When a salt-stratified fluid is cooled from the side, a two-dimensional convection pattern of cells is formed along the vertical side-wall and develops into horizontal intrusions which grow away from the wall. Such conditions exist in the oceans along melting icebergs, and the growth of these intrusions prevents melt-water from rising to the surface. As the intrusions grow, a series of layers is created in the salt water, with stepped temperature and salinity profiles. In this talk, I will describe an experimental and theoretical study carried out while at the ITG in Cambridge on the formation and growth of these double-diffusive intrusions. Observations were made of growth rates of the intrusions, of internal velocities, and of temperature and salinity distributions. The rate of growth of the intrusions was found, surprisingly, to depend on the length of the experimental tank, with the end-wall playing a role in their evolution right from the beginning of the experiment (Malki-Epshtein, Phillips and Huppert, JFM 2004). Internal waves are visualised using particle tracing methods and are shown to propagate throughout the experimental tank, maintaining hydrostatic equilibrium and having a strong role in setting up the layers. Future application of the results of this study to the large scale could have significant implications for the modelling of oceanic double-diffusive processes, which are believed to drive large vertical and lateral fluxes of heat and salt.

This is the first lecture of a short course on non-geometric backgrounds. For more information on the course and the schedule, please visit http://www.strings.ph.qmw.ac.uk/index.htm and follow the link to the Graduate Program in String/Field Theory.

We study an N-particle, two-mode Bose-Hubbard system, modelling a Bose-Einstein condensate in a double-well potential. By introducing effective complex energies to the modes we describe a coupling to a continuum. The eigenvalues of the resulting non-Hermitian matrix model are in general complex where the imaginary parts (resonance widths) describe the decay rate into the continuum. In dependence on the parameters the spectrum shows an intricate structure of exceptional points, at which two or more eigenvalues as well as the corresponding eigenstates are degenerate. In the present talk the effect of the interplay between the particle interaction and the non-Hermiticity on the spectrum is analysed, drawing special attention to the occurrence and unfolding of exceptional points. Some peculiarities are clarified using perturbational methods.

In analogy to Beck and Cohen's superstatistics (1), we connect the canonical Gaussian ensembles of the random-matrix theory (RMT) to their superstatistical generalizations through the fluctuation of an intensive parameter, the local density of states (2). On one hand, the superstatistical RMT, seen from the present perspective, may bear interest per se because of the additional nontrivial fluctuations introduced in a simple model. On the other hand, it may constitute a useful statistical paradigm for the analysis of the spectral fluctuations of systems with mixed regular-chaotic dynamics. In contrast to other proposals for applying RMT to mixed dynamics, the superstatistical approach yields ensemble of matrices, which are invariant with respect to base transformation. The formalism has been checked by the analysis of experimental resonance spectra of mixed microwave billiards (3). The spectra for each billiard are represented as time series in which the level order plays the role of time. Each series is shown to have two relaxation times as required by superstatistics, which involves the folding of two distribution functions. Analysis of the time series suggests that the superstatistical parameter has an inverse-chi-square distribution. The experimental distribution nearest-neighbor level spacings and strength functions agree with the corresponding predicted distributions. (1) C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003). (2) A.Y. Abul-Magd, Phys.Rev. E 71, 066207 (2005). (3) A.Y. Abul-Magd, B. Dietz, T. Friedrich, and A. Richter, Phys. R

We point out a special corner in the space of Calabi-Yau compactifications where standard-like models tend to emerge. We show how these scenarios are inter-related via a mathematical process of transgression of bundles, a generalisation of the conifold transition. Perhaps our world is special and we live in this oasis within the multitude of vacua.

I will discuss several constructions of superalgebras associated to the Killing spinors of a supergravity background, with special emphasis on the ten- and eleven-dimensional supergravities.

The understanding of the nature of spacetime singularity and whether and how it is resolved is one of the most important problem in quantum gravity. Important examples are black hole singularity and cosmological singularity in the big bang. In this talk we will be interested in the later type and an approach to the problem using AdS/CFT correspondence for time-dependent background will be discussed. Our gauge theory results suggest that spacetime singularity is indeed resolved and the mechanism will be discussed.

Suppose we could calculate the string partition function to all genera using worldsheet methods. What could we learn from this expression about a potentially underlying (non-perturbative) target space description of the theory? We address this question in the context of the open topological A-model.

I will begin with basic review on the integrabilities in AdS/CFT correspondence, and move on discussing the role of scattering matrices in gauge and string thoeries. I will then explain the formation of magnon boundststates in gauge theory and their corresponding classical string solution. The scattering of magnon boundstates and their classifications will also be discussed in this seminar. I will also mention some work in progress.

I will present a modification of the Berkovits twistor string model which gives Einstein supergravity coupled to Yang-Mills, and has a limit in which the gravity modes can be decoupled to give pure gauge theory amplitudes. I will start by reviewing a number of relevant aspects of twistor theory, including special features associated with different space-time signatures, supertwistor space, the Penrose transform, the infinity twistor and Penrose's non-linear graviton construction. I will then review the Witten and Berkovits twistor strings, with emphasis on the latter. The world-sheet formulation of the Berkovits model involves so-called beta-gamma systems, I will describe the symmetries of such systems and their gauging, and explain how the analysis can be applied to the construction of a family of new gauged Berkovits twistor strings which are free from world-sheet anomalies. I will also describe the corresponding spectra in space-time, and show that they give Einstein supergravities instead of the higher derivative conformal supergravities arising in the original twistor string models. The new theories include one with the spectrum of N = 8 supergravity, two theories with the spectrum of N = 4 supergravity coupled to N = 4 Yang-Mills, a family of N greater than 0 models with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills, and a non-supersymmetric string with the spectrum of self-dual gravity coupled to self-dual Yang-Mills and a scalar. Time permitting, I will discuss what is known about the interactions.

We show the existence of an N=1 supersymmetric vacuum in string theory whose observable sector has exactly the matter content of the MSSM without exotic particles and vector-like pairs of any type. This is done so by compactifying the E_8 x E_8 heterotic string on a Calabi-Yau threefold endowed with an SU(4) vector bundle which has been constructed after extensive search. In addition, we discuss the Yukawa couplings and Higgs mu-terms in this model.

Kreimer discovered a Hopf algebra structure underlying the combinatorics of renormalization in perturbative quantum field theory. Later, Connes and Kreimer explored the link to non-commutative geometry via a Hopf algebra of rooted trees and described a Hopf algebra of Feynman graphs. After reviewing these developments in some detail we show in this talk how to organize the combinatorics of renormalization in terms of unipotent triangular matrix representations. A simple decomposition of such matrices is used to characterize the process of renormalization. We thereby recover a matrix (anti-)representation of the Birkhoff decomposition of Connes and Kreimer.

Four dimensional N=4 super Yang-Mills theory contains a bigger superalgebra than AdS or superconformal algebra, su(2,2/4). It corresponds to a noncentral extension of the latter. The talk is for both physicsts and mathematicans interested in a novel way of obtaining noncentral extensions of Lie algebras.