Abstract: 

The study of arrangements of hyperplanes goes back to the 19th century and was boosted after the Seventies by work of Arnol'd, Brieskorn and Deligne on configuration spaces and Artin groups of finite type. A hallmark of this classical theory is the strong interaction between geometry, combinatorics and topology. 

Arrangements theory recently broadened its scope beyond the linear case to include arrangements in the complex torus, in products of elliptic curves and, more generally, in connected Abelian Lie groups. This also expanded the range of its connections and applications within and beyond pure mathematics.

In this talk I will introduce arrangements of hypersurfaces, survey some of the classical theory and present some recent advances in the non-linear case. I will highlight a new notion of "geometric" group actions on posets that arises in this context. Time permitting, I will discuss some applications to group theory.