Compact moduli of plane curves

We construct a compactification M_d of the moduli space of plane curves of degree d. We regard a plane curve C as a surface-divisor pair (P^2,C) and define M_d as a moduli space of pairs (X,D) where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stack M_d is smooth and the degenerate surfaces X can be described explicitly.Comment: 46 pages. Final version to be published in Duke Mathematical Journa

The moduli space of curves is rigid

We prove that the moduli stack of stable curves of genus g with n marked points is rigid, i.e., has no infinitesimal deformations. This confirms the first case of a principle proposed by Kapranov. It can also be viewed as a version of Mostow rigidity for the mapping class group.Comment: 11 pages. v2: Proof rewritten to avoid use of log structures. Example of nonrigid moduli space of surfaces adde

"Why does it happen like this?". Consulting with users and providers prior to an evaluation of services for children with life-limiting conditions and their families

Background: Children with life-limiting conditions and their families have complex needs. Evaluations must consider their views and perspectives to ensure care is relevant, appropriate and acceptable. Aims: We consulted with children, young people, their parents and local professionals to gain a more informed picture of issues affecting them prior to preparing a bid to evaluate services in the area. Design: Multiple methods included focus groups, face-to-face and telephone interviews and participatory activities. Recordings and products from activities were analysed for content to identify areas of relevance and concern. Results: An overarching theme from parents was “Why does it happen like this?” Services did not seem designed to meet their needs. Whilst children and young people expressed ideas related to quality of environment,services and social life, professionals focused on ways of meeting the families’ needs. The theme that linked families’ concerns with those of professionals was ‘assessing individual needs’. Two questions to be addressed by the evaluation are: (1) to what extent are services designed to meet the needs of children and families, and (2) to what extent are children, young people and their families consulted about what they need? Conclusion: Consultations with families and service providers encouraged us to continue their involvement as partners in the evaluatio

Homological mirror symmetry for log Calabi-Yau surfaces

Given a log Calabi-Yau surface $Y$ with maximal boundary $D$ and distinguished complex structure, we explain how to construct a mirror Lefschetz fibration $w: M \to \mathbb{C}$, where $M$ is a Weinstein four-manifold, such that the directed Fukaya category of $w$ is isomorphic to $D^b \text{Coh}(Y)$, and the wrapped Fukaya category $\mathcal{W} (M)$ is isomorphic to $D^b \text{Coh}(Y \backslash D)$. We construct an explicit isomorphism between $M$ and the total space of the almost-toric fibration arising in the work of Gross-Hacking-Keel; when $D$ is negative definite this is expected to be the Milnor fibre of a smoothing of the dual cusp of $D$. We also match our mirror potential $w$ with existing constructions for a range of special cases of $(Y,D)$, notably in work of Auroux-Katzarkov-Orlov and Abouzaid.Comment: Comments welcome

'Working our way to health': Final Evaluation Report

This summary presents the findings of an independent evaluation of the ‘Working our Way to Health’ programme. This programme was delivered by Sefton PCT, funded through the Neighbourhood Renewal Fund, and was aimed at improving the health of men in three of the most deprived wards in its locality. It aimed to encourage men to be health aware and increase access to health and leisure services in order to improve key lifestyle behaviours and advance gender equity. The programme included: • Community agency and health staff training • Peer mentoring programme • Healthy lifestyle programme It aimed to promote community partnerships to assist the expansion of health advice and services into a new community arena and engage a previously unattainable section of the male population in healthier lifestyle interventions