The greatest Ricci lower bound, conical Einstein metrics and the Chern number inequality

We partially confirm a conjecture of Donaldson relating the greatest Ricci lower bound $R(X)$ to the existence of conical Kahler-Einstein metrics on a Fano manifold $X$. In particular, if $D\in |-K_X|$ is a smooth simple divisor and the Mabuchi $K$-energy is bounded below, then there exists a unique conical Kahler-Einstein metric satisfying $Ric(g) = \beta g + (1-\beta) [D]$ for any $\beta \in (0,1)$. We also construct unique smooth conical toric Kahler-Einstein metrics with $\beta=R(X)$ and a unique effective Q-divisor $D\in [-K_X]$ for all toric Fano manifolds. Finally we prove a Miyaoka-Yau type inequality for Fano manifolds with $R(X)=1$

A Simple Geometric Representative for μ\mu of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $\mu$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.Comment: Updated 2018 to published version. 8 pages, AmS-TeX, no figure

Biochemistry Changes That Occur after Death: Potential Markers for Determining Post-Mortem Interval

Death is likely to result in very extensive biochemical changes in all body tissues due to lack of circulating oxygen, altered enzymatic reactions, cellular degradation, and cessation of anabolic production of metabolites. These biochemical changes may provide chemical markers for helping to more accurately determine the time since death (post-mortem interval), which is challenging to establish with current observation-based methodologies. In this study blood pH and changes in concentration of six metabolites (lactic acid, hypoxanthine, uric acid, ammonia, NADH and formic acid) were examined post-mortem over a 96 hour period in blood taken from animal corpses (rat and pig) and blood from rats and humans stored in vitro. The pH and the concentration of all six metabolites changed post-mortem but the extent and rate of change varied. Blood pH in corpses fell from 7.4 to 5.1. Concentrations of hypoxanthine, ammonia, NADH and formic acid all increased with time and these metabolites may be potential markers for postmortem interval. The concentration of lactate increased and then remained at an elevated level and changes in the concentration were different in the rat compared to the human and pig. This is the first systematic study of multiple metabolic changes post-mortem and demonstrates the nature and extent of the changes that occur, in addition to identifying potential markers for estimating post-mortem interval

An elliptic boundary value problem for G2G_{2} structures

We show that the $G_{2}$ holonomy equation on a manifold with boundary, with prescribed 3-form on the boundary, is elliptic. The main point is to set up a suitable linear elliptic boundary value problem. This result leads to a deformation theory. In particular we establish the existence of certain $G_{2}$ cobordisms between two small deformations of a Calabi-Yau 3-fold.Comment: Some minor changes. This is the final version, to appear in Annales de l'Institut Fourie

University of Glasgow - Case study in funding research data management

This case study was written by Mary Donaldson as part of the Funder Requirements for Research Data project. This project was funded by JISC as part of the wider Research Data Management Business Case and Costings (RDM-BCC) project. The case study examines how the University of Glasgow supports RDM, how their service sustainability is achieved, and how other RDM activities are paid for