Groups and Related Topics : Proceedings of the First Max Born Symposium

Part 1 Quantum groups: Sugawara construction and the Q-deformation of Virasoro algebra complex quantum groups and their dual Hopf algebras external projector and universal R-matrix for quantized contragredient lie (super)algebras quantum deformations of D=4 Poincare algebra "Quantum Group" strecture and "Covariant" differential calculus on symmetric algebras corresponding to commutation factors on Zn remarks on the use of R-matrices construction of some Hopf algebras realifications of complex quantum groups. Part 2 Non commutative differential geometry: on multigraded differential calculus Yang Mills fields and symmetry breaking - from lie super-algebras to non commutative geometry differential and integral calculus on the quantum C-plane. Part 3 Integrable systems: rigorous approach to Abelian Chern-simons theory the conformal block structure of perturbation theory in two dimensions an alternative dynamical description of quantum systems on the solutions of the Yang-Baxter equations state sum invariants of compact 3-manifolds with boundary and 6j-symbols. Part 4 Miscellaneous: product of states quantum measurements and information theory a comment on a 3-dimensional euclidean supersymmetry chiral nets and modular methods chiral symmetry breaking-rigorous results on a twister shift in particle and string dynamics the metric of bures and the geometric phase.