Holomorphic symplectic geometry: a problem list

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

Curve classes on irreducible holomorphic symplectic varieties

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.Comment: 15 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

Ideology, Grandstanding, and Strategic Party Disloyalty in British Parliament

Strong party discipline is a core feature of Westminster parliamentary systems. Parties typically compel Members of Parliament (MPs) to support the party position regardless of MPs' individual preferences. Rebellion, however, does occur. Using an original dataset of MP votes and speeches in the British House of Commons from 1992 to 2015, coupled with new estimations of MPs' ideological positions within their party, we find evidence that MPs use rebellion to strategically differentiate themselves from their party. The strategy that MPs employ is contingent upon an interaction of ideological extremity with party control of government. Extremists are loyal when their party is in the opposition, but these same extremists become more likely to rebel when their party controls government. Additionally, they emphasize their rebellion through speeches. Existing models of rebellion and party discipline do not account for government agenda control and do not explain these patterns

Surfactant effects in monodisperse magnetite nanoparticles of controlled size

Monodisperse magnetite Fe3O4 nanoparticles of controlled size within 6 and 20 nm in diameter were synthesized by thermal decomposition of an iron organic precursor in an organic medium. Particles were coated with oleic acid. For all samples studied, saturation magnetization Ms reaches the expected value for bulk magnetite, in contrast to results in small particle systems for which Ms is usually much smaller due to surface spin disorder. The coercive field for the 6 nm particles is also similar to that of bulk magnetite. Both results suggest that the oleic acid molecules covalently bonded to the nanoparticle surface yield a strong reduction in the surface spin disorder. However, although the saturated state may be similar, the approach to saturation is different and, in particular, the high-field differential susceptibility is one order of magnitude larger than in bulk materials. The relevance of these results in biomedical applications is discussed.Comment: 3 pages, 3 figures. Presented at JEMS 2006 (San Sebastian, Spain). Submitted to JMM

Responses to the 2014 Police Shooting of Michael Brown: Cosmology Episodes and Enacted Environments

This is a consensual multi-dyadic exploration of the diverse perspectives of seven community subgroups’ perceptions of events before, during, and after the 2014 police-involved shooting death of Michael Brown, Jr. in Ferguson, Missouri. Recognizing an enacted environment in the complex history that preceded the uprising, findings were contextualized and framed through the cosmology episode trauma model. A multicultural and visibly diverse research team conducted 34 interviews with involved citizens (protesters), law enforcement, clergy, politicians, business owners, media personnel, and educators. A culturally diverse cross-analysis team triangulated social perspective through consensus coding and audit. Consensual multi-dyadic method preserved the unique characteristics of each subgroup’s phenomenology, to ensure culturally sensitive and decolonized research methods, enabling an in depth look at the factors necessary for conciliation. Insight into motivational factors, narrative meaning-making, and implications for intervention and treatment are discussed. View Full-Tex

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