Title: Classification of Weyl groupoids

Abstract: Finite Weyl groupoids (these are certain simplicial arrangements in a lattice) were completely classified in a series of papers by Heckenberger and myself. However, this classification is based on two computer proofs checking millions of cases. In this talk, I want to report on recent progress in finding a shorter proof. In particular, we prove without using a computer that, up to equivalence, there are only finitely many irreducible finite Weyl groupoids in each rank greater than two.