I will discuss the main features of the string compactifications with magnetized (or equivalently intersecting) D-branes and explain why they represent a very interesting setup for phenomenological applications. In particular, I will discuss how to use string techniques to systematically derive brane world effective actions for models with magnetized (or equivalently intersecting) D-branes.

I will discuss interesting aspects of the duality of gauge theories and string theories in new scenarios.

The classification of RCFT means different things to different people, but the most accessible, and perhaps the prettiest, aspect of it is the classification of modular invariant (torus) partition functions, which tell you the spectrum of the theory. I'll review the progress made recently on this problem, for the case where the chiral algebras come from affine Kac-Moody algebras (the so-called Wess-Zumino-Witten models). I'll also comment on the classification of cyclindrical partition functions (the so-called NIM-reps), which are more directly relevant for the framework of Fuchs-Runkel-Schweigert.

Kreimer discovered a Hopf algebra structure underlying the combinatorics of renormalization in perturbative quantum field theory. Later, Connes and Kreimer explored the link to non-commutative geometry via a Hopf algebra of rooted trees and described a Hopf algebra of Feynman graphs. After reviewing these developments in some detail we show in this talk how to organize the combinatorics of renormalization in terms of unipotent triangular matrix representations. A simple decomposition of such matrices is used to characterize the process of renormalization. We thereby recover a matrix (anti-)representation of the Birkhoff decomposition of Connes and Kreimer.