We review the role played by the Yangian symmetry generated by non-local charges in a range of integrable models, and in particular the non-linear sigma models, describing briefly the representation theory of the Yangian and its implications for physics. We explain how an integrable boundary naturally reduces this to a 'twisted Yangian' symmetry.

The Bethe ansatz for integrable quantum field theories in two dimensions may well be exact. It can be checked in the conformal limit, where it yields interesting character identities with deep links to algebraic K-theory.

We compute the beta function at 2 loops for an open string gauge field F in any (parallelizable) curved background. The beta function is exact in F. We discuss the implications of this result to curvature corrections to the Born - Infeld action. Taking the large F limit, we relate these corrections to the equations of motion for D0-branes in curved backgrounds, eg. to corrections to the dielectric effect.

The recent discovery of supersymmetric black ring solutions has important implications for black hole uniqueness and other aspects of black hole physics in higher dimensions. The construction of these solutions is investigated, and a generalization of the single ring solution to a system of concentric (multi-charge) rings is presented. The entropy of some of these solutions is particularly interesting.

Motivated by string theory arguments, we analyse quantum field theory in a specific space time with closed timelike curves. We conjecture and partly show that, for discrete values of the gravitational coupling constant, the resulting theory is unitary. These discrete values are obtained in two independent ways, using high energy scattering in quantum gravity and using string dualities to rephrase the quantization condition as quantization of charge of certain extended objects.

We show that certain exactly marginal and relevant deformations of N=4 theory which preserve N=1 supersymmetry, exhibit rich infrared dynamics. These theories have moduli spaces with discrete (Higgs) branches. On certain branches the theory flows to the Klebanov-Witten conifold SCFT, while on other branches the theory undergoes a Seiberg duality cascade terminating in an N=1 theory with a mass gap. Using the matrix model approach the quantum moduli spaces and quantum superpotentials of these theories can be computed exactly. In the D-brane picture these quantum moduli spaces correspond to the Calabi-Yau space in the geometric dual description of the gauge theory.

Riemann Spheres are extremely useful as objects to build Conformal Field Theory on. Graded Riemann Spheres turn out to be extremely useful in the study Superconformal Field Theory. In particular, I will look at the conformal algebras of vector fields that arise, and their associated primary fields that are given by the geometry. I will also look at some peculiarities that arise in N=4 theories.

The talk shall present chosen aspects of a compact quantum-algebraic description of D-brane geometry in WZW models, extending beyond the semiclassical approximation of the original fuzzy matrix models. It shall be argued that a class of unital algebras - the so-called Reflection Algebras intimately related to Drinfeld--Jimbo algebras - captures certain essential features of stringy geometries, both untwisted and twisted, in compact WZW models and their (simple current) orbifolds, while giving rise to some well-known, and some less so, noncommutative geometries (e.g. Podles sphere, quantum projective plane).

We will illustrate some of the consequences of allowing for a fundamental length scale in supersymmetric theories, in particular the world volume theory of the D9-brane. We will show how to construct kappa-symmetric derivative corrections using superembeddings and spinorial cohomology.

Some attempts to go beyond the standard model will be reviewed, largely motivated by data from neutrino experiments and the microwave anisotropy observations. An attempt at a unified description will be discussed.

The general subject is factorized scattering theory for massive integrable field theories in 1+1 dimensions. The talk will be about boundary supersymmetry, about a construction of supersymmetric scattering and reflection matrices from non-supersymmetric ones, and about the application of the construction to specific models (boundary sine-Gordon model, boundary affine Toda theories) perhaps.

A self-contained introduction to the idea of identifying Kac-Moody type symmetries in all known gravity theories.

We will present a string scenario for localization of gravity in four dimensions. We will discuss the field theory model, proposed by Dvali Gabadadze and Porrati and details its problems and their resolutions. We will explain that this model presents issues well posed in string theory and address their resolution in this context.