## Domenico Catalano

## Quadrangle groups inclusions

A finitely generated discrete subgroup of the group of all conformal homeomorphisms of the upper half-plane is called a

interested only on those Fuchsian groups having fundamental regions of finite volume and generated by four elliptic elements, called

*Fuchsian group*. Here we areinterested only on those Fuchsian groups having fundamental regions of finite volume and generated by four elliptic elements, called

*quadrangle groups*. We discuss the classification of all finite index inclusions between quadrangle groups obtained by generalising a result of Singerman (1972) on triangle groups.

Rui Duarte

## From parking functions to the regions of the Shi arrangement

In the nineties Pak and Stanley introduced a labelling λ of the regions of the Shi arrangement with parking functions. In this talk we present an algorithm that returns a region R out of λ(R). This is done by relating λ to another bijection, that labels every region S of the braid arrangement with r(S), the unique central parking function f such that λ^{-1 }(f) ⊆ S. In addition, we present a variant of the parking algorithm that is in the very origin of the term “parking function”.

This is joint work with António Guedes de Oliveira.