetries of solutions on some compact graphs. This is joint work with Colette De Coster (CERAMATHS/DMATHS, France) and Christophe Troestler (UMONS, Belgium).