We've known since childhood that symmetry can be a very powerful tool in solving partial differential equations. With a little symmetry, one can reduce the number of independent variables, whereas with some more symmetry one can usually separate variables and reduce the problem to solving ordinary differential equations. Given enough symmetry, though, partial differential equations become algebraic. A large body of current research in our field requires finding solutions to the (super)gravity field equations and in this talk I will motivate the search for homogeneous supergravity backgrounds and mention some recent results in this area.

String theory phenomenology generically suffers from either too much flexibility (and lack of predictability) or from the a high specialization to case by case studies. I will discuss how F-theory GUT model building manages to get around these pitfall, in particular, I will explain, how to systematically include global string consistency conditions, which are independent of the specific compactification, and which come with the benefit of highly constraining the class of GUT models that can arise from F-theory.

I will give an overview of recent developments in F-theory GUT model building. First I will discuss the basic ideas of F-theory model building, exemplifying this by the construction of supersymmetric SU(5) GUTs. Then I will outline how global string theoretic consistency requirements impact the SUSY phenomenology. The main focus of this talk will be on the phenomenological implications of these models.

The ABJM model is a superconformal Chern-Simons theory with N = 6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.

We present some new perspectives on N=1 gauge theories, especially SQCD, D-Brane Quiver Theories and the MSSM, from the stand-point of recent advances in computational and algorithmic algebraic geometry and commutative algebra. We introduce the plethystic program which systematically count gauge invariants and encodes certain hidden symmetries. Moreover, we discuss special structures of the vacuum moduli space, such as that of SQCD being Calabi-Yau.

In this talk, I will discuss work in progress with Bertrand Eynard, in which we derive the BKMP remodelling the B-model conjecture, in the large radius limit. This is the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of the mirror curve. Our method consists in explicitly constructing a matrix model which reproduces the topological string partition function obtained via the vertex formalism, and then demonstrating that the spectral curve of this matrix model coincides with the mirror geometry.

In this seminar, I will give an introduction to a series of ideas which suggest that many aspects of quantum fied theories, including the celebrated N=4 super Yang-Mills, may be most simply understood in terms of a dual theory in twistor space. No previous knowledge of string theory or twistor theory will be assumed.

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.