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

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

Music for Thought: Examining Saudi Identities Expressed Through Music on Social Media

The aim of this chapter is to investigate how social media help create and diffuse popular music in Saudi Arabia and how such music questions the officially accepted identities and social practices. Social media are widely used as means of promotion among artists around the world; yet Saudi Arabia deserves special attention. This is because traditional media act much more strictly as gatekeepers in the kingdom; hence, social media offer greater possibility for circulation of popular entertainment, especially when it touches upon the questions related to the core values of the Saudi society. Such is the case of recordings by Hesham Fageeh “No woman, No drive” (2013) or the recently trending video clip “Hwages” that, both, received peak visibility online and sparked debates about women empowerment. Similarly, some videos trending online prompted a dance craze, for instance, “Barbs” showed a choreography that was subsequently copied by fans who uploaded their performances online. Dancing is a prohibition among the conservative segments of society; yet, the vastly young population of Saudi Arabia seeks entertainment.Social media in Saudi Arabia have become primordial means of communication in the kingdom with highest rates of social media participation in the Middle East and seventh rank in the world (2016). Consequently, this chapter employs a mixed-method approach in order to uncover how social media breaks the monopoly on entertainment by promoting different musical genres and encouraging social debate

Magnetization of ferrofluids with dipolar interactions - a Born--Mayer expansion

For ferrofluids that are described by a system of hard spheres interacting via dipolar forces we evaluate the magnetization as a function of the internal magnetic field with a Born--Mayer technique and an expansion in the dipolar coupling strength. Two different approximations are presented for the magnetization considering different contributions to a series expansion in terms of the volume fraction of the particles and the dipolar coupling strength.Comment: 19 pages, 11 figures submitted to PR

Identifying component modules

A computer-based system for modelling component dependencies and identifying component modules is presented. A variation of the Dependency Structure Matrix (DSM) representation was used to model component dependencies. The system utilises a two-stage approach towards facilitating the identification of a hierarchical modular structure. The first stage calculates a value for a clustering criterion that may be used to group component dependencies together. A Genetic Algorithm is described to optimise the order of the components within the DSM with the focus of minimising the value of the clustering criterion to identify the most significant component groupings (modules) within the product structure. The second stage utilises a 'Module Strength Indicator' (MSI) function to determine a value representative of the degree of modularity of the component groupings. The application of this function to the DSM produces a 'Module Structure Matrix' (MSM) depicting the relative modularity of available component groupings within it. The approach enabled the identification of hierarchical modularity in the product structure without the requirement for any additional domain specific knowledge within the system. The system supports design by providing mechanisms to explicitly represent and utilise component and dependency knowledge to facilitate the nontrivial task of determining near-optimal component modules and representing product modularity

P2Y1 receptor modulation of endogenous ion channel function in Xenopus oocytes: Involvement of transmembrane domains

Agonist activation of the hP2Y1 receptor expressed in Xenopus oocytes stimulated an endogenous voltage-gated ion channel, previously identified as the transient inward (Tin) channel. When human P2Y1 (hP2Y1) and skate P2Y (sP2Y) receptors were expressed in Xenopus oocytes, time-to-peak values (a measure of the response to membrane hyperpolarization) of the Tin channel were significantly reduced compared to oocytes expressing the hB1-bradykinin receptor or the rat M1-muscarinic (rM1) receptor. Differences in activation were also observed in the Tin currents elicited by various P2Y receptor subtypes. The time-to-peak values of the Tin channel in oocytes expressing the hP2Y4, hP2Y11, or hB1-bradykinin receptors were similar, whereas the channel had significantly shorter time-to-peak values in oocytes expressing either the hP2Y1 or sP2Y receptor. Amino acid substitutions at His-132, located in the third transmembrane domain (TM3) of the hP2Y1 receptor, delayed the onset of channel opening, but not the kinetics of the activation process. In addition, Zn2+ sensitivity was also dependent on the subtype of P2Y receptor expressed. Replacement of His-132 in the hP2Y1 receptor with either Ala or Phe increased Zn2+ sensitivity of the Tin current. In contrast, truncation of the C-terminal region of the hP2Y1 receptor had no affect on activation or Zn2+ sensitivity of the Tin channel. These results suggested that TM3 in the hP2Y1 receptor was involved in modulating ion channel function and blocker pharmacology of the Tin channel

Observation of the Dynamic Beta Effect at CESR with CLEO

Using the silicon strip detector of the CLEO experiment operating at the Cornell Electron-positron Storage Ring (CESR), we have observed that the horizontal size of the luminous region decreases in the presence of the beam-beam interaction from what is expected without the beam-beam interaction. The dependence on the bunch current agrees with the prediction of the dynamic beta effect. This is the first direct observation of the effect.Comment: 9 page uuencoded postscript file, postscritp file also available through http://w4.lns.cornell.edu/public/CLNS, submitted to Phys. Rev.