Tensor triangular geometry -- Notes for an Oberwolfach Seminar

These are the notes from lectures I gave at the Oberwolfach Seminar “Tensor Triangular Geometry and Interactions” which was held in October 2025. The aim of these notes is twofold: We develop notions of support for triangulated categories, and we apply them to classify thick and localising tensor ideals of categories that arise in modular representation theory of finite groups.