Abstract: Weather and climate models comprise a so-called 'adiabatic dynamical core' and a collection of 'parametrizations' (often given the unfortunate name of 'physics'). The former is a more or less well understood numerical solution of dynamical equations based on the Euler equations. The latter attempt to represent a wide variety of physical processes. 

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Abstract: A new theory of viscous oscillatory flows has been developed. Our theory represents an adaptation of the Vishik-Lyusternik approach combined with the two-timing and averaging methods. We consider high Reynold's number viscous incompressible flows driven by a vibrating boundary for the simple geometry of a half-space.  From the physical viewpoint the required boundary conditions may be seen as the tangential vibrations of material points of a plane stretchable membrane. The main result is the construction of general, global, and uniformly valid asymptotic solutions of the Navier-Stokes equations. These solutions satisfy general oscillating boundary conditions and three different regimes of the scaling parameters (that correspond to the strong, moderate, and weak nonlinearities).

Abstract: We prove by an explicit construction that solutions to incompressible 3D Euler equations, defined in the periodic cube, can be mapped bijectively to a new system of equations whose solutions are globally regular.  We establish that the usual Beale-Kato-Majda criterion for finite-time singularity (or blowup) of a solution to the 3D Euler system is equivalent to a condition on the corresponding regular solution of the new system.

Abstract: Several dispersive wave equations can be formulated as Hamiltonian PDEs.  Steady travelling waves can then be interpreted as critical points of the Hamiltonian functional.  Furthermore, their stability is linked to the spectrum of the Hessian of this functional.  In this talk, the Maslov index, an index defined on paths of Lagrangian spaces, is used to study this spectrum in the case of traveling waves arising in various higher-order Korteweg-de Vries-type equations.

Abstract: In this talk I shall present the "reflection Hopf algebra" formalism. This formalism may be used in boundary scattering theory and is a natural extension of the usual Hopf algebra for the analysis of the reflection processes. I shall give several examples where this formalism proved to be very useful. They include the (generalized) twisted Yangians in AdS/CFT correspondence and the coideal quantum affine algebra of the Deformed Hubbard Chain. The talk will be based on arXiv: 1010.3761, 1101.6062 and 1110.4596.

Abstract: We illustrate the role of non-Abelian T-duality in string theory  with emphasis on backgrounds with non-vanishing Ramond flux fields. We discuss generic features such as the fate  of geometric isometries and of supersymmetry. We present important examples in the gauge/gravity correspondence,  that is AdS_3 X S^3 X T^4 and AdS_5 X S^5$. In conjunction, we comment on possible integrable structures in the  T-dual theory.

The AdS/CFT correspondence has produced remarkable connections between different areas of physics and mathematics. In this talk I will start by reviewing the relation between the Wilson loop observable in gauge theories and the problem of finding minimal area surfaces in hyperbolic (or AdS) space. Until recently only very few explicit solutions were known to such problem but I will show how, using Riemann theta functions an infinite parameter family of new solutions can be found. Moreover a one parameter family of deformations is identified such that the area is preserved. The solution to this problem uses methods from the theory of solitons and non-linear differential equations and sheds a new interesting light on the connection between the Wilson loop observable in gauge theories and integrable systems.

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Abstract: Superstring theory on AdS_5 x S^5 is classically equivalent, via the Pohlmeyer reduction, to a fermionic generalization of an extended sine-Gordon model. The Pohlmeyer-reduced and light-cone gauge string S-matrices turn out to be different limits of a larger interpolating S-matrix, based on the q-deformed R-matrix of Beisert and Koroteev, 2008. In this talk I will briefly review the reduction before discussing recent progress in constructing the quantum S-matrix of the reduced and interpolating theories. It is suggested that the interpolating S-matrix may provide a new way to regularize computations in the string theory.

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Abstract: In this talk, I will discuss how a new kind of quantized geometry, the quantum Nambu geometry, arises in string theory. I will also describe its mathematical properties and demonstrate that the quantum Nambu geometry is intrinsically different from the ordinary Lie algebra type noncommutative geometry. I will also discuss a proposal for a matrix model description of M5-brane in a constant C-field.

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: TBA

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems

Abstract: An informal overview of quantum mechanics, from first principles to path integrals and quantum integrable systems