Chosen aspects of twisted brane geometry in the Wess-Zumino-Witten models of type A_2n shall be discussed, both classical and stringy, in reference to a class of coideal subalgebras of Drinfel'd-Jimbo quantum groups known as twisted orthogonal quantum groups. An explicit relation between the two families of algebras, together with a realisation of the latter as (twisted) Reflection Equation Algebras shall be invoked to emphasise the role played by them in a compact algebraic description of quantum twisted branes on SU(2n+1) in the framework of R-matrix Reflection Equations and associated quantum group geometries.

I will explain how to do concrete computations in bosonic closed string field theory. For this, I will show how to numerically describe the geometry of the four-point contact interaction, by computing the boundary of the relevant region of the moduli space of the four-punctured spheres, and by computing everywhere in this region the local coordinates around each punctures, in terms of a Strebel quadratic differential and mapping radii. I will then explain how these results are used and checked in the recent paper of Yang and Zwiebach by considering marginal fields in closed bosonic string field theory.

I explain how arbitrary correlators of string theory in the Euclidean AdS3 can be computed from the correlators of Liouville theory. This makes use of the KZ-BPZ correspondence, which relates on the one hand the Knizhnik-Zamolodchikov equations reflecting the group symmetry in AdS3, on the other hand the Belavin-Polyakov-Zamolodchikov equations reflecting the presence of degenerate fields in the Liouville correlators.

The physics of glassy systems at low temperatures differs in striking and unexpected ways from that of their crystalline counterparts, in that thermal, transport and dynamic response properties exhibit unusual temperature variation. Atomic or molecular tunneling centers are believed to be at the origin of these phenomena, which show a remarkable degree of universality across a wide spectrum of diverse amorphous substances, ranging from window glass to polystyrene. We describe recent advances in understanding these phenomena, using a microscopic modelling approach. It has for the first time allowed to identify a mechanism responsible for the occurrence of tunneling systems, to characterize them quantitatively, and to provide a simple and transparent explanation for the unusual universality of glassy low temperature anomalies.

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.