Science fiction for Catalan and Shi arrangements

Catalan and Shi arrangements for finite Weyl groups and their discrete-geometric structure have been considered in many contexts in Algebraic Combinatorics. Unfortunately, they have resisted from being generalized to more general finite reflection groups so far. I will start this talk with recalling in detail this discrete-geometric structure, and will then discuss surprising numerical observations in the module of derivations of a hyperplane arrangement that indicate that we still miss the "correct" combinatorics to study Catalan and Shi arrangements for general reflection groups. This talk can be seen as a combinatorial guidance of joint work with Torsten Hoge, Toshiyuki Mano and Gerhard Roehrle.