The Discovery of Sgr A*

The compact radio source Sgr A* is associated with a 3.6 million black hole at the center of the Milky Way. The radio source was discovered in February 1974 by Bruce Balick and Robert L.Brown. The National Radio Astronomy Observatory's Green Bank 35 km radio link interferometer was used. We discuss other observations in the years 1965-1985 as well as early VLBI observations. The name Sgr A* was used for the first time in 1982 by Robert L.Brown and has become the accepted name in the intervening years.Comment: 8 pages,2 figures. Conference proceedings: "The central 300 parsecs of the Milky Way", editors A.Cotera, H.Falcke, T.R.Geballe, S.Markof

Afterthoughts | Complexities of Potency

Afterthoughts to themed perspectives on Complexities of Potency

Moduli of PT-semistable objects II

We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ as an Artin stack of finite type that is universally closed. In the absence of strictly semistable objects, we construct the moduli as a proper algebraic space of finite type.Comment: 34 pages. Exposition improved based on referee's comments, especially the proofs of Prop 2.6 and 2.17 (of this version). References added; typos corrected. Openness and separatedness now in a separate section. Sections 4 and 5 of previous version removed. Accepted for publication by the Transactions of the American Mathematical Society. This is the sequel to http://arxiv.org/abs/1011.568

A relation between higher-rank PT stable objects and quotients of coherent sheaves

On a smooth projective threefold, we construct an essentially surjective functor $\mathcal{F}$ from a category of two-term complexes to a category of quotients of coherent sheaves, and describe the fibers of this functor. Under a coprime assumption on rank and degree, the domain of $\mathcal{F}$ coincides with the category of higher-rank PT stable objects, which appear on one side of Toda's higher-rank DT/PT correspondence formula. The codomain of $\mathcal{F}$ is the category of objects that appear on one side of another correspondence formula by Gholampour-Kool, between the generating series of topological Euler characteristics of two types of quot schemes.Comment: 19 page

China, the ‘East Asian Model’ and Late Development

There is an influential, neo-liberal proposition in the scholarly literature on China’s economic transformation since the late 1970s. It states that China’s reformed economic institutions are a mix of market-conforming and market-supplanting elements, that its developmental achievements so far have been ascribable to the conforming elements whereas the accumulated problems being ascribable to the supplanting elements, and that the problems have tended to outweigh the achievements as the country’s economic transition progresses from the allegedly easy phase to the difficult phase. This paper offers an alternative interpretation of the Chinese experience. The central proposition is that China’s economic institutions could be seen in favourable light both theoretically and with reference to the East Asian development experience. Specifically, the developmental implications of the market-conforming and market-supplanting elements should not be understood in any absolute sense, but rather depend on the appropriate match or otherwise between the institutions and the external environment. The developmental achievements to date indicate that China’s economic reform has managed to achieve a basically appropriate match between the two aspects, although enormous uncertainties still cloud over the future prospects owing to changes both in the external environment and the reform strategies of the state leadership