This mini-workshop will be a continuation of a sequence of successful such workshops held in Kingston in 2004, Ottawa in 2005, and at the Field Institute in 2006. These past events have established a fruitful and on-going dialog between two research communities who had been using different techniques to study similar mathematical problems. The two groups are algebraic combinatorialists who have been studying important and interesting G-modules, for finite groups G generated by reflections; and commutative algebraists who have been studying resolutions and inverse systems in Gorenstein Artinian situations. Using these connections, several new and interesting ideas are now being studied, and it seems natural to exploit the expertise of both communities. Each of the previous workshops has introduced new features in this dialog.