Spinorial geometry techniques provide new ways to analyze supersymmetric solutions of supergravity theories in a systematic fashion. I will describe how one can apply these methods to classify solutions of type IIB supergravity which preserve large amounts of supersymmetry. In particular, this provides a proof that solutions preserving exactly 31/32 of the supersymmetry do not exist, which resolves a long-standing open question.

We will describe the recent progresses in the computation of four-graviton amplitudes at higher-loop order in maximal supergravity and string theory in various dimensions. We will discuss the constraints from dualities and the extended supersymmetry on the structure of the amplitudes. We will explain that the cross-symmetry of gravity, maximal supersymmetry, and the constraints from higher dimensions play an important role in the improved ultraviolet behaviour of maximal supergravity in four dimensions.

I describe work aimed at combining the advances in moduli stabilisation and supersymmetry breaking with that in building D-brane models with realistic chiral matter spectra. The framework is models of D3/D7 branes at del Pezzo singularities embedded in the LARGE volume scenario of moduli stabilisation. I describe the general phenomenological properties that emerge and discuss the difficulties in computing visible sector soft terms.

Scattering amplitudes in N=4 super-Yang-Mills theory can be defined in dimensional regularization near four dimensions, and have a number of remarkable features. There is good evidence for an exact, all-loop formula for the planar four- and five-point scattering amplitudes in terms of four functions of the coupling alone, one of which is the cusp anomalous dimension. For six gluons this particular formula fails. However, for the 'MHV' helicity configuration, an equivalence to a Wilson line expectation value on a hexagon persists at two loops, as does a certain 'dual conformal invariance'. These properties are connected to features of string propagation in AdS(5) x S5, in particular T duality.

In this talk we discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. We will see that combining T-duality along four directions in Poincare parametrization of AdS5 with a similar duality transformation on some of the fermionic variables maps the superstring action into itself. One implication is that, after duality, the superstring has a 'dual' superconformal symmetry group. Furthermore this dual superconformal symmetry can be seen as a consequence of the integrability of the superstring. This will also suggest that the dual superconformal charges correspond to non-local charges of the original model before T-duality.

I will review the computation of the quark-antiquark potential within the AdS/CFT correspondence. I will explain in detail the conformal case and apply this machinery in more general backgrounds, where multivalued potentials appear and stability issues have to be considered in order to isolate the physical branches of the potential. Finally I will extend this idea in the case of dyons and baryons. Mechanical analogues of the above configurations will be given.

We discuss how non-perturbative instanton effects in supersymmetric gauge theories can be described using open strings and D-branes. We analyse ordinary gauge instantons as well as novel 'exhotic instanton' configurations of purely stringy nature, and discuss their applications and effets in the low-energy effective theory.

I will describe and analyse general two-body decays of primitive and non-primitive 1/4-BPS dyons in four-dimensional type IIB string compactifications. For half-BPS decays, a relation is found between walls of marginal stability and the mathematics of Farey sequences and Ford circles. The relationship of marginal decay to the breakup of multi-centred dyons will also be discussed.

I'll discuss (from a mathematician's perspective) the process of extracting an effective quiver gauge theory from a D3-brane probing a singularity in a Calabi-Yau 3-fold.

Given two conformal field theories, one of which is defined on the upper half plane and the other on the lower half plane, one can ask for conformally invariant ways to join them along the real line. The resulting interface is called a defect line. These defects contain interesting information about the CFT, such as its symmetries, order-disorder dualities and T-dualities. They also provide relations between string theories on different target spaces.

Berry's phase is a beautiful and simple idea in quantum mechanics, with application to many areas of condensed matter physics. After reviewing the non-Abelian version of Berry's phase, I will explain how this concept naturally fits together with supersymmetry. I will then show how to compute Berry's phase in D-brane systems, using both traditional quantum mechanics, as well as AdS/CFT techniques.

I will reconsider toroidal compactifications of bosonic string theory with particular regard to the phases (cocycles) necessary for a consistent definition of the vertex operators, the boundary states, and the T-duality rules. I will then use these ingredients to compute the planar multi-loop partition function describing the interaction among magnetised or intersecting D-branes. Finally I will examine the degeneration limit of the 2-loop partition function and show that one obtains known and new tree-level 3-point correlators between twist fields.