Holomorphic symplectic geometry: a problem list

A list of open problems on holomorphic symplectic, contact and Poisson manifolds

Measurement of the total cross section for e^+e^-→hadrons at √s=10.52 GeV

Using the CLEO detector at the Cornell Electron Storage Ring, we have made a measurement of R≡σ(e^+e^-→hadrons)/σ(e^+e^-→μ^+μ^-)=3.56±0.01±0.07 at √s=10.52 GeV. This implies a value for the strong coupling constant of α_s(10.52 GeV)=0.20±0.01±0.06, or α_s(MZ)=0.13±0.005±0.03

Supersymmetric Yang-Mills Theory On A Four-Manifold

By exploiting standard facts about $N=1$ and $N=2$ supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory.Comment: 55 page

Symplectic involutions on deformations of K3^[2]

Let X be a Hyperk\"{a}hler variety deformation equivalent to the Hilbert square on a K3 surface and let f be an involution preserving the symplectic form. We prove that the fixed locus of f consists of 28 isolated points and 1 K3 surface, moreover the anti-invariant lattice of the induced involution on H^2(X,Z) is isomorphic to E_8(-2). Finally we prove that any couple consisting of one such variety and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a Nikulin involution on the K3 surface.Comment: Final version, to appear on Central European Journal of Mathematic

Bcl3 prevents acute inflammatory lung injury in mice by restraining emergency granulopoiesis

Granulocytes are pivotal regulators of tissue injury. However, the transcriptional mechanisms that regulate granulopoiesis under inflammatory conditions are poorly understood. Here we show that the transcriptional coregulator B cell leukemia/lymphoma 3 (Bcl3) limits granulopoiesis under emergency (i.e., inflammatory) conditions, but not homeostatic conditions. Treatment of mouse myeloid progenitors with G-CSF — serum concentrations of which rise under inflammatory conditions — rapidly increased Bcl3 transcript accumulation in a STAT3-dependent manner. Bcl3-deficient myeloid progenitors demonstrated an enhanced capacity to proliferate and differentiate into granulocytes following G-CSF stimulation, whereas the accumulation of Bcl3 protein attenuated granulopoiesis in an NF-κB p50–dependent manner. In a clinically relevant model of transplant-mediated lung ischemia reperfusion injury, expression of Bcl3 in recipients inhibited emergency granulopoiesis and limited acute graft damage. These data demonstrate a critical role for Bcl3 in regulating emergency granulopoiesis and suggest that targeting the differentiation of myeloid progenitors may be a therapeutic strategy for preventing inflammatory lung injury

The Unyvero P55 ‘sample-in, answer-out’ pneumonia assay: A performance evaluation

Background: O’Neill’s recent Review on Antimicrobial Resistance expressed the view that by 2020 high-income countries should make it mandatory to support antimicrobial prescribing with rapid diagnostic evidence whenever possible. Methods: Routine microbiology diagnosis of 95 respiratory specimens from patients with severe infection were compared with those generated by the Unyvero P55 test, which detects 20 pathogens and 19 antimicrobial resistance markers. Supplementary molecular testing for antimicrobial resistance genes, comprehensive culture methodology and 16S rRNA sequencing were performed. Results: Unyvero P55 produced 85 valid results, 67% of which were concordant with those from the routine laboratory. Unyvero P55 identified more potential pathogens per specimen than routine culture (1.34 vs. 0.47 per specimen). Independent verification using 16S rRNA sequencing and culture (n = 10) corroborated 58% of additional detections compared to routine microbiology. Overall the average sensitivity for organism detection by Unyvero P55 was 88.8% and specificity was 94.9%. While Unyvero P55 detected more antimicrobial resistance markers than routine culture, some instances of phenotypic resistance were missed. Conclusions: The Unyvero P55 is a rapid pathogen detection test for lower respiratory specimens, which identifies a larger number of pathogens than routine microbiology. The clinical significance of these additional organisms is yet to be determined. Further studies are required to determine the effect of the test in practise on antimicrobial prescribing and patient outcomes

Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and c_1(L) is primitive. Assume that the two dimensional subspace H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex coefficients, intersects trivially the integral cohomology. We prove that the linear system of L is base point free and it induces a Lagrangian fibration on X. In particular, the line-bundle L is effective. A determination of the semi-group of effective divisor classes on X follows, when X is projective. For a generic such pair (X,L), not necessarily projective, we show that X is bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated improvement to the exposition and corrected typos according to the referees suggestions. To appear in the proceedings of the conference Algebraic and Complex Geometry, Hannover 201