Self-avoidance in higher dimensions -- facts and open questions Heiko von der Mosel (Aachen) Abstract: The mathematical modeling of self-avoidance is a crucial issue for many topologically constrained variational problems. For curves there is variety of now well-investigated self-avoidance energies ranging from soft repulsive potentials to hard "steric" constraints. But the generalization of these singular and non-local energies to higher dimensional objects in arbitrary co-dimension is challenging. In this talk we give a survey on the currently known facts and discuss some open questions.