This talk will highlight new combinatorial objects associated with Coxeter groups, called "shadows". The motivation to introduce and study these obects originated in the study of the dimensions of affine Deligne-Lusztig varieties by means of folded galleries in Coxeter complexes (jww Milicevic and Thomas). Folded galleries have previously appeared in other places, e.g. in relation with Hecke algebras and other representation theoretic questions.

Studying shadows on their own will highlight some of their intrinsic structural properties, hopefully provide for new methods and tools as well as create some interesting combinatorial objects.