I will describe a how to construct the supergravity solution for a pair of NS5-branes, intersecting on R^{1,3} and localised in all directions except a single transverse circle. Such solutions are rare, and yet may have many potential applications in gauge-gravity duality and model building. The construction invovles developing an explicit map between the conifold metric and the geometry of two intersecting NS5-branes. I will also describe additional intersecting brane solutions corresponding to smoothing out the intersection by, for example, separating branes or putting a metric on the intersection.

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.

I will start by discussing the 4d N=4 supersymmetric Yang-Mills theory on two spaces with a boundary - a half-line (times three infinite dimensions) and four dimensional anti-de Sitter space. I will review in detail the possible choices of boundary conditions for this theory, and then exhibit the solutions of string theory (supergravity) that are holographically dual to the N=4 SYM theory on these spaces. The same methods used to obtain these duals can also be used to find duals for 3d N=4 and 4d N=2 superconformal field theories that appear in brane configurations, and I will discuss these solutions as well.

We briefly review some models of dark energy. We start with the cosmological constant including models arising in string theory, before discussing dynamical models where a scalar field may be responsible for the observed late time acceleration. The possibility that we are not fully in control of the gravity sector is discussed and the possibility that the acceleration may be some manifestation of modified gravity on large scales is shown. All cases require some degree of fine tuning for the models to be compatible with observation. Finally, we briefly discuss some recent fun work involving scalar-tensor theories of gravity in which a self-tuning mechanism exists leading to the same late time cosmology independently of the size of the cosmological constant. Solutions include having radiation and matter dominated like regimes whilst the energy density remains dominated by a cosmological constant.

We will review the conjecture that the Kac-Moody Symmetry E_11 is an underlying symmetry of strings and branes. We will show that it leads to a generalised geometry involving an extension of our usual formulation of space-time.

This colloquium reviews old and new no go theorems that severely constrain possible interactions of massless high spin particles. Massive particles can interact with gauge fields and gravity, but often they are plagued by pathologies such as superluminal propagation in nontrivial backgrounds. The last part of the talk uses the example of open string theory to show that such pathologies can be avoided by an appropriate choice of non-minimal interactions.