Curve-counting invariants for crepant resolutions

We construct curve counting invariants for a Calabi-Yau threefold $Y$ equipped with a dominant birational morphism $\pi:Y \to X$. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when $\pi:Y\to Y$ is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in the case when $Y$ is a crepant resolution of $X$, the coarse space of a Calabi-Yau orbifold $\mathcal{X}$ satisfying the hard Lefschetz condition. In this case, our partition function is equal to the Pandharipande-Thomas partition function of the orbifold $\mathcal{X}$. Our methods include defining a new notion of stability for sheaves which depends on the morphism $\pi$. Our notion generalizes slope stability which is recovered in the case where $\pi$ is the identity on $Y$. Our proof is a generalization of Bridgeland's proof of the PT/DT correspondence via the Hall algebra and Joyce's integration map.Comment: In this version, Jim Bryan has been added as an author and the required boundedness result for our stability condition has been added. arXiv admin note: text overlap with arXiv:1002.4374 by other author

On Rota's Conjecture and nested separations in matroids

We prove that for each finite field $\mathbb F$ and integer $k\in \mathbb Z$ there exists $n\in \mathbb Z$ such that no excluded minor for the class of $\mathbb F$-representable matroids has $n$ nested $k$-separations.Comment: 12 pages. This revised version includes revisions suggested by referees. The paper will appear in JCT

Rogue Athlete Endorsers: Using Social Identity Theory to Assess Brand Fit

Athlete endorsement deals typically assume that the brand will benefit from an association with the celebrity athlete\u27s public persona. When athletes find themselves in trouble with the law, spouses or frustrated fans, brands like Nike, Reebok, Buick, Wrangler and others must ask, \u27Can these rogue sports celebrity endorsers resurrect their image and their endorsement power? Are there certain rebellious products that may be better suited for endorsement from such rogue celebrities? These are the key questions addressed in this research. Survey results asking respondents to assess real athlete endorsers with either a \u27rebel\u27 or benign brand show that matching rebel endorsers with rebel brands can lead to positive brand attitudes and purchase intentions. Social identity theory, which shows how consumers identify with the athlete, and how that rubs off on the brand, is sued to explain the effects found in the study. Implications are addressed for marketers considering athletes are endorsers

Occupational fatalities amongst farm workers in Ireland, 1992 – 2008

working paperBackground: Whilst occupational fatalities amongst farm workers have been studied internationally little research has been published concerning farm fatalities or the demography farm fatalities in Ireland. Aims 1) To establish the incidence of farm fatalities during the 1992 – 2009 period in Ireland, 2) to explore the changing age profile of those experiencing fatal injuries on farms in Ireland. Methods: An official dataset containing the details of every fatal farm accident during the 1992 – 2009 period is used to evaluate changes in the number and age profile of farm fatalities in Ireland. Results: There were 304 deaths on farms during the 1992 – 2009 period in Ireland. The average number of annual fatalities is declining having fallen by 16% from 18 to 16 per year during this time. The fatality rate has however increased from 15 to 22 per 100,000 workers. This has been driven by a reduction in the number of workers employed on farms and, it is hypothesised, rapid ageing of the farm workforce. The demographic profile of those killed on farms changed significantly over the period. There are fewer deaths amongst younger cohorts. Older farmers, those over 55 years of age, now account for the vast majority of all fatal accidents. Conclusion: These findings highlight the changing nature of fatal farm incidents over the 1993 – 2009 period in Ireland. The increasing number of fatalities amongst older farmers suggests that Ireland’s Farm Safety Partnership needs to place greater emphasis of raising awareness amongst older farmers of fatality risks

A spatial analysis of agriculture in the Republic of Ireland, 1991 to 2000

End of year projectBy linking farm census and administrative data from the CSO and DAF to a geographic information system and analysing the mapping output, this project shows the continued broad division of farming in the state into marginal farming areas in the north and west and more commercial farming areas in the south and east. While this division was compounded by the 1992 CAP reforms, and commercial farming became more spatially concentrated over the 1990s, the influence of the development in the non-farm economy, particularly in peri-urban rural areas across the state, provided local drivers of change that encouraged enterprise substitution to beef production, the farming system most readily combined by farm holders with another job. A full report on the mapping output will be produced in a forthcoming publication (see publications list)