The Grothendieck and Picard groups of a complete toric DM stack

We compute the Grothendieck and Picard groups of a complete smooth toric Deligne-Mumford stack by using a suitable category of graded modules over a polynomial ring.Comment: keywords: Graded rings, graded modules, toric DM stacks, Grothendieck group, Picard group. This is the final published versio

Redesigning procurement in the public sector will be a vital part of meeting budget reductions.

In 2008/09, the public sector spent £220 billion on goods and services alone, accounting for one third of all spending. However, there is multiple overlap in terms of procurement processes and structures across the public sector and collaboration across organisational boundaries has been slow to develop. Chris Cox and Paul Rainford report from a recent seminar organised by the London School of Economics and the Design Council in which it was argued that innovative procurement will be crucial if the public sector is to reduce duplication, provide value for money and survive austerity.

A geometric characterisation of the blocks of the Brauer algebra

We give a geometric description of the blocks of the Brauer algebra $B_n(\delta)$ in characteristic zero as orbits of the Weyl group of type $D_n$. We show how the corresponding affine Weyl group controls the representation theory of the Brauer algebra in positive characteristic, with orbits corresponding to unions of blocks.Comment: 26 pages, 24 figure