Noncommutative resolutions of ADE fibered Calabi-Yau threefolds

In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The threefolds under consideration are fibered over a complex plane with the fibers being deformed Kleinian singularities. The construction is in terms of a noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE quiver algebra"

Deep Hole States in Medium Mass Nuclei

Supported by the National Science Foundation and Indiana Universit

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

Sheaves on fibered threefolds and quiver sheaves

This paper classifies a class of holomorphic D-branes, closely related to framed torsion-free sheaves, on threefolds fibered in resolved ADE surfaces over a general curve C, in terms of representations with relations of a twisted Kronheimer--Nakajima-type quiver in the category Coh(C) of coherent sheaves on C. For the local Calabi--Yau case C\cong\A^1 and special choice of framing, one recovers the N=1 ADE quiver studied by Cachazo--Katz--Vafa.Comment: 13 pages, 2 figures, minor change

Equivariant volumes of non-compact quotients and instanton counting

Motivated by Nekrasov's instanton counting, we discuss a method for calculating equivariant volumes of non-compact quotients in symplectic and hyper-K\"ahler geometry by means of the Jeffrey-Kirwan residue-formula of non-abelian localization. In order to overcome the non-compactness, we use varying symplectic cuts to reduce the problem to a compact setting, and study what happens in the limit that recovers the original problem. We implement this method for the ADHM construction of the moduli spaces of framed Yang-Mills instantons on $\R^{4}$ and rederive the formulas for the equivariant volumes obtained earlier by Nekrasov-Shadchin, expressing these volumes as iterated residues of a single rational function.Comment: 34 pages, 2 figures; minor typos corrected, to appear in Comm. Math. Phy

'Reclaiming the criminal' : the role and training of prison officers in England, 1877-1914

This article examines the role and training of prison officers in England, between 1877 and 1914. It is concerned with the changing penal philosophies and practices of this period and how these were implemented in local prisons, and the duties of the prison officer. More broadly, this article argues that the role of the prison officer and their training (from 1896) reflect wider ambiguities in prison policy and practice during this period

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Testing sensory drive speciation in cichlid fish:Linking light conditions to opsin expression, opsin genotype and female mate preference

Ecological speciation is facilitated when divergent adaptation has direct effects on selective mating. Divergent sensory adaptation could generate such direct effects, by mediating both ecological performance and mate selection. In aquatic environments, light attenuation creates distinct photic environments, generating divergent selection on visual systems. Consequently, divergent sensory drive has been implicated in the diversification of several fish species. Here, we experimentally test whether divergent visual adaptation explains the divergence of mate preferences in Haplochromine cichlids. Blue and red Pundamilia co-occur across south-eastern Lake Victoria. They inhabit different photic conditions and have distinct visual system properties. Previously, we documented that rearing fish under different light conditions influences female preference for blue versus red males. Here, we examine to what extent variation in female mate preference can be explained by variation in visual system properties, testing the causal link between visual perception and preference. We find that our experimental light manipulations influence opsin expression, suggesting a potential role for phenotypic plasticity in optimizing visual performance. However, variation in opsin expression does not explain species differences in female preference. Instead, female preference covaries with allelic variation in the long-wavelength-sensitive opsin gene (LWS), when assessed under broad-spectrum light. Taken together, our study presents evidence for environmental plasticity in opsin expression and confirms the important role of colour perception in shaping female mate preferences in Pundamilia. However, it does not constitute unequivocal evidence for the direct effects of visual adaptation on assortative mating.</p

The epigenetic regulators CBP and p300 facilitate leukemogenesis and represent therapeutic targets in acute myeloid leukemia.

Growing evidence links abnormal epigenetic control to the development of hematological malignancies. Accordingly, inhibition of epigenetic regulators is emerging as a promising therapeutic strategy. The acetylation status of lysine residues in histone tails is one of a number of epigenetic post-translational modifications that alter DNA-templated processes, such as transcription, to facilitate malignant transformation. Although histone deacetylases are already being clinically targeted, the role of histone lysine acetyltransferases (KAT) in malignancy is less well characterized. We chose to study this question in the context of acute myeloid leukemia (AML), where, using in vitro and in vivo genetic ablation and knockdown experiments in murine models, we demonstrate a role for the epigenetic regulators CBP and p300 in the induction and maintenance of AML. Furthermore, using selective small molecule inhibitors of their lysine acetyltransferase activity, we validate CBP/p300 as therapeutic targets in vitro across a wide range of human AML subtypes. We proceed to show that growth retardation occurs through the induction of transcriptional changes that induce apoptosis and cell-cycle arrest in leukemia cells and finally demonstrate the efficacy of the KAT inhibitors in decreasing clonogenic growth of primary AML patient samples. Taken together, these data suggest that CBP/p300 are promising therapeutic targets across multiple subtypes in AML.Funding in the Huntly laboratory comes from Cancer Research UK, Leukemia Lymphoma Research, the Kay Kendal Leukemia Fund, the Leukemia lymphoma Society of America, the Wellcome Trust, The Medical Research Council and an NIHR Cambridge Biomedical Research Centre grant. Patient samples were processed in the Cambridge Blood and Stem Cell Biobank.This is the author accepted manuscript. The final version is available via NPG at http://dx.doi.org/10.1038/onc.2015.9