Abstract.
The Shi- and Ish- arrangements are well-known arrangements of hyperplanes, which divide R^n into different regions. Armstrong and Rhoades (2012) studied them in detail and asked for an explicit bijection between these Shi- and Ish regions, which additionally preserves certain properties. The main topic of the talk is the construction of such a bijection which preserves so-called ceiling-partitions and dominance, as described by Leven, Rhoades and Wilson in 2014.