Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

The New Science Intensive Standard of Master Preparation in Sphere of Competitive Intelligence on the Basis of Systemological Knowledge-Oriented Technologies

Methodological, theoretical and technological bases of the new branch standard of Ukraine higher education which regulates preparation process of masters - professionals in the information area and information analysts are considered. The new systemological knowledge-oriented technologies developed in KNURE which considerably surpass foreign analogues are put as the basis of training.

Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion

2000 Mathematics Subject Classification: 60G18, 60E07