Recent developments in integrable systems and related topics of mathematical physics

Content: Victor Buchstaber, Sotiris Konstantinou-Rizos and Alexander Mikhailov, Introduction.- P. G. Grinevich and P. M. Santini, Numerical instability of the Akhmediev breather and a finite-gap model of it.- V.Yu. Novokshenov, Movable poles of Painleve I transcendents and singularities of monodromy data manifolds.- Vladimir Sokolov, Elliptic Calogero-Moser Hamiltonians and compatible Poisson brackets.- A.V. Tsiganov, Backlund transformations and new integrable systems on the plane.- V. Rubtsov, Quadro-cubic Cremona transformations and Feigin-Odesskii-Sklyanin algebras with 5 generators.- Dimitri Gurevich and Pavel Saponov, From Reflection Equation Algebra to Braided Yangians.- G. Sharygin and A. Konyaev, Survey of the Deformation Quantization of Commutative Families.- Dmitry Millionshchikov, Graded Thread Modules over the Positive Part of the Witt (Virasoro) Algebra.- Andrei Shafarevich, Localized solutions of the Schroedinger equation on hybrid spaces. Relation to the behavior of geodesics and to analytic number theory.- A. V. Fursikov, Normal equation generated from Helmholtz system: nonlocal stabilization by starting control and properties of stabilized solutions.