Damien Galant will give a talk on 10/28/2025.

As pointed out in the previous talk, the study of the reduced problem associated to the almost linear regime is in general delicate. In this talk, we perform this study on a specific example: the tetrahedron graph, made of four vertices pairwise joined by edges, all of the same length. We explain how the symmetries of the domain give rise to families of critical points. Then, we show their uniqueness and nondegeneracy using computer-assisted proofs based on interval arithmetic. This leads us to uniqueness and symmetry results for some sign-changing solutions, in particular for the “nodal action ground states”, in the almost linear regime. This is joint work with Colette De Coster (CERAMATHS/DMATHS, France) and Christophe Troestler (UMONS, Belgium).