"Shadows in the wild -- folded galleries and their applications"
by Petra Schwer has been recently uploaded to the arXiv!
Link to the paper: arXiv:2109.02293
This survey is about combinatorial objects related to reflection groups and their applications in representation theory and arithmetic geometry. Folded galleries in Coxeter complexes are introduced and it is explained how they relate to retractions in Bruhat--Tits buildings and the geometry of affine flag varieties and affine Grassmannians. The goal is to make these topics accessible to a wide audience.