Universal D-modules and stacks of \'etale germs of n-dimensional varieties

We introduce stacks classifying \'etale germs of pointed n-dimensional varieties. We show that quasi-coherent sheaves on these stacks are universal D- and O-modules. We state and prove a relative version of Artin's approximation theorem, and as a consequence identify our stacks with classifying stacks of automorphism groups of the n-dimensional formal disc. We introduce the notion of convergent universal modules, and study them in terms of these stacks and the representation theory of the automorphism groups.Comment: 61 pages. Version 1 had a gap: Artin's approximation theorem was misstated and the incorrect version was used. This gap has been fixed, using new material in sections 2 and 5. Section 8 has been added, to treat the dg-categorical version of the results. The paper has been restructured and the introduction has been expanded. Version 3: minor change

Overview of the labour market [November 2012]

Inevitably interest in the Scottish labour market continues to focus on the levels and trends in employment and unemployment and again we return to these themes. In addition the UK Government proposals to reform public sector terms and conditions of employment have emerged (see the Public Sector employment section of this Commentary). The employment law proposals emanating from in the Beecroft Report continued to surface at the recent Conservative Party conference (see the February and June issues of the Commentary)

Explorations in Evolutionary Design of Online Auction Market Mechanisms

This paper describes the use of a genetic algorithm (GA) to find optimal parameter-values for trading agents that operate in virtual online auction “e-marketplaces”, where the rules of those marketplaces are also under simultaneous control of the GA. The aim is to use the GA to automatically design new mechanisms for agent-based e-marketplaces that are more efficient than online markets designed by (or populated by) humans. The space of possible auction-types explored by the GA includes the Continuous Double Auction (CDA) mechanism (as used in most of the world’s financial exchanges), and also two purely one-sided mechanisms. Surprisingly, the GA did not always settle on the CDA as an optimum. Instead, novel hybrid auction mechanisms were evolved, which are unlike any existing market mechanisms. In this paper we show that, when the market supply and demand schedules undergo sudden “shock” changes partway through the evaluation process, two-sided hybrid market mechanisms can evolve which may be unlike any human-designed auction and yet may also be significantly more efficient than any human designed market mechanism

Overview of the labour market [February 2012]

Inevitably current interest in the Scottish labour market continues to focus on the levels and trends in employment and unemployment and again we return to these themes. In addition the UK Government has announced plans to 'radically reform employment relations' (Vince Cable 23.11.2011), in Scotland the proposals to introduce both a national police force and national fire service have been published. Attention also focussed on the rates of pay and bonuses in the financial sector to the neglect of pay relativities, other changes in pay, earnings and pensions for other groups, the subject of industrial action within the public sector at the end of 2011

Public Sector employment in Scotland [February 2012]

Some 300,000 public sector workers in Scotland participated in the UK wide public sector strike at the end of November 2011, in response to plans to change pension arrangements, pension links to the CPI, retirement age and contributions. The Government announced a revised arrangement, broadly, although not universally accepted, on 20th December. Public sector employment in Scotland continues to decline. The latest data (Q3 2011) indicates that there were 588,900 (546,000 excluding public sector financial institutions) employed in the public sector in Scotland, a decrease of 23,500 (3.8%) since Q3 2010. Employment in the devolved public sector declined by 21,200 (4.1%) to 492,000, due mainly to a decline in local government employment (down 13,300 over the year). Public sector employment (headcount and excluding public sector financial institutions) is now at its lowest since Q4 2001 and in percentage terms the lowest in the current data set (1999 - 2011)

Overview of the labour market [March 2013]

Inevitably interest in the Scottish labour market continues to focus on the trends in employment and unemployment and again we return to these themes. Concern is increasingly focusing on the rise in underemployment and the productivity puzzle - why has employment performed better in this recession, whilst the fall in labour productivity is larger and more persistent than in previous recessions. In addition the UK Government proposals reform public sector terms and conditions of employment continue to emerge as do a number of previously heralded changes to employment

Differential labour and competitive advantage : embedding resource-based theory within Marx's labour theory of value

School of Managemen