Andreev billiards consist of a normal metal billiard in contact with a superconductor. Based on the Bogoliubov-de Gennes equation the excitation spectrum (Andreev states) and the density of states are calculated for different Andreev billiards (integrable, pseudointegrable and chaotic). The exact quantum results are in very good agreement with those obtained from the Bohr-Sommerfeld approximation. The AdS/CFT correspondence predicts the matching of N=4 SYM scaling dimensions with IIB string light-cone energies on AdS5xS5. Scaling dimensions can conveniently be obtained as the eigenvalues of the theory’s dilatation generator. Its possible quantum deformations are tightly constrained by superconformal symmetry and Feynman diagram topologies. We demonstrate how these fix the generator up to some loop order in a purely algebraic way. Interestingly, this dilatation generator seems to be integrable in the planar limit, at one-loop as well as at higher orders of the coupling constant. Non-thermal yet disordered, strongly dissipative yet rigid, the mechanics of packings of grains has fascinated physicists and engineers at least since the time of Coulomb. This talk will focus on one of the classical problems in this field, the behavior of dense granular flows driven by gravity. I will give examples of such flows drawn from geophysics, and then introduce some of the ideas of Ralph Bagnold, who developed the concepts on which the modern study of granular flows are based. A systematic phenomenology of dense granular flows down inclines has recently been developed, based both on numerical work and on experiments. This phenomenology emphasizes the role of inelastic collapse in controlling the rheology of these flows, and hints at the structure of an ultimate theory of dense flows. There is a close connection between (rational) conformal field theory in two dimensions, topological field theory in three dimensions and algebras in tensor categories. Correlators of a 2dCFT can be understood as states of a 3dTFT, which are associated to the two-dimensional boundary of a three-manifold. The 3dTFT in turn can be obtained from an algebraic construction starting from a so-called modular tensor category. A given 3dTFT can allow for the construction of different 2dCFTs, and this amounts to the choice of an algebra in the modular tensor category. Properties of the algebra are then directly linked to properties of the 2dCFT. For example, modules of the algebra correspond to boundary conditions of the CFT. Lóbjectif est de donner une introduction à la biologie moléculaire, en montrant en particulier límportance des idées issues de la physique pour la compréhension du vivant.

Eötvös University, Department of Physics of Complex Systems Budapest, Hungary